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    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
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    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
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    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
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    <link:label id="lab_us-gaap_OffsettingDerivativeAssetsAbstract_019e2363-9f61-7bf6-b873-f8fbfd5530e0_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_OffsettingDerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Derivative Assets [Abstract]</link:label>
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    <link:label id="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts_019e2363-9ff0-777a-b44e-32039c8c855e_terseLabel_en-US" xlink:label="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for investment transferred to consolidated trusts</link:label>
    <link:label id="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts_label_en-US" xlink:label="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Held for Investment Transferred to Consolidated Trusts</link:label>
    <link:label id="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts_documentation_en-US" xlink:label="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Held for Investment Transferred to Consolidated Trusts</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:to="lab_agm_LoansHeldForInvestmentTransferredToConsolidatedTrusts" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019e2363-9f61-7ac6-af16-9a72a4244ea5_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
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    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_019e2363-9f61-71ec-b8fd-f7b179f74f3d_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_019e2363-9f61-7b65-ab68-a20e3b1c375c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale Securities [Table]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019e2363-9ecc-7a58-a28d-acb7d3d27c80_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income, diluted EPS</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
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    <link:label id="lab_agm_DueYearTwoMember_019e2363-9f61-78df-9317-fa2bf468c50f_terseLabel_en-US" xlink:label="lab_agm_DueYearTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year two</link:label>
    <link:label id="lab_agm_DueYearTwoMember_label_en-US" xlink:label="lab_agm_DueYearTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due Year Two [Member]</link:label>
    <link:label id="lab_agm_DueYearTwoMember_documentation_en-US" xlink:label="lab_agm_DueYearTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due year two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueYearTwoMember" xlink:href="agm-20260630.xsd#agm_DueYearTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueYearTwoMember" xlink:to="lab_agm_DueYearTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_019e2363-9ecc-7202-a555-038917419d5b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total weighted - average rate</link:label>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_019e2363-9f61-788d-87e1-2cc8f36973fc_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable"/>
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    <link:label id="lab_agm_GainLossOnFairValueHedgesDerivativeInterestSettlements_019e2363-9ecc-7f2c-ab01-e902d8e437f9_terseLabel_en-US" xlink:label="lab_agm_GainLossOnFairValueHedgesDerivativeInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amounts related to interest settlements on derivatives</link:label>
    <link:label id="lab_agm_GainLossOnFairValueHedgesDerivativeInterestSettlements_label_en-US" xlink:label="lab_agm_GainLossOnFairValueHedgesDerivativeInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Fair Value Hedges, Derivative Interest Settlements</link:label>
    <link:label id="lab_agm_GainLossOnFairValueHedgesDerivativeInterestSettlements_documentation_en-US" xlink:label="lab_agm_GainLossOnFairValueHedgesDerivativeInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Fair Value Hedges, Derivative Interest Settlements</link:label>
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    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgedStatusAxis_019e2363-9ecc-7deb-84bf-f88109a6e4ce_terseLabel_en-US" xlink:label="lab_us-gaap_PledgedStatusAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged Status [Axis]</link:label>
    <link:label id="lab_us-gaap_PledgedStatusAxis_label_en-US" xlink:label="lab_us-gaap_PledgedStatusAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledged Status [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PledgedStatusAxis"/>
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    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019e2363-9ecc-72c8-86c2-9904082429ae_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
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    <link:label id="lab_us-gaap_OtherAssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Fair Value Disclosure</link:label>
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    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
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    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset-Backed Securities [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPeriodAxis"/>
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    <link:label id="lab_us-gaap_NotesReceivableMember_label_en-US" xlink:label="lab_us-gaap_NotesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivable [Member]</link:label>
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    <link:label id="lab_dei_EntityAddressCityOrTown_019e2363-9ecc-77b7-86ae-e7a7db830f0f_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_019e2363-9ecc-7655-bebc-fd7b3ccca8fe_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff_019e2363-9f61-7bdd-8004-b9aed725e5d4_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year One, Originated, Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019e2363-9ecc-7615-bfd7-6666ca92bd7b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesReceivableNetAbstract_019e2363-9f61-75b2-b79e-4bbbbd9c0069_terseLabel_en-US" xlink:label="lab_us-gaap_NotesReceivableNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans:</link:label>
    <link:label id="lab_us-gaap_NotesReceivableNetAbstract_label_en-US" xlink:label="lab_us-gaap_NotesReceivableNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, after Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesReceivableNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesReceivableNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesReceivableNetAbstract" xlink:to="lab_us-gaap_NotesReceivableNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_019e2363-9f61-7a97-bf5f-11d29a01692d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">90 Days and Greater</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuarantyAssets_019e2363-9ecc-79a0-89ce-00ca3715efd8_terseLabel_en-US" xlink:label="lab_us-gaap_GuarantyAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment fees receivable</link:label>
    <link:label id="lab_us-gaap_GuarantyAssets_019e2363-9ecc-7adc-9bcd-b9264e6a6ba7_verboseLabel_en-US" xlink:label="lab_us-gaap_GuarantyAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment fees receivable</link:label>
    <link:label id="lab_us-gaap_GuarantyAssets_label_en-US" xlink:label="lab_us-gaap_GuarantyAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guaranty Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuarantyAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GuarantyAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuarantyAssets" xlink:to="lab_us-gaap_GuarantyAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019e2363-9f61-714b-882c-cd188d50912c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities_019e2363-9ff0-755d-8e9d-ad750bbb8378_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Netting Adjustments</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Security Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralObligationToReturnSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:to="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAverageVariableInterestRate_019e2363-9ecc-7815-b0a2-277bcaee5f45_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageVariableInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Receive Rate</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageVariableInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageVariableInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Variable Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageVariableInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAverageVariableInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAverageVariableInterestRate" xlink:to="lab_us-gaap_DerivativeAverageVariableInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_019e2363-9ecc-7e18-9f45-7853b1673ba1_terseLabel_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains /(losses) , before tax</link:label>
    <link:label id="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, before Reclassifications, before Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:to="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019e2363-9f61-78dd-b5fa-cdfc4126427d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
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    <link:label id="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock_019e2363-9ecc-7d06-934e-83989577d033_terseLabel_en-US" xlink:label="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Hedged Items in Fair Value Hedging Relationships</link:label>
    <link:label id="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock_label_en-US" xlink:label="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Items In Fair Value Hedging Relationships [Table Text Block]</link:label>
    <link:label id="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock_documentation_en-US" xlink:label="lab_agm_HedgedItemsInFairValueHedgingRelationshipsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hedged Items in Fair Value Hedging Relationships [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract_019e2363-9ecc-7b9b-b869-ba145ca601e3_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss):</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract"/>
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    <link:label id="lab_us-gaap_ExchangeClearedMember_019e2363-9ecc-7275-943a-f16a1c9ae527_terseLabel_en-US" xlink:label="lab_us-gaap_ExchangeClearedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange Cleared</link:label>
    <link:label id="lab_us-gaap_ExchangeClearedMember_label_en-US" xlink:label="lab_us-gaap_ExchangeClearedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exchange Cleared [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExchangeClearedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ExchangeClearedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExchangeClearedMember" xlink:to="lab_us-gaap_ExchangeClearedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019e2363-9f61-7adf-94f3-2419f20f9c54_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive loss net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019e2363-9f61-7359-8003-8514a1e9b4e7_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive (loss)/income net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_019e2363-9ecc-7ff7-856c-dc49c96aec30_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Two years</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPeriodTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities_019e2363-9f61-7db4-ae9a-0b257c8702f3_terseLabel_en-US" xlink:label="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities of consolidated trusts held by third parties</link:label>
    <link:label id="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities_label_en-US" xlink:label="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Consolidated, Fair Value Disclosure, Liabilities</link:label>
    <link:label id="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities_documentation_en-US" xlink:label="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Consolidated, Fair Value Disclosure, Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:href="agm-20260630.xsd#agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:to="lab_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsLineItems_019e2363-9f61-7b71-aa01-16be5e9de905_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantor Obligations [Line Items]</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsLineItems_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GuaranteeObligationsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsLineItems" xlink:to="lab_us-gaap_GuaranteeObligationsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_019e2363-9ecc-74a3-9e2d-e0494643878e_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019e2363-9f61-745d-8966-ada52bf45b85_negatedLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019e2363-9f61-711b-986a-9912ee07f2ca_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019e2363-9f61-7297-b802-b4b7b21ae11e_periodStartLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019e2363-9f61-7259-89a7-99afa6b0a456_periodEndLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_019e2363-9f61-7d60-b110-1aca2a259a5d_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_019e2363-9f61-7fe3-901a-80c1947a7539_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_019e2363-9ecc-7169-b3c5-29ac5e50a48a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic EPS</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:to="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_019e2363-9ecc-771d-ae92-2936c74fd934_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maturities of notes</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_019e2363-9ecc-7af9-a07d-c13bfefd546a_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisSwapMember_019e2363-9f61-7915-b712-00af87848d76_terseLabel_en-US" xlink:label="lab_us-gaap_BasisSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis swaps</link:label>
    <link:label id="lab_us-gaap_BasisSwapMember_label_en-US" xlink:label="lab_us-gaap_BasisSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisSwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisSwapMember" xlink:to="lab_us-gaap_BasisSwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_019e2363-9f61-7b4e-a2d1-77eb889a16a2_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Next Twelve Months, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Next Twelve Months, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:href="agm-20260630.xsd#agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:to="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_019e2363-9ecc-76e4-8def-7c8592d4c445_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax benefit related to other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_019e2363-9ecc-7725-ae49-98271e78c1ad_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss), provision (benefit)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueWithinOneYearMember_019e2363-9f61-7f76-8fe8-9830df8e137b_terseLabel_en-US" xlink:label="lab_agm_DueWithinOneYearMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_agm_DueWithinOneYearMember_label_en-US" xlink:label="lab_agm_DueWithinOneYearMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due Within One Year [Member]</link:label>
    <link:label id="lab_agm_DueWithinOneYearMember_documentation_en-US" xlink:label="lab_agm_DueWithinOneYearMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due Within One Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueWithinOneYearMember" xlink:href="agm-20260630.xsd#agm_DueWithinOneYearMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueWithinOneYearMember" xlink:to="lab_agm_DueWithinOneYearMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019e2363-9ecd-792c-9672-0a7cbc65434b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive (loss)/income, net of tax</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019e2363-9f61-74bd-a9af-ee64a7dd8a12_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassBMember_019e2363-9f61-7c5b-ab2c-58746bad4b26_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class B voting common stock</link:label>
    <link:label id="lab_us-gaap_CommonClassBMember_label_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class B [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassBMember" xlink:to="lab_us-gaap_CommonClassBMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_019e2363-9f61-7420-97ed-d6ac58a1ace2_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableModificationToTotalFinancingReceivablesExcludingAccruedInterestPercent_019e2363-9f61-7f9d-8d96-77110f2d6944_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableModificationToTotalFinancingReceivablesExcludingAccruedInterestPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of Total by Financing Class</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableModificationToTotalFinancingReceivablesExcludingAccruedInterestPercent_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableModificationToTotalFinancingReceivablesExcludingAccruedInterestPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Modified in Period, to Total Financing Receivables, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableModificationToTotalFinancingReceivablesExcludingAccruedInterestPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableModificationToTotalFinancingReceivablesExcludingAccruedInterestPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableModificationToTotalFinancingReceivablesExcludingAccruedInterestPercent" xlink:to="lab_us-gaap_FinancingReceivableModificationToTotalFinancingReceivablesExcludingAccruedInterestPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019e2363-9f61-760e-83af-178c60965661_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per common share:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019e2363-9f61-7d2f-93bf-119e0704e3cd_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
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    <link:label id="lab_us-gaap_Liabilities_019e2363-9f61-78b7-a405-f7738f22178d_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_019e2363-9f61-70d9-832a-db50cfbe07f0_terseLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value of Liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019e2363-9ecd-720f-87be-f4f30d748f1e_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
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    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_019e2363-9ff1-70da-8cf0-442732b7d0cf_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:to="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019e2363-9ecc-7cde-8b42-9a0fdd72f9b2_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale, at fair value (amortized cost of $15,249,174 and $13,813,551, respectively)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019e2363-9ecc-71d1-b7b5-179a4ddf914c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AFS investment securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019e2363-9ecc-7f3a-b499-891eb724cb73_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total fair value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueYearFourMember_019e2363-9ecc-7809-a80c-f18ac138a6fe_terseLabel_en-US" xlink:label="lab_agm_DueYearFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year four</link:label>
    <link:label id="lab_agm_DueYearFourMember_label_en-US" xlink:label="lab_agm_DueYearFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due Year Four [Member]</link:label>
    <link:label id="lab_agm_DueYearFourMember_documentation_en-US" xlink:label="lab_agm_DueYearFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due year four [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueYearFourMember" xlink:href="agm-20260630.xsd#agm_DueYearFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueYearFourMember" xlink:to="lab_agm_DueYearFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_019e2363-9f61-70b2-a09c-026bce791e88_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Losses [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_019e2363-9f61-7371-a2c1-2c3c8006f2c9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (losses)/gains included&#160;in other comprehensive income</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_019e2363-9ecc-76c2-a8e4-08f27be63576_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of available-for-sale investment securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt"/>
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    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_019e2363-9f61-72dd-8d3c-18607d8e84c6_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_019e2363-9f61-7b86-ac23-272035678edb_negatedLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less reclassification adjustments, before tax</link:label>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_019e2363-9ecc-7df1-b869-4660e49580bd_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
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    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_019e2363-9ecd-75e9-8f4c-2ef8bf5051fe_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of dilutive securities</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDilutedAbstract"/>
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    <link:label id="lab_us-gaap_MediumTermNotesMember_019e2363-9ecc-785c-be41-d1b8c858690e_verboseLabel_en-US" xlink:label="lab_us-gaap_MediumTermNotesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Medium-term notes</link:label>
    <link:label id="lab_us-gaap_MediumTermNotesMember_label_en-US" xlink:label="lab_us-gaap_MediumTermNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Medium-Term Note [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MediumTermNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MediumTermNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MediumTermNotesMember" xlink:to="lab_us-gaap_MediumTermNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_019e2363-9f61-79b9-adc5-f424e835b1b3_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year One, Originated, Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_SeriesIPreferredStockMember_019e8921-32d7-7795-b6c6-c8e26fbc262a_terseLabel_en-US" xlink:label="lab_agm_SeriesIPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">6.875% Non-Cumulative Preferred Stock, Series I</link:label>
    <link:label id="lab_agm_SeriesIPreferredStockMember_019eafbb-b13b-7cc3-94f8-05fe196359fa_verboseLabel_en-US" xlink:label="lab_agm_SeriesIPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Series I</link:label>
    <link:label id="lab_agm_SeriesIPreferredStockMember_label_en-US" xlink:label="lab_agm_SeriesIPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series I Preferred Stock [Member]</link:label>
    <link:label id="lab_agm_SeriesIPreferredStockMember_documentation_en-US" xlink:label="lab_agm_SeriesIPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series I Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_SeriesIPreferredStockMember" xlink:href="agm-20260630.xsd#agm_SeriesIPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_SeriesIPreferredStockMember" xlink:to="lab_agm_SeriesIPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019e2363-9f61-7fb6-9c42-0ff64ee05ad0_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_019e2363-9ecc-7008-bba9-ee8c1349289d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quarterly dividend on all classes of common stock (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockDividendsPerShareCashPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:to="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_019e2363-9ecc-7c77-962e-9e63fca25b6b_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. Treasuries</link:label>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_019e2363-9ecc-7ff1-bf10-a5678d34c9ac_verboseLabel_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">U.S. Treasuries</link:label>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasurySecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_USTreasurySecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasurySecuritiesMember" xlink:to="lab_us-gaap_USTreasurySecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitiesTable_019e2363-9ecc-7c91-8c5d-c8a817d021d6_terseLabel_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:label id="lab_dei_EntitiesTable_label_en-US" xlink:label="lab_dei_EntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitiesTable" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitiesTable" xlink:to="lab_dei_EntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnsecuritizedMember_019e2363-9ecc-78fd-b930-f723e058a391_terseLabel_en-US" xlink:label="lab_agm_UnsecuritizedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecuritized</link:label>
    <link:label id="lab_agm_UnsecuritizedMember_label_en-US" xlink:label="lab_agm_UnsecuritizedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecuritized [Member]</link:label>
    <link:label id="lab_agm_UnsecuritizedMember_documentation_en-US" xlink:label="lab_agm_UnsecuritizedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecuritized, no in a trust[Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnsecuritizedMember" xlink:href="agm-20260630.xsd#agm_UnsecuritizedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnsecuritizedMember" xlink:to="lab_agm_UnsecuritizedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019e2363-9f61-780b-997b-0ec6e24c5190_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Unobservable Input Reconciliation</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_019e2363-9f61-722b-b675-4d2d378b637d_verboseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, at amortized cost</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_019e2363-9f61-720a-baa9-ecdbdef7ddf9_netLabel_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:label id="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="agm-20260630.xsd#agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract_019e2363-9f61-7d8e-95b7-72a74f38e6fe_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income:</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestAndDividendIncomeOperatingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperatingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueAfterYearFourMember_019e2363-9ff0-7241-ab8e-ec8b4f3639eb_terseLabel_en-US" xlink:label="lab_agm_DueAfterYearFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_DueAfterYearFourMember_label_en-US" xlink:label="lab_agm_DueAfterYearFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due After Year Four [Member]</link:label>
    <link:label id="lab_agm_DueAfterYearFourMember_documentation_en-US" xlink:label="lab_agm_DueAfterYearFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueAfterYearFourMember" xlink:href="agm-20260630.xsd#agm_DueAfterYearFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueAfterYearFourMember" xlink:to="lab_agm_DueAfterYearFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_019e2363-9f61-7d46-8443-251b8c762370_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation cost</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019e2363-9f61-767a-b337-563bbac96304_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities" xlink:to="lab_us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_019e2363-9ecd-79c6-b8a1-fbd22c1c7a2f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetsAbstract" xlink:to="lab_us-gaap_DerivativeAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_019e2363-9ecc-7f49-95d9-fa5d115c99a3_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateSwapMember_019e2363-9f61-7561-8802-84647c88039e_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swap</link:label>
    <link:label id="lab_us-gaap_InterestRateSwapMember_label_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestRateSwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateSwapMember" xlink:to="lab_us-gaap_InterestRateSwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember_019e2363-9ecc-7a44-aa64-09cd76fb2da2_terseLabel_en-US" xlink:label="lab_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Broadband Infrastructure</link:label>
    <link:label id="lab_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember_label_en-US" xlink:label="lab_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rural Infrastructure, Broadband Infrastructure Segment [Member]</link:label>
    <link:label id="lab_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember_documentation_en-US" xlink:label="lab_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rural Infrastructure, Broadband Infrastructure Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember" xlink:href="agm-20260630.xsd#agm_RuralInfrastructureBroadbandInfrastructureSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember" xlink:to="lab_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019e2363-9ecc-7d8e-bfb0-c662cc8757f7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NOTES PAYABLE</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TreasuryFundingSegmentMember_019e2363-9ecc-7c4d-85f9-ecf6fb5ee204_terseLabel_en-US" xlink:label="lab_agm_TreasuryFundingSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funding</link:label>
    <link:label id="lab_agm_TreasuryFundingSegmentMember_label_en-US" xlink:label="lab_agm_TreasuryFundingSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury, Funding Segment [Member]</link:label>
    <link:label id="lab_agm_TreasuryFundingSegmentMember_documentation_en-US" xlink:label="lab_agm_TreasuryFundingSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury, Funding Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TreasuryFundingSegmentMember" xlink:href="agm-20260630.xsd#agm_TreasuryFundingSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TreasuryFundingSegmentMember" xlink:to="lab_agm_TreasuryFundingSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_019e2363-9f61-757e-bb15-b350c7709d65_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_019e2363-9ecc-717d-8e91-06ac9d551157_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_label_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Weighted Average Yield, Single Maturity Date [Abstract]</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_documentation_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities, Debt Maturities, Weighted Average Yield, Single Maturity Date [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:href="agm-20260630.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:to="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_019e2363-9ecc-705e-bb09-259b0e619c0c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash dividends, common stock</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStockCash" xlink:to="lab_us-gaap_DividendsCommonStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019e2363-9ecc-70cd-9d9a-503b2b4adcc7_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019e2363-9ecc-78d4-8b90-f331d22f0c7a_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning Balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019e2363-9ecc-7b42-8d03-d2986835b7c8_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending Balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacy_019e2363-9f61-704f-be22-d4c504045d7b_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital required for capital adequacy</link:label>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacy_label_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CapitalRequiredForCapitalAdequacy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:to="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019e2363-9ecc-7f63-9410-15cf8845f9e1_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentDeferralMember_019f6a25-f1dd-7cf8-bef0-4783c4083d5e_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentDeferralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payment Deferrals</link:label>
    <link:label id="lab_us-gaap_PaymentDeferralMember_label_en-US" xlink:label="lab_us-gaap_PaymentDeferralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment Deferral [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentDeferralMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentDeferralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentDeferralMember" xlink:to="lab_us-gaap_PaymentDeferralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherInvestments_019e2363-9ecd-76af-a8a8-34ad666a1be6_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_us-gaap_OtherInvestments_label_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherInvestments" xlink:to="lab_us-gaap_OtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember_019e2363-9f61-7313-b866-93920958b35d_terseLabel_en-US" xlink:label="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember_label_en-US" xlink:label="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, After Period Five [Member]</link:label>
    <link:label id="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember_documentation_en-US" xlink:label="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Period after five representing period after fifth most current period of debt redemption features under terms of the debt agreement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:href="agm-20260630.xsd#agm_DebtInstrumentRedemptionAfterPeriodFiveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:to="lab_agm_DebtInstrumentRedemptionAfterPeriodFiveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_019e2363-9ecc-75c2-b48b-27f0685fc722_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivable Credit Quality Indicators</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Credit Quality Indicators [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:to="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
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    <link:label id="lab_agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted_documentation_en-US" xlink:label="lab_agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Banking, Advisory, Brokerage, And Underwriting Fees And Commissions, Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted" xlink:href="agm-20260630.xsd#agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted"/>
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    <link:label id="lab_us-gaap_PerformanceSharesMember_019e2363-9ecc-7810-a860-002200070c29_terseLabel_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Shares</link:label>
    <link:label id="lab_us-gaap_PerformanceSharesMember_label_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Shares [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PerformanceSharesMember" xlink:to="lab_us-gaap_PerformanceSharesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_019e2363-9ecc-7e9a-aba9-5469911d4782_terseLabel_en-US" xlink:label="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_label_en-US" xlink:label="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Weighted Average Yield, Single Maturity Date [Abstract]</link:label>
    <link:label id="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_documentation_en-US" xlink:label="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Weighted Average Yield, Single Maturity Date [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:href="agm-20260630.xsd#agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract"/>
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    <link:label id="lab_us-gaap_NumberOfOperatingSegments_019e2363-9ecc-75c7-8067-86b7b4294e3f_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_019e2363-9ecc-7783-9d6a-081204465863_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive securities excluded from earnings per share (in shares)</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019e2363-9f61-7cd1-8823-de27d30eadad_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_019e2363-9f61-727b-ba8a-03fc8b327c4d_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net interest income after provision for losses</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), after Provision for Loan Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss"/>
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    <link:label id="lab_us-gaap_ScheduleOfGuaranteeObligationsTable_019e2363-9ecc-7942-a9a9-7734007e5b3a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Guarantor Obligations [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGuaranteeObligationsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfGuaranteeObligationsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:to="lab_us-gaap_ScheduleOfGuaranteeObligationsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_019e2363-9f61-7b8b-b274-d3072833d02b_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract"/>
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    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
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    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019e2363-9f61-795b-a2e0-7f4a3cf34d52_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
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    <link:label id="lab_us-gaap_DividendsPreferredStockCash_019e2363-9f61-7b4a-b570-3c02387db3b3_negatedLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Cash dividends, preferred stock</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Preferred Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPreferredStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsPreferredStockCash"/>
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    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_019e2363-9ecc-7af5-b9f4-3c5ae98b1c67_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, dividend rate</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
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    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_019e2363-9f61-719d-90e5-ce16987b328c_verboseLabel_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Designated as hedge</link:label>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_label_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Designated as Hedging Instrument [Member]</link:label>
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    <link:label id="lab_us-gaap_SeriesGPreferredStockMember_019e2363-9ecc-76c3-84d8-44bd3584b916_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesGPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">4.875% Non-Cumulative Preferred Stock, Series G</link:label>
    <link:label id="lab_us-gaap_SeriesGPreferredStockMember_019e2363-9ecc-778e-96d8-0175dc68e018_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesGPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series G</link:label>
    <link:label id="lab_us-gaap_SeriesGPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesGPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series G Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesGPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeriesGPreferredStockMember"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance_019e2363-9ecc-746a-880e-0a527abac3a3_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonaccrual loans with no associated allowance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrualNoAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, No Allowance</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019e2363-9f61-76c6-8144-e1407461fad4_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Loss</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019e2363-9f61-73df-bfe6-e4bced8e5880_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other comprehensive (loss)/ income:</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
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    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgedAssetFairValueHedge_019e2374-c9d3-75d1-9f31-7e8db132d953_terseLabel_en-US" xlink:label="lab_us-gaap_HedgedAssetFairValueHedge" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying amount of hedged assets</link:label>
    <link:label id="lab_us-gaap_HedgedAssetFairValueHedge_label_en-US" xlink:label="lab_us-gaap_HedgedAssetFairValueHedge" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Asset, Fair Value Hedge</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgedAssetFairValueHedge" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgedAssetFairValueHedge"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgedAssetFairValueHedge" xlink:to="lab_us-gaap_HedgedAssetFairValueHedge" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019e2363-9ecc-7911-b7fa-2ecb663996dc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019e2363-9ecc-7ac2-8602-2307600e6e94_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019e2363-9ecc-7f53-886f-44b7d8f9f987_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_Assets_019e2363-9ecc-7dd8-be81-3b20922d61e1_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value of Assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CallOptionMember_019e2363-9ecc-7ac5-aabf-229fe21c648e_terseLabel_en-US" xlink:label="lab_us-gaap_CallOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Call Option</link:label>
    <link:label id="lab_us-gaap_CallOptionMember_label_en-US" xlink:label="lab_us-gaap_CallOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Call Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CallOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CallOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CallOptionMember" xlink:to="lab_us-gaap_CallOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList_019e2363-9f61-7d55-b88c-c02a584debc4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Asset, Gain (Loss), Statement of Other Comprehensive Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList_label_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Asset, Gain (Loss), Statement of Other Comprehensive Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:to="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExtendedMaturityMember_019f6a25-f1dd-737e-8e68-738826364931_terseLabel_en-US" xlink:label="lab_us-gaap_ExtendedMaturityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Extensions</link:label>
    <link:label id="lab_us-gaap_ExtendedMaturityMember_label_en-US" xlink:label="lab_us-gaap_ExtendedMaturityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extended Maturity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExtendedMaturityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ExtendedMaturityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExtendedMaturityMember" xlink:to="lab_us-gaap_ExtendedMaturityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss_019e2363-9f61-7dff-90c1-bde68972a09d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, accrued interest excluded</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseOperating_019e2363-9ecc-75fe-8441-a95fecc65b25_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_019e2363-9ecc-7c60-87b4-5f6697471547_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Total Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_019e2363-9ecc-77c5-8912-1526b1943422_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">(Interest expense)/benefit</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseOperating" xlink:to="lab_us-gaap_InterestExpenseOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_019e2363-9ff0-7b4f-92d9-9d9888c72a39_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InternalCreditAssessmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InternalCreditAssessmentDomain" xlink:to="lab_us-gaap_InternalCreditAssessmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_019e2363-9ecc-794b-8338-b521fca22691_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unconsolidated VIE</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_019e2363-9f61-73e8-8df9-106bd8295382_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019e2363-9ecc-7a6f-8499-75e4743bafa5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense on interest rate swaps</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseNonoperating" xlink:to="lab_us-gaap_InterestExpenseNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_019e2363-9f61-7ae5-8ba6-2f6ffe328a67_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gains</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TreasuryInvestmentsSegmentMember_019e2363-9f61-78d5-91df-3ae9bcd07085_terseLabel_en-US" xlink:label="lab_agm_TreasuryInvestmentsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_agm_TreasuryInvestmentsSegmentMember_label_en-US" xlink:label="lab_agm_TreasuryInvestmentsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury, Investments Segment [Member]</link:label>
    <link:label id="lab_agm_TreasuryInvestmentsSegmentMember_documentation_en-US" xlink:label="lab_agm_TreasuryInvestmentsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury, Investments Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TreasuryInvestmentsSegmentMember" xlink:href="agm-20260630.xsd#agm_TreasuryInvestmentsSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TreasuryInvestmentsSegmentMember" xlink:to="lab_agm_TreasuryInvestmentsSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent_019e2363-9df4-784f-8cc9-465699d26d30_terseLabel_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive (loss)/income before reclassifications</link:label>
    <link:label id="lab_us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent_019e2363-9df4-7873-bf9a-bfdf1fdc9b2a_totalLabel_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss) before reclassifications</link:label>
    <link:label id="lab_us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, before Reclassifications, Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent"/>
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    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
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    <link:label id="lab_us-gaap_SharesOutstanding_019e2363-9f61-7723-b36a-7704dbfae55e_periodStartLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance ( in shares)</link:label>
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    <link:label id="lab_agm_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_label_en-US" xlink:label="lab_agm_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Asset Gain Loss Statement Of Income Extensible List Not Disclosed Flag</link:label>
    <link:label id="lab_agm_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_documentation_en-US" xlink:label="lab_agm_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Asset Gain Loss Statement Of Income Extensible List Not Disclosed Flag</link:label>
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    <link:label id="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome_label_en-US" xlink:label="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Amounts of Line Items Presented in the Consolidated Statement of Income</link:label>
    <link:label id="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome_documentation_en-US" xlink:label="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total Amounts of Line Items Presented in the Consolidated Statement of Income</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:to="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_019e2363-9ff0-7cad-a54d-2e4b3437faf6_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
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    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Next Twelve Months, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:href="agm-20260630.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield"/>
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    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalAdjusted_label_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal), Adjusted</link:label>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalAdjusted_documentation_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal), Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalAdjusted" xlink:href="agm-20260630.xsd#agm_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalAdjusted"/>
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    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
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    <link:label id="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss_019e2363-9f61-72c0-9a8f-144e2eeec87d_terseLabel_en-US" xlink:label="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Losses</link:label>
    <link:label id="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss_label_en-US" xlink:label="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Allowance for Credit Loss</link:label>
    <link:label id="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss_documentation_en-US" xlink:label="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss" xlink:href="agm-20260630.xsd#agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss"/>
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    <link:label id="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction_019e2363-9ecd-777b-ba9f-6155a8cd285a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial instruments pledged</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Deduction of Financial Instrument Not Offset</link:label>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_019e2363-9ecc-7949-99e5-448970e7f496_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained Earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019e2363-9f61-7eac-93bc-91b6b45bc857_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
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    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
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    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_019e2363-9f61-789c-989f-fb2b99c7c9f9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, by Balance Sheet Grouping</link:label>
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    <link:label id="lab_agm_MediumTermNotesCalledDuringThePeriod_label_en-US" xlink:label="lab_agm_MediumTermNotesCalledDuringThePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Medium Term Notes Called During the Period</link:label>
    <link:label id="lab_agm_MediumTermNotesCalledDuringThePeriod_documentation_en-US" xlink:label="lab_agm_MediumTermNotesCalledDuringThePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Medium Term Notes Called During the Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_MediumTermNotesCalledDuringThePeriod" xlink:href="agm-20260630.xsd#agm_MediumTermNotesCalledDuringThePeriod"/>
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    <link:label id="lab_agm_ProvisionForLoanLeaseAndOtherLossesNoncash_019e2363-9ecc-7fa6-adc8-65613c21bcc0_terseLabel_en-US" xlink:label="lab_agm_ProvisionForLoanLeaseAndOtherLossesNoncash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total provision for allowance for losses</link:label>
    <link:label id="lab_agm_ProvisionForLoanLeaseAndOtherLossesNoncash_label_en-US" xlink:label="lab_agm_ProvisionForLoanLeaseAndOtherLossesNoncash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Provision for Loan, Lease, And Other Losses, Noncash</link:label>
    <link:label id="lab_agm_ProvisionForLoanLeaseAndOtherLossesNoncash_documentation_en-US" xlink:label="lab_agm_ProvisionForLoanLeaseAndOtherLossesNoncash" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Provision for Loan, Lease, And Other Losses, Noncash</link:label>
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    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingAssetsTableTextBlock"/>
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    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax_019e2363-9f61-7009-a3ff-6e0d4ee46618_negatedLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less reclassification adjustments, provision (benefit)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationFromAociCurrentPeriodTax"/>
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    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_019e2363-9ecc-78a7-b000-536759cf70d0_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Assets:</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Financial Assets, Balance Sheet Groupings [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract"/>
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    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock_019e2363-9ecc-7bc2-860f-e91a23e491d0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Recently Adopted Accounting Guidance</link:label>
    <link:label id="lab_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Standards Update and Change in Accounting Principle [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfNewAccountingPronouncementsAndChangesInAccountingPrinciplesTextBlock"/>
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    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_019e2363-9ecc-75fd-b726-e3e7deec294a_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage-Backed Security, Issued by US Government-Sponsored Enterprise [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract_019e2363-9ecc-754d-93c5-434e79f0a6cb_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">HTM:</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, before Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesClassifiedAbstract"/>
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    <link:label id="lab_us-gaap_NotionalAmountOfDerivativesAbstract_019e2363-9f61-7827-a1a5-ee97bb2bbe6d_terseLabel_en-US" xlink:label="lab_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_NotionalAmountOfDerivativesAbstract_label_en-US" xlink:label="lab_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notional Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotionalAmountOfDerivativesAbstract"/>
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    <link:label id="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock_019e2363-9f61-74b2-a7cf-b25563aefc57_terseLabel_en-US" xlink:label="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Standby Purchase Commitments</link:label>
    <link:label id="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock_label_en-US" xlink:label="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Standby Purchase Commitments [Table Text Block]</link:label>
    <link:label id="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock_documentation_en-US" xlink:label="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Standby Purchase Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock" xlink:href="agm-20260630.xsd#agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock"/>
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    <link:label id="lab_us-gaap_LongtermDebtWeightedAverageInterestRate_019e2363-9f61-733f-b8b8-8ddfb0309f32_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average rate</link:label>
    <link:label id="lab_us-gaap_LongtermDebtWeightedAverageInterestRate_019e2363-9f61-756d-8968-7c0df78e3b38_verboseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Rate</link:label>
    <link:label id="lab_us-gaap_LongtermDebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Weighted Average Interest Rate, at Point in Time</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtWeightedAverageInterestRate"/>
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    <link:label id="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount_019e2363-9ecc-7b82-a8a4-120503f74ebb_negatedTotalLabel_en-US" xlink:label="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net amount</link:label>
    <link:label id="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount_label_en-US" xlink:label="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Including Not Subject To Master Netting Arrangement, After Offset And Deduction, Net Amount</link:label>
    <link:label id="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount_documentation_en-US" xlink:label="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Liability, Including Not Subject To Master Netting Arrangement, After Offset And Deduction, Net Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount" xlink:href="agm-20260630.xsd#agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount"/>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember_019e2363-9ecc-7533-8f63-86e1d90fda29_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Four years</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Four [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPeriodFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableFairValueDisclosure_019e2363-9f61-7fc4-b55f-66930ff0e3cc_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes payable</link:label>
    <link:label id="lab_us-gaap_NotesPayableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayableFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_CollateralAxis_019e2363-9ecc-79ba-a2e8-d5ac6ef70cb7_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral [Axis]</link:label>
    <link:label id="lab_us-gaap_CollateralAxis_label_en-US" xlink:label="lab_us-gaap_CollateralAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Held [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralAxis" xlink:to="lab_us-gaap_CollateralAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield_019e2363-9ecc-7b44-b728-0f9816c87226_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, After Five Through Ten Years, Weighted Average Yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, After Five Through Ten Years, Weighted Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:href="agm-20260630.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:to="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving_019e2363-9f61-7619-b407-fc71fb45d7a8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Revolving</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestRevolving"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_019e2363-9ecc-74ca-84b0-8cdb3d27bec5_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_019e2363-9f61-79d6-b8aa-af2ccfcd0dd2_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Allowance for Losses</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019e2363-9f61-7014-85d4-918a5b5948ed_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning Balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019e2363-9f61-7b51-ba02-48294ffd7595_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending Balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree_019e2363-9ecc-7cbf-95ba-c8d3c3c6e5a1_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Three</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:href="agm-20260630.xsd#agm_LongTermDebtWithInterestRateResetMaturityYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ClearedSwapsMember_019e2363-9f61-7273-bda0-fab02ae08955_terseLabel_en-US" xlink:label="lab_agm_ClearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cleared Swaps</link:label>
    <link:label id="lab_agm_ClearedSwapsMember_label_en-US" xlink:label="lab_agm_ClearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cleared Swaps [Member]</link:label>
    <link:label id="lab_agm_ClearedSwapsMember_documentation_en-US" xlink:label="lab_agm_ClearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cleared Swaps</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ClearedSwapsMember" xlink:href="agm-20260630.xsd#agm_ClearedSwapsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ClearedSwapsMember" xlink:to="lab_agm_ClearedSwapsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne_019e2363-9f61-7f76-bde4-4c9e65abd902_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost Excluding Accrued Interest, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne"/>
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    <link:label id="lab_dei_EntityInformationLineItems_019e2363-9f61-7a0f-978f-d23b81e88493_terseLabel_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:label id="lab_dei_EntityInformationLineItems_label_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInformationLineItems" xlink:to="lab_dei_EntityInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember_019e2363-9f61-7afe-915a-2b0d18732aeb_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CPR</link:label>
    <link:label id="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Constant Prepayment Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputConstantPrepaymentRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:to="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract_019e2363-9ecc-70d4-a985-e62964cff822_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year:</link:label>
    <link:label id="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Current and Noncurrent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtCurrentAndNoncurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:to="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_PaymentsToAcquireTaxCredits_019e2363-9f61-7ef4-b0d1-30a9e96ee1ce_negatedTerseLabel_en-US" xlink:label="lab_agm_PaymentsToAcquireTaxCredits" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of tax credits</link:label>
    <link:label id="lab_agm_PaymentsToAcquireTaxCredits_label_en-US" xlink:label="lab_agm_PaymentsToAcquireTaxCredits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Tax Credits</link:label>
    <link:label id="lab_agm_PaymentsToAcquireTaxCredits_documentation_en-US" xlink:label="lab_agm_PaymentsToAcquireTaxCredits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments to Acquire Tax Credits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_PaymentsToAcquireTaxCredits" xlink:href="agm-20260630.xsd#agm_PaymentsToAcquireTaxCredits"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_019e2363-9ecc-7cd7-8b5c-c88fe27f2e22_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Unrealized Loss</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_019e2363-9ff0-7b89-ae60-5701eaf1c669_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_019e2363-9f61-73d2-a1fe-143793adb846_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockLineItems"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMember" xlink:to="lab_us-gaap_LongTermDebtMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
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    <link:label id="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_019e2363-9ecd-74a8-bf67-6ac1f345c6ef_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems"/>
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    <link:label id="lab_us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1_019f82f5-1bc0-79b6-a92a-01813f7dfc08_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableModificationsSubsequentDefaultRecordedInvestment1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequently defaulted</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
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    <link:label id="lab_us-gaap_DerivativeAssetFairValueNetAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset of Collateral [Abstract]</link:label>
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    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
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    <link:label id="lab_agm_StockAppreciationRightsAndRestrictedStockMember_019e2363-9ecc-73ed-a977-c65c343660ee_terseLabel_en-US" xlink:label="lab_agm_StockAppreciationRightsAndRestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights and Restricted Stock</link:label>
    <link:label id="lab_agm_StockAppreciationRightsAndRestrictedStockMember_label_en-US" xlink:label="lab_agm_StockAppreciationRightsAndRestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights and Restricted Stock [Member]</link:label>
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    <link:label id="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember_019e2363-9ecc-74d3-91a9-cde5bd41c310_verboseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest-Only Farmer Mac Guaranteed Securities</link:label>
    <link:label id="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government-sponsored Enterprises Debt Securities [Member]</link:label>
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    <link:label id="lab_us-gaap_CollateralPledgedMember_019e2363-9ecc-7571-bdf8-bc7c7ee73178_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralPledgedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral Pledged</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralPledgedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CollateralPledgedMember"/>
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    <link:label id="lab_us-gaap_TransactionMarketMethodDomain_label_en-US" xlink:label="lab_us-gaap_TransactionMarketMethodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Market Method [Domain]</link:label>
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    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_019e2363-9f61-747c-8bdf-ba0a380ab1f0_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining authorized amount for repurchase</link:label>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_label_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Remaining Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:to="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount_019e2363-9ecc-7a28-873a-475e5b7a273d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unamortized premiums, discounts, fair value hedge basis adjustment, and other cost basis adjustments</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Unamortized Loan Cost (Fee) and Purchase Premium (Discount)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:to="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_019e2363-9df4-7a56-a92a-3a188a28aa6e_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019e2363-9ecc-7636-bf8a-f67546f88f72_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019e2363-9f61-7199-93d4-108a697b19f1_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_019e2363-9f61-7a0a-ac20-fbc9aaab4f5e_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Unrealized Loss</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoanRestructuringModificationAxis_019f6a25-f1dd-7743-94ae-0fa83102814f_terseLabel_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Axis]</link:label>
    <link:label id="lab_us-gaap_LoanRestructuringModificationAxis_label_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoanRestructuringModificationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoanRestructuringModificationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoanRestructuringModificationAxis" xlink:to="lab_us-gaap_LoanRestructuringModificationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NetEffectiveSpread_019e2363-9f61-7142-bfba-13acd4679cfa_totalLabel_en-US" xlink:label="lab_agm_NetEffectiveSpread" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net effective spread</link:label>
    <link:label id="lab_agm_NetEffectiveSpread_label_en-US" xlink:label="lab_agm_NetEffectiveSpread" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Effective Spread</link:label>
    <link:label id="lab_agm_NetEffectiveSpread_documentation_en-US" xlink:label="lab_agm_NetEffectiveSpread" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Effective Spread</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NetEffectiveSpread" xlink:href="agm-20260630.xsd#agm_NetEffectiveSpread"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NetEffectiveSpread" xlink:to="lab_agm_NetEffectiveSpread" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_RuralInfrastructurePowerUtilitiesSegmentMember_019e2363-9ecc-78ec-8d42-56fc22ac2a0f_terseLabel_en-US" xlink:label="lab_agm_RuralInfrastructurePowerUtilitiesSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Power &amp; Utilities</link:label>
    <link:label id="lab_agm_RuralInfrastructurePowerUtilitiesSegmentMember_label_en-US" xlink:label="lab_agm_RuralInfrastructurePowerUtilitiesSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rural Infrastructure, Power &amp; Utilities Segment [Member]</link:label>
    <link:label id="lab_agm_RuralInfrastructurePowerUtilitiesSegmentMember_documentation_en-US" xlink:label="lab_agm_RuralInfrastructurePowerUtilitiesSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rural Infrastructure, Power &amp; Utilities Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_RuralInfrastructurePowerUtilitiesSegmentMember" xlink:href="agm-20260630.xsd#agm_RuralInfrastructurePowerUtilitiesSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_RuralInfrastructurePowerUtilitiesSegmentMember" xlink:to="lab_agm_RuralInfrastructurePowerUtilitiesSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted_019e2363-9f61-7d08-9310-63fd6fc13c54_negatedTerseLabel_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses</link:label>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted_label_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense, Excluding Loan, Lease and Other Losses, Adjusted</link:label>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted_documentation_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noninterest Expense, Excluding Loan, Lease and Other Losses, Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted" xlink:href="agm-20260630.xsd#agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted" xlink:to="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OffBalanceSheetProgramAssets_019e2363-9ecc-783e-90c6-a3f40e590610_negatedTerseLabel_en-US" xlink:label="lab_agm_OffBalanceSheetProgramAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Off-balance sheet assets under management</link:label>
    <link:label id="lab_agm_OffBalanceSheetProgramAssets_label_en-US" xlink:label="lab_agm_OffBalanceSheetProgramAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Off Balance Sheet Program Assets</link:label>
    <link:label id="lab_agm_OffBalanceSheetProgramAssets_documentation_en-US" xlink:label="lab_agm_OffBalanceSheetProgramAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Off Balance Sheet Program Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OffBalanceSheetProgramAssets" xlink:href="agm-20260630.xsd#agm_OffBalanceSheetProgramAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OffBalanceSheetProgramAssets" xlink:to="lab_agm_OffBalanceSheetProgramAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019e2363-9ecc-71bb-afe0-34c16ed83208_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FAIR VALUE DISCLOSURES</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019e2363-9ecc-7688-bdaa-fde071f13528_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_019e2363-9ecc-7294-b007-82c2971320d0_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract"/>
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    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_019e2363-9f61-7773-9ff5-9437787d1ec3_terseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">USDA Securities</link:label>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government Agencies Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_USGovernmentAgenciesDebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:to="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_RegulatoryFees_019e2363-9ecc-7e62-b6b1-48e38a0577e6_terseLabel_en-US" xlink:label="lab_agm_RegulatoryFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Regulatory fees</link:label>
    <link:label id="lab_agm_RegulatoryFees_label_en-US" xlink:label="lab_agm_RegulatoryFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Regulatory Fees</link:label>
    <link:label id="lab_agm_RegulatoryFees_documentation_en-US" xlink:label="lab_agm_RegulatoryFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Regulatory Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_RegulatoryFees" xlink:href="agm-20260630.xsd#agm_RegulatoryFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_RegulatoryFees" xlink:to="lab_agm_RegulatoryFees" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member_019e2363-9ff0-7cc6-a50f-8156bcf0c36f_terseLabel_en-US" xlink:label="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment obligation</link:label>
    <link:label id="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member_label_en-US" xlink:label="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantee obligations issued after January 1, 2003 [Member]</link:label>
    <link:label id="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member_documentation_en-US" xlink:label="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Guarantee obligations issued after January 1, 2003 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:href="agm-20260630.xsd#agm_GuaranteeobligationsissuedafterJanuary12003Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:to="lab_agm_GuaranteeobligationsissuedafterJanuary12003Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralMember_019e2363-9ecc-7603-8d30-525021afbe0b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Pledged as Collateral</link:label>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralMember_label_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Pledged as Collateral [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetPledgedAsCollateralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:to="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses_019e2363-9f61-73be-9f8b-877cb23c1c0b_totalLabel_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Operating expenses</link:label>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses_label_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense, Excluding Loan, Lease and Other Losses</link:label>
    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses_documentation_en-US" xlink:label="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noninterest Expense, Excluding Loan, Lease and Other Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:href="agm-20260630.xsd#agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:to="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InConsolidatedTrustsMember_019e2363-9f61-799b-b4dd-3455492df293_terseLabel_en-US" xlink:label="lab_agm_InConsolidatedTrustsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">In Consolidated Trusts</link:label>
    <link:label id="lab_agm_InConsolidatedTrustsMember_label_en-US" xlink:label="lab_agm_InConsolidatedTrustsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">In Consolidated Trusts [Member]</link:label>
    <link:label id="lab_agm_InConsolidatedTrustsMember_documentation_en-US" xlink:label="lab_agm_InConsolidatedTrustsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">In Consolidated Trusts [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InConsolidatedTrustsMember" xlink:href="agm-20260630.xsd#agm_InConsolidatedTrustsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InConsolidatedTrustsMember" xlink:to="lab_agm_InConsolidatedTrustsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_019e2363-9ecc-714a-a871-bff8b8557e30_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCash_019e2363-9ecd-7395-a9c3-4dd20c36f341_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCash" xlink:to="lab_us-gaap_RestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest_019e2363-9f61-78d3-b23e-e2bcd50fd8d4_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Allowance for Credit Loss, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember_019e2363-9f61-7b90-b8c8-84402b881136_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">30-59 Days</link:label>
    <link:label id="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, 30 to 59 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivables30To59DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_019e2363-9f61-7718-b90c-777fd71a0361_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, after Ten Years, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, after Ten Years, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:href="agm-20260630.xsd#agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:to="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgedLiabilityFairValueHedge_019e2374-57a7-7762-a724-d2cfd8c2330e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_HedgedLiabilityFairValueHedge" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Carrying amount of hedged liabilities</link:label>
    <link:label id="lab_us-gaap_HedgedLiabilityFairValueHedge_label_en-US" xlink:label="lab_us-gaap_HedgedLiabilityFairValueHedge" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Liability, Fair Value Hedge</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgedLiabilityFairValueHedge" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgedLiabilityFairValueHedge"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgedLiabilityFairValueHedge" xlink:to="lab_us-gaap_HedgedLiabilityFairValueHedge" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_019e2373-072f-773b-bd45-9a9aebc0d042_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Capital_019e2363-9f61-74ed-8986-1b4a6dfe7b78_terseLabel_en-US" xlink:label="lab_us-gaap_Capital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital</link:label>
    <link:label id="lab_us-gaap_Capital_label_en-US" xlink:label="lab_us-gaap_Capital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Capital, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Capital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Capital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Capital" xlink:to="lab_us-gaap_Capital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_019e2363-9ecc-7dad-8dec-ca736208e1a9_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-interest income/(expense):</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoninterestIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeAbstract" xlink:to="lab_us-gaap_NoninterestIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e2363-9f61-7e18-8749-304fbfeca371_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents (includes restricted cash of $26,984 and $24,475, respectively)</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e2363-9f61-7af0-92dc-4aa2bb1c6da3_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, and restricted cash at beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019e2363-9f61-70f2-a3e9-f00b25e71f60_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, and restricted cash at end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_019e2363-9ecc-7f91-b359-bcb1651766e0_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralRightToReclaimCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:to="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_019e2363-9ecc-7b57-ad80-803dcf0541d0_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reclassification out of Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_019e2363-9f61-7222-940d-c9c3c7e56f61_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Losses [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_019e2363-9ecc-7afa-b0e1-94b918c061d6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_019e2363-9ff0-7f2c-aea4-c0ef209991db_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019e2363-9ecc-794c-b0e5-3e8c66e05e41_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_019e2363-9df4-75d5-a711-e543ecfe0801_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_019e2363-9ecc-7d00-a812-67856bec934b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of common stock</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesMember_019e2363-9f61-7c97-bde7-01710be2930d_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Government/GSE guaranteed MBS</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Mortgage-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageBackedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBackedSecuritiesMember" xlink:to="lab_us-gaap_MortgageBackedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019e2363-9f61-7bff-9f6e-ffb7175a0fe6_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Range [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
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    <link:label id="lab_us-gaap_AwardTypeAxis_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss_019e2363-9f61-73df-a66a-3cb8b1bb753c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale securities, amortized cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
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    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019e2363-9f61-79f7-85e0-9b0e228edf3a_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
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    <link:label id="lab_srt_ProductOrServiceAxis_019e2363-9f61-716b-92ab-bd25c72bcefe_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
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    <link:label id="lab_us-gaap_CommonStockMember_019e2363-9ecc-7015-857f-0d7dcd256d41_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
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    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_019e2363-9f61-7463-a470-5fcc1be03a10_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table]</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable"/>
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    <link:label id="lab_agm_IncomeTaxExpenseBenefitAdjusted_019e2363-9ff0-7157-be9a-af72622b8508_negatedLabel_en-US" xlink:label="lab_agm_IncomeTaxExpenseBenefitAdjusted" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_agm_IncomeTaxExpenseBenefitAdjusted_label_en-US" xlink:label="lab_agm_IncomeTaxExpenseBenefitAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit), Adjusted</link:label>
    <link:label id="lab_agm_IncomeTaxExpenseBenefitAdjusted_documentation_en-US" xlink:label="lab_agm_IncomeTaxExpenseBenefitAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit), Adjusted</link:label>
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    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_019e2363-9ecc-71b6-bcfd-281f00bfc194_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract_019e2363-9f61-7016-b0f1-0a29fc1f62dd_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year Three</link:label>
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    <link:label id="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Two Years before Latest Fiscal Year</link:label>
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    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_019e2363-9f61-70b5-8ec8-01abfba89e40_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Past Due</link:label>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialAssetPastDueMember"/>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance_019e2363-9ecc-7204-90a0-9e71b3182aac_terseLabel_en-US" xlink:label="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total on- and off-balance sheet segment assets at principal balance</link:label>
    <link:label id="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance_label_en-US" xlink:label="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">On And Off Balance Sheet Program Assets, At Principal Balance</link:label>
    <link:label id="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance_documentation_en-US" xlink:label="lab_agm_OnAndOffBalanceSheetProgramAssetsAtPrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">On And Off Balance Sheet Program Assets, At Principal Balance</link:label>
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    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_019e2363-9f61-7521-b852-45952584ae3c_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Purchases</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
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    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax_019e2363-9ecc-78dd-9800-7272be0dd96d_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest settlements reclassified from AOCI into net income on derivatives</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax"/>
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    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019e2363-9f61-7cbb-a3cf-12229df9ffa5_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
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    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_019e2363-9ecc-764e-a7c5-3b85c7c9abbf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByAssetClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByAssetClassAxis"/>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019e2363-9f61-734e-9d11-1b1e09c3208a_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
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    <link:label id="lab_us-gaap_NotesPayableToBanksMember_019e2363-9ecc-7a42-aaf0-dcbeb6cba065_verboseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableToBanksMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Discount notes</link:label>
    <link:label id="lab_us-gaap_NotesPayableToBanksMember_label_en-US" xlink:label="lab_us-gaap_NotesPayableToBanksMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable to Banks [Member]</link:label>
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    <link:label id="lab_us-gaap_PaymentsToAcquireHeldToMaturitySecurities_019e2363-9f61-7c51-9408-64e1889b7cf5_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireHeldToMaturitySecurities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of held-to-maturity investment securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireHeldToMaturitySecurities_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireHeldToMaturitySecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Held-to-Maturity Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireHeldToMaturitySecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireHeldToMaturitySecurities"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
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    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_019e2373-072f-7904-986b-434f9128524f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_019e2363-9ecc-7ea2-abe5-4ade0bea2bd1_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAverageFixedInterestRate_019e2363-9ecd-7a60-aec0-8de1354ba609_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Pay Rate</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageFixedInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Fixed Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageFixedInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAverageFixedInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAverageFixedInterestRate" xlink:to="lab_us-gaap_DerivativeAverageFixedInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember_019e2363-9f61-7a13-b47a-c74abb65ca69_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">60-89 Days</link:label>
    <link:label id="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, 60 to 89 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivables60To89DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_019e2363-9f61-79b2-b0cb-2a15960cfe79_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgingDesignationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationAxis" xlink:to="lab_us-gaap_HedgingDesignationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019e2363-9ecc-71c8-819d-cab6e17d3faa_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Assets at fair value</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019e2363-9f61-7da8-9dab-80ee3c2218ea_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019e2363-9ecc-7490-b994-2d3a57a319e8_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems_019e2363-9f61-7d10-8fe3-0e3e0a5fd073_terseLabel_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Line Items]</link:label>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems_label_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Line Items]</link:label>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems_documentation_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:href="agm-20260630.xsd#agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:to="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_019e2363-9f61-7b02-984f-fc95694aa106_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_label_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Fee Income, Financing Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestAndFeeIncomeLoansAndLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:to="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019e2363-9ecc-7ab6-acc6-25327576c6b1_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment_019e2363-9ecd-70bd-98b5-a7291fbed3c3_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of loans held for investment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Acquisition, Loan, Held-for-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireLoansHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:to="lab_us-gaap_PaymentsToAcquireLoansHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets_019e2363-9ecc-7761-9d42-73adc5e91dc0_terseLabel_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of level three fair value assets and liabilities</link:label>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets_label_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Fair Value as Percent of Total Assets</link:label>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets_documentation_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Fair Value as Percent of Total Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:href="agm-20260630.xsd#agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:to="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsNatureDomain_019e2363-9ecc-7a1a-b2b6-881d33a65ee9_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsNatureDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Nature [Domain]</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsNatureDomain_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsNatureDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Nature [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsNatureDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GuaranteeObligationsNatureDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsNatureDomain" xlink:to="lab_us-gaap_GuaranteeObligationsNatureDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_019e2363-9f61-79cb-a68b-1dacb29cbf9c_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable (includes $37,189 and $40,945, respectively, related to consolidated trusts)</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_019e2363-9f61-7b0b-b572-ccd8841922ef_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_019e2363-9df4-7199-ab22-f72e31297191_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.250% Non-Cumulative Preferred Stock, Series F</link:label>
    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_019e2363-9df4-75c6-a409-45c534165a1a_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Series F</link:label>
    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series F Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesFPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeriesFPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesFPreferredStockMember" xlink:to="lab_us-gaap_SeriesFPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ReserveForLosses_019e2363-9ecc-717f-baa4-25c32a22c056_terseLabel_en-US" xlink:label="lab_agm_ReserveForLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for losses</link:label>
    <link:label id="lab_agm_ReserveForLosses_label_en-US" xlink:label="lab_agm_ReserveForLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reserve For Losses</link:label>
    <link:label id="lab_agm_ReserveForLosses_documentation_en-US" xlink:label="lab_agm_ReserveForLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The reserve for guarantee losses is a liability account in the consolidated balance sheets that reflects an estimate of incurred credit losses related to the guaranty of unconsolidated trusts and other credit guarantees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ReserveForLosses" xlink:href="agm-20260630.xsd#agm_ReserveForLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ReserveForLosses" xlink:to="lab_agm_ReserveForLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_019e2363-9ecc-7904-9ad9-c8c674103fe3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts and Financing Receivables [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_019e2363-9f61-7695-b576-a662380f9dae_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Five years</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueYearThreeMember_019e2363-9f61-7be3-8dce-378e28dd0eb5_terseLabel_en-US" xlink:label="lab_agm_DueYearThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year three</link:label>
    <link:label id="lab_agm_DueYearThreeMember_label_en-US" xlink:label="lab_agm_DueYearThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due Year Three [Member]</link:label>
    <link:label id="lab_agm_DueYearThreeMember_documentation_en-US" xlink:label="lab_agm_DueYearThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due year three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueYearThreeMember" xlink:href="agm-20260630.xsd#agm_DueYearThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueYearThreeMember" xlink:to="lab_agm_DueYearThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings_019e2363-9df4-702f-b766-682277529bb3_totalLabel_en-US" xlink:label="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net effects of fair value hedging relationships</link:label>
    <link:label id="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings_label_en-US" xlink:label="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Fair Value Hedges Recognized in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:to="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019e2363-9ecc-7285-8580-b0aab566f968_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net change in cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss_019e2363-9f61-7bee-9bfb-770db34cde1b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale, accrued interest excluded</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019e2363-9ecc-7484-b15b-2565abd27ac5_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019e2363-9ecc-7c71-934a-bcb456c2426b_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019e2363-9ecc-75c8-aa7b-99241887d56b_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo_019e2363-9ecc-7a4c-87a5-0c1148fa9b59_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Two</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:href="agm-20260630.xsd#agm_LongTermDebtWithInterestRateResetMaturityYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_019e2363-9ecc-792f-b3b8-ab017f63ea58_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivables Past Due [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFinancingReceivablesPastDueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_019e2363-9ecc-7e82-8021-2e1dc9c5bfe4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income, Net of Tax</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_019e2363-9ecc-7a39-a295-1c5b0f00ae91_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of notes payable</link:label>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromNotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromNotesPayable" xlink:to="lab_us-gaap_ProceedsFromNotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue_019e2363-9ff0-79d7-b161-17454817a6a1_terseLabel_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial instruments level three percent</link:label>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue_label_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities, Fair Value as Percent of Total Financial Instruments Measured at Fair Value</link:label>
    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue_documentation_en-US" xlink:label="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities, Fair Value as Percent of Total Financial Instruments Measured at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:href="agm-20260630.xsd#agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:to="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalFinancialInstrumentsMeasuredAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TreasurySegmentMember_019e2363-9ecc-701e-aab0-8beb44c52f91_terseLabel_en-US" xlink:label="lab_agm_TreasurySegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury</link:label>
    <link:label id="lab_agm_TreasurySegmentMember_label_en-US" xlink:label="lab_agm_TreasurySegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Segment [Member]</link:label>
    <link:label id="lab_agm_TreasurySegmentMember_documentation_en-US" xlink:label="lab_agm_TreasurySegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TreasurySegmentMember" xlink:href="agm-20260630.xsd#agm_TreasurySegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_TreasurySegmentMember" xlink:to="lab_agm_TreasurySegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019e2363-9ecc-76b2-a713-cfe2fb825953_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Range [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019e2363-9ecc-7fff-9186-2ac5ab6dd9e9_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
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    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_019e2363-9ecd-72fb-affc-c278c7b25857_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Netting adjustments</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_019e2363-9ecd-784c-8c90-851579db6ca0_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts offset in the Consolidated Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Asset Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityFairValueGrossAsset"/>
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    <link:label id="lab_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions_019e2363-9ecc-760e-8ed0-a2fc0c0584b3_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment fees</link:label>
    <link:label id="lab_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions_label_en-US" xlink:label="lab_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Banking, Advisory, Brokerage, and Underwriting Fees and Commissions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions"/>
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    <link:label id="lab_agm_AgVantageSecuritiesMember_019e2363-9f61-7829-bece-1fe3a19bf9ec_terseLabel_en-US" xlink:label="lab_agm_AgVantageSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AgVantage</link:label>
    <link:label id="lab_agm_AgVantageSecuritiesMember_019e2363-9f61-7578-8b6a-135867b02413_verboseLabel_en-US" xlink:label="lab_agm_AgVantageSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">AgVantage</link:label>
    <link:label id="lab_agm_AgVantageSecuritiesMember_label_en-US" xlink:label="lab_agm_AgVantageSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AgVantage Securities [Member]</link:label>
    <link:label id="lab_agm_AgVantageSecuritiesMember_documentation_en-US" xlink:label="lab_agm_AgVantageSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AgVantage Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AgVantageSecuritiesMember" xlink:href="agm-20260630.xsd#agm_AgVantageSecuritiesMember"/>
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    <link:label id="lab_us-gaap_CommonStockValue_019e2363-9ecc-7a1c-b25a-d3e7dfd9a679_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
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    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_019e2363-9ecc-7242-9e3d-e713a0f2dd03_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Tax payments related to share-based awards</link:label>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment, Tax Withholding, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
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    <link:label id="lab_us-gaap_AuctionRateSecuritiesMember_019e2363-9f61-7449-9c77-e364f117dc71_terseLabel_en-US" xlink:label="lab_us-gaap_AuctionRateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auction-rate certificates backed by Government guaranteed student loans</link:label>
    <link:label id="lab_us-gaap_AuctionRateSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_AuctionRateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auction Rate Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AuctionRateSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AuctionRateSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AuctionRateSecuritiesMember" xlink:to="lab_us-gaap_AuctionRateSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_019e2363-9f61-702e-9945-86fa234b2a2e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments</link:label>
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    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDeterminationDate"/>
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    <link:label id="lab_us-gaap_FinancingReceivablesTextBlock_019e2363-9ecc-7f3a-8b1c-df9026287692_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LOANS</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivables [Text Block]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableModifiedPastDueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableModifiedPastDueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableModifiedPastDueTableTextBlock" xlink:to="lab_us-gaap_FinancingReceivableModifiedPastDueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_019e2363-9ecc-7961-9441-30ab06192328_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Loss, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract_019e2363-9ecc-7179-86e7-949a64c43f14_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year Two</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated in Fiscal Year before Latest Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated in Fiscal Year before Latest Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:href="agm-20260630.xsd#agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InfrastructureFinanceMember_019e2363-9f61-7074-a3d6-b7519f448dc5_terseLabel_en-US" xlink:label="lab_agm_InfrastructureFinanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Infrastructure Finance</link:label>
    <link:label id="lab_agm_InfrastructureFinanceMember_019e2363-9f61-7f1e-9338-e11a92fafd66_verboseLabel_en-US" xlink:label="lab_agm_InfrastructureFinanceMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Infrastructure Finance loans</link:label>
    <link:label id="lab_agm_InfrastructureFinanceMember_019e2363-9f61-7844-a277-f2f45cdb0ebb_netLabel_en-US" xlink:label="lab_agm_InfrastructureFinanceMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Infrastructure Finance loans</link:label>
    <link:label id="lab_agm_InfrastructureFinanceMember_label_en-US" xlink:label="lab_agm_InfrastructureFinanceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Infrastructure Finance [Member]</link:label>
    <link:label id="lab_agm_InfrastructureFinanceMember_documentation_en-US" xlink:label="lab_agm_InfrastructureFinanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Infrastructure Finance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InfrastructureFinanceMember" xlink:href="agm-20260630.xsd#agm_InfrastructureFinanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InfrastructureFinanceMember" xlink:to="lab_agm_InfrastructureFinanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019e2363-9ecc-732c-903c-d016a0d8065f_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_019e2363-9f61-7c88-be0f-9bafd178383d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonaccrual Loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_019e2363-9ecc-76c5-8bc7-c9ffcd2cf60d_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxContingencyLineItems_019e2363-9ecc-76d9-84c3-f37d314c2f2c_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxContingencyLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Contingency [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxContingencyLineItems_label_en-US" xlink:label="lab_us-gaap_IncomeTaxContingencyLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Contingency [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxContingencyLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxContingencyLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxContingencyLineItems" xlink:to="lab_us-gaap_IncomeTaxContingencyLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019e2363-9f61-7413-a478-aa5d9282c130_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember_019e2363-9ecc-7909-aeb3-b9163aee6658_terseLabel_en-US" xlink:label="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farm &amp; Ranch</link:label>
    <link:label id="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember_019e2363-9ecc-7aed-951e-02c6e8f037f1_verboseLabel_en-US" xlink:label="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Farm &amp; Ranch</link:label>
    <link:label id="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember_019e2363-9ecc-72c0-8496-25cab5353789_netLabel_en-US" xlink:label="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Agricultural Finance - Farm &amp; Ranch loans</link:label>
    <link:label id="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember_label_en-US" xlink:label="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agriculture Finance, Farm And Ranch Segment [Member]</link:label>
    <link:label id="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember_documentation_en-US" xlink:label="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Farm &amp; Ranch [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:href="agm-20260630.xsd#agm_AgricultureFinanceFarmAndRanchSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:to="lab_agm_AgricultureFinanceFarmAndRanchSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_019e2363-9f61-7125-826f-e27ec5c960b0_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NetEffectsOfDerivativesAndTradingSecurities_019e2363-9ecc-7bf6-8612-cced273050f7_terseLabel_en-US" xlink:label="lab_agm_NetEffectsOfDerivativesAndTradingSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net effects of derivatives and trading securities</link:label>
    <link:label id="lab_agm_NetEffectsOfDerivativesAndTradingSecurities_label_en-US" xlink:label="lab_agm_NetEffectsOfDerivativesAndTradingSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Effects Of Derivatives And Trading Securities</link:label>
    <link:label id="lab_agm_NetEffectsOfDerivativesAndTradingSecurities_documentation_en-US" xlink:label="lab_agm_NetEffectsOfDerivativesAndTradingSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Effects Of Derivatives And Trading Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NetEffectsOfDerivativesAndTradingSecurities" xlink:href="agm-20260630.xsd#agm_NetEffectsOfDerivativesAndTradingSecurities"/>
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    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_019e2363-9ecc-7a11-86ee-72e1d6b3e43e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Recorded Investment [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableRecordedInvestmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_019fa908-7770-7385-9fd3-06c09dc6b61f_terseLabel_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unfunded Lending Commitment</link:label>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_label_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unfunded Loan Commitment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnfundedLoanCommitmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:to="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsAbstract_019e2363-9f61-7e17-a4e7-a2955d22f052_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities:</link:label>
    <link:label id="lab_us-gaap_InvestmentsAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsAbstract" xlink:to="lab_us-gaap_InvestmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019e2363-9f61-7a5f-8710-cf22f1869c60_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
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    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome_019e2363-9f61-7830-84d7-6cd82845ad87_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest received on nonaccrual loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual, Interest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableNonaccrualInterestIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:to="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_019e2363-9f61-7cd7-9476-29648082a7f9_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Interest Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet"/>
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    <link:label id="lab_us-gaap_NoninterestIncome_019e2363-9f61-74f7-b8a5-9b9b4a52d018_totalLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncome" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Non-interest income</link:label>
    <link:label id="lab_us-gaap_NoninterestIncome_label_en-US" xlink:label="lab_us-gaap_NoninterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoninterestIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncome" xlink:to="lab_us-gaap_NoninterestIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NumberOfSubsidiaries_019e2363-9f61-7e3d-9c4d-a965deff8809_terseLabel_en-US" xlink:label="lab_agm_NumberOfSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of subsidiaries</link:label>
    <link:label id="lab_agm_NumberOfSubsidiaries_label_en-US" xlink:label="lab_agm_NumberOfSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Subsidiaries</link:label>
    <link:label id="lab_agm_NumberOfSubsidiaries_documentation_en-US" xlink:label="lab_agm_NumberOfSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Subsidiaries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NumberOfSubsidiaries" xlink:href="agm-20260630.xsd#agm_NumberOfSubsidiaries"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NumberOfSubsidiaries" xlink:to="lab_agm_NumberOfSubsidiaries" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_019e2363-9f61-76e4-86aa-5bbeb6fbbb7e_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019e2363-9ecc-7a94-ab55-dd19282b1a52_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019e2363-9ecc-720b-909b-bdd6b78167f5_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_019e2363-9ecd-77d6-a3d3-230f525841f1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on common and preferred stock</link:label>
    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfOrdinaryDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfOrdinaryDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfOrdinaryDividends" xlink:to="lab_us-gaap_PaymentsOfOrdinaryDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019e2363-9ecc-7c36-8989-54fb0e799165_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum borrowing capacity from U.S. Treasury</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_019e2363-9ecc-73c8-b90b-fba67604d232_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding, Amount</link:label>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtCurrent" xlink:to="lab_us-gaap_LongTermDebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor_019e2363-9ecc-7317-b974-007de6eb31b6_terseLabel_en-US" xlink:label="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining maturity</link:label>
    <link:label id="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor_label_en-US" xlink:label="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Remaining Maturity, Loans Underlying Guarantees Not Held By Transferor</link:label>
    <link:label id="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor_documentation_en-US" xlink:label="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Remaining Maturity, Loans Underlying Guarantees Not Held By Transferor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:href="agm-20260630.xsd#agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_019e2363-9ecc-78a5-8aed-14ac19b7931c_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total loans, net of allowance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
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    <link:label id="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember_019e2363-9f61-78e8-8e4c-68392547f318_terseLabel_en-US" xlink:label="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held-to-Maturity Securities</link:label>
    <link:label id="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember_label_en-US" xlink:label="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Held-To-Maturity, Parent [Member]</link:label>
    <link:label id="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember_documentation_en-US" xlink:label="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Held-To-Maturity, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember" xlink:href="agm-20260630.xsd#agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember" xlink:to="lab_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019e2363-9f61-7bfe-89c7-9c569c3c730e_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Accounting Standards</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_019e2363-9f61-7732-973c-8342e30f0d0a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Common Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_019e2363-9ecd-7053-8baf-a1704967688b_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Custodial deposit liability</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability"/>
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    <link:label id="lab_us-gaap_FutureMember_019e2363-9ecc-75b9-ad6d-ff56d26afa11_terseLabel_en-US" xlink:label="lab_us-gaap_FutureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury futures</link:label>
    <link:label id="lab_us-gaap_FutureMember_label_en-US" xlink:label="lab_us-gaap_FutureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Future [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FutureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FutureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FutureMember" xlink:to="lab_us-gaap_FutureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_019e2363-9f61-71d9-9508-d846ec15e64a_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total principal net of discounts</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebt"/>
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    <link:label id="lab_us-gaap_ShortTermBorrowingsAbstract_label_en-US" xlink:label="lab_us-gaap_ShortTermBorrowingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermBorrowingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShortTermBorrowingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermBorrowingsAbstract" xlink:to="lab_us-gaap_ShortTermBorrowingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_019e2363-9ecd-74dc-9a74-dfde59440a96_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Three, Originated, Two Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_019e2363-9ecc-7909-9b87-bba3b38e44b6_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net change in:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019e2363-9ecc-7c9f-b3c0-be2a6ba68806_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_019e2363-9f61-70b6-a582-de0f276c2c8d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralObligationToReturnCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:to="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019e2363-9f61-76b6-81c0-4e5f8c10d0bb_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019e2363-9ecc-7811-a6d4-0d274dd501aa_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EQUITY</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019e2363-9ecd-7b86-a4b7-a45b2582ddb1_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransactionMarketMethodAxis_019effe2-1e02-73c3-937c-8fb5e6523bc3_terseLabel_en-US" xlink:label="lab_us-gaap_TransactionMarketMethodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction Market Method [Axis]</link:label>
    <link:label id="lab_us-gaap_TransactionMarketMethodAxis_label_en-US" xlink:label="lab_us-gaap_TransactionMarketMethodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Market Method [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransactionMarketMethodAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransactionMarketMethodAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransactionMarketMethodAxis" xlink:to="lab_us-gaap_TransactionMarketMethodAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_019e2363-9ecc-76a5-a2d3-6418b5aa556a_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Year Two Through Five, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Year Two Through Five, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:href="agm-20260630.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:to="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate_019e2363-9ecc-7851-a079-6d930065fac3_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost Excluding Accrued Interest, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateReset_019e2363-9ecc-7b9d-88e8-02d1e5c13b76_totalLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateReset" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total principal net of discounts</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateReset_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateReset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateReset_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateReset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateReset" xlink:href="agm-20260630.xsd#agm_LongTermDebtWithInterestRateReset"/>
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    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019e2363-9f61-7fb7-b939-33dd751204f4_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinanceReceivableAccruedInterestPayable_019e2363-9ecc-793b-bb18-81f0999bee3d_terseLabel_en-US" xlink:label="lab_agm_FinanceReceivableAccruedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_agm_FinanceReceivableAccruedInterestPayable_label_en-US" xlink:label="lab_agm_FinanceReceivableAccruedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Receivable, Accrued Interest Payable</link:label>
    <link:label id="lab_agm_FinanceReceivableAccruedInterestPayable_documentation_en-US" xlink:label="lab_agm_FinanceReceivableAccruedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Receivable, Accrued Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinanceReceivableAccruedInterestPayable" xlink:href="agm-20260630.xsd#agm_FinanceReceivableAccruedInterestPayable"/>
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    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_019e2363-9ecc-770b-8e20-8ec69bffedac_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities at fair value</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_019e2363-9f61-742d-b2b9-ee9f37f91661_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160;Value</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_019e2363-9ecc-7724-95ea-05e4c4348b93_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities_019e2363-9ecc-70ac-824c-c2e2f2a83a2d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Netting Adjustments</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Security Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralRightToReclaimSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:to="lab_us-gaap_DerivativeCollateralRightToReclaimSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_MarketableSecuritiesFairValueDisclosure_019e2363-9ecc-7dda-84e7-3785aec9dae2_verboseLabel_en-US" xlink:label="lab_agm_MarketableSecuritiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Investment securities</link:label>
    <link:label id="lab_agm_MarketableSecuritiesFairValueDisclosure_label_en-US" xlink:label="lab_agm_MarketableSecuritiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities, Fair Value Disclosure</link:label>
    <link:label id="lab_agm_MarketableSecuritiesFairValueDisclosure_documentation_en-US" xlink:label="lab_agm_MarketableSecuritiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marketable Securities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_MarketableSecuritiesFairValueDisclosure" xlink:href="agm-20260630.xsd#agm_MarketableSecuritiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_MarketableSecuritiesFairValueDisclosure" xlink:to="lab_agm_MarketableSecuritiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent_019e2363-9f61-747f-a1cd-50f63c1a227e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amounts reclassified from AOCI</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent_019e2363-9f61-74ab-ab7c-c12172181419_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Less reclassification adjustments, provision (benefit)</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from AOCI, Current Period, Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent" xlink:to="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_019e2363-9ecc-782d-aa5c-137c62c9fe43_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net amortization of debt premiums, discounts, and issuance costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs and Discounts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCostsAndDiscounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:to="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue_019e2363-9f61-7218-a1a4-a310c3deb992_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_019e2363-9ecc-7731-84f3-cdc1411004d6_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash activity:</link:label>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_label_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Investing and Financing Items [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncashInvestingAndFinancingItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_019e2363-9f61-7abe-89d4-cec68422c8a2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of other investment securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireOtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale_019e2363-9f61-7b76-a9d8-38d9a9c5bd1d_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from repayment of loans purchased as held for sale</link:label>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Collection, Loan, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromCollectionOfLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:to="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis_019e2363-9f61-7694-b62b-dcf7ff2b8039_terseLabel_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees [Axis]</link:label>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis_label_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees [Axis]</link:label>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis_documentation_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees, pertinent information about guarantee obligations issued [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:href="agm-20260630.xsd#agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:to="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_019e2363-9ecc-7e2b-9288-3d8a7021a884_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_019e2363-9ecc-758d-a9c6-55b4cd97dc31_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total AFS Investment Securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesMember" xlink:to="lab_us-gaap_DebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_019e2363-9ecc-7463-a37f-aee496f48421_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019e2363-9ecc-763a-b16b-ae7da8090cdd_totalLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Weighted-average shares, diluted EPS (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_019e2363-9ecc-7d3c-9d16-cd1a0efc135c_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_label_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsNotesAndLoansReceivableLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:to="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019e2363-9ecc-71ec-9f95-5572ecdb1d06_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueAfterFourYearsMember_019e2363-9f61-771b-92c7-aa4a72a601d4_terseLabel_en-US" xlink:label="lab_agm_DueAfterFourYearsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_DueAfterFourYearsMember_label_en-US" xlink:label="lab_agm_DueAfterFourYearsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due After Four Years [Member]</link:label>
    <link:label id="lab_agm_DueAfterFourYearsMember_documentation_en-US" xlink:label="lab_agm_DueAfterFourYearsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due After Four Years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueAfterFourYearsMember" xlink:href="agm-20260630.xsd#agm_DueAfterFourYearsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueAfterFourYearsMember" xlink:to="lab_agm_DueAfterFourYearsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_019e2363-9ecd-7bf5-bfa3-a4c3f915ca0f_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loans held for investment, at amortized cost</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_019e2363-9ecd-7713-86c8-c8698009d168_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract_019e2363-9ecc-788a-b3b1-0123d52dc03d_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year One</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated in Current Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated in Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:href="agm-20260630.xsd#agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019e2363-9f61-743d-b6d7-78733cb6ef9f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FINANCIAL DERIVATIVES</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss_019e2363-9f61-7cd3-a17d-80a3c86be55b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Losses</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Accumulated Unrecognized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue_019e2363-9ecc-76fd-901a-14845c841281_verboseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment obligation</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Current Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GuaranteeObligationsCurrentCarryingValue"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_019e2363-9f61-7c1e-a78e-6dd4d40ffd50_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Max Exposure to Loss</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:to="lab_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_019e2363-9f61-7dc2-a625-d492d0a7a5b9_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Gross Amount Recognized</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepayableFinancialAssetClosedPortfolioLastOfLayerAmortizedCost_019f82a5-ced5-7d10-ade9-81b0b83cd1b7_terseLabel_en-US" xlink:label="lab_us-gaap_PrepayableFinancialAssetClosedPortfolioLastOfLayerAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Closed portfolio of securities hedged, amortized cost</link:label>
    <link:label id="lab_us-gaap_PrepayableFinancialAssetClosedPortfolioLastOfLayerAmortizedCost_label_en-US" xlink:label="lab_us-gaap_PrepayableFinancialAssetClosedPortfolioLastOfLayerAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Closed Portfolio, Portfolio Layer Method, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepayableFinancialAssetClosedPortfolioLastOfLayerAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepayableFinancialAssetClosedPortfolioLastOfLayerAmortizedCost"/>
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    <link:label id="lab_agm_OtherAssets1Member_019e2366-61a5-7738-a35c-5126a71d77eb_terseLabel_en-US" xlink:label="lab_agm_OtherAssets1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:label id="lab_agm_OtherAssets1Member_label_en-US" xlink:label="lab_agm_OtherAssets1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets1 [Member]</link:label>
    <link:label id="lab_agm_OtherAssets1Member_documentation_en-US" xlink:label="lab_agm_OtherAssets1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Assets1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OtherAssets1Member" xlink:href="agm-20260630.xsd#agm_OtherAssets1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OtherAssets1Member" xlink:to="lab_agm_OtherAssets1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AgriculturalFinanceMember_019e2363-9f61-7ca1-8326-bd44e40d56be_terseLabel_en-US" xlink:label="lab_agm_AgriculturalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agricultural Finance loans</link:label>
    <link:label id="lab_agm_AgriculturalFinanceMember_019e2363-9f61-7fb2-bc66-747e8aa79f48_verboseLabel_en-US" xlink:label="lab_agm_AgriculturalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total Agricultural Finance loans</link:label>
    <link:label id="lab_agm_AgriculturalFinanceMember_label_en-US" xlink:label="lab_agm_AgriculturalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agricultural Finance [Member]</link:label>
    <link:label id="lab_agm_AgriculturalFinanceMember_documentation_en-US" xlink:label="lab_agm_AgriculturalFinanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agricultural Finance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AgriculturalFinanceMember" xlink:href="agm-20260630.xsd#agm_AgriculturalFinanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AgriculturalFinanceMember" xlink:to="lab_agm_AgriculturalFinanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InvestmentTaxCreditPricePerCredit_019e2363-9ecc-776b-8cf9-68e5a30a069c_terseLabel_en-US" xlink:label="lab_agm_InvestmentTaxCreditPricePerCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Renewable energy investment tax credits, price per credit</link:label>
    <link:label id="lab_agm_InvestmentTaxCreditPricePerCredit_label_en-US" xlink:label="lab_agm_InvestmentTaxCreditPricePerCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Tax Credit, Price Per Credit</link:label>
    <link:label id="lab_agm_InvestmentTaxCreditPricePerCredit_documentation_en-US" xlink:label="lab_agm_InvestmentTaxCreditPricePerCredit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Tax Credit, Price Per Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InvestmentTaxCreditPricePerCredit" xlink:href="agm-20260630.xsd#agm_InvestmentTaxCreditPricePerCredit"/>
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    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_019e2363-9f61-740b-812c-c628261cb3f8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:to="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_DerivativeAssetNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetNotionalAmount" xlink:to="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_CollateralDomain_019e2363-9f61-7d80-8751-6cddd497d498_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral [Domain]</link:label>
    <link:label id="lab_us-gaap_CollateralDomain_label_en-US" xlink:label="lab_us-gaap_CollateralDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Held [Domain]</link:label>
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    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditEnergyRelatedAmount_019e2363-9ecc-778b-b8f0-79fdf7736cbd_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditEnergyRelatedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Renewable energy investment tax credits, tax benefit</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditEnergyRelatedAmount_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditEnergyRelatedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Credit, Energy-Related, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditEnergyRelatedAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditEnergyRelatedAmount"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements"/>
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    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList"/>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019e2363-9ecc-78c9-8366-c9e6096ac6ac_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Basic and Diluted EPS</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_LiabilitiesAbstract_019e2363-9ecc-739c-9155-4dfcbb35de61_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_019e2363-9ecc-7533-9344-069d5e14e31d_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement Location [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeLocationBalanceAxis"/>
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    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_019e2363-9ff0-7baf-ad8a-1f37fe07c064_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
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    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss_019e2363-9ecc-740a-a174-ffcec8725bef_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest on cleared swaps</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfNotesPayable_019e2363-9f61-7648-96e0-0e6fbe2eda49_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Payments to redeem notes payable</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfNotesPayable_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfNotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfNotesPayable" xlink:to="lab_us-gaap_RepaymentsOfNotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncomeOtherOperatingIncome_019e2363-9ecc-74f5-a986-6362bedf0f19_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeOtherOperatingIncome_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income, Other Operating Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoninterestIncomeOtherOperatingIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:to="lab_us-gaap_NoninterestIncomeOtherOperatingIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable_019e2363-9ecc-74ec-a67a-65af3371132b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivable, Allowance for Credit Losses [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_019e2363-9ecd-7800-a5a3-7097a238739b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
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    <link:label id="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet_019e2363-9f61-7809-bfa6-7219c455b600_negatedTerseLabel_en-US" xlink:label="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: reconciling adjustments</link:label>
    <link:label id="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet_label_en-US" xlink:label="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciling Adjustments From Net Interest Income To Net Effective Spread, Net</link:label>
    <link:label id="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet_documentation_en-US" xlink:label="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reconciling Adjustments From Net Interest Income To Net Effective Spread, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:href="agm-20260630.xsd#agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_019e2363-9ff0-705c-a1dc-d613624aa386_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue"/>
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    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardExrcPrice"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss_019e2363-9ecc-7959-aa39-d484857cb195_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss_019e2363-9ecc-7958-90bc-c75762581ed2_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
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    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_019e2363-9ecc-7ac1-9b9f-93f0cc7b2984_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingInformationLineItems"/>
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    <link:label id="lab_us-gaap_PaymentsToPurchaseLoansHeldForSale_019e643b-d204-7793-b427-67766cdcc5ba_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToPurchaseLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of loans held for sale</link:label>
    <link:label id="lab_us-gaap_PaymentsToPurchaseLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_PaymentsToPurchaseLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Purchase, Loan, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToPurchaseLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToPurchaseLoansHeldForSale"/>
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    <link:label id="lab_dei_DocumentQuarterlyReport_019e2363-9f61-7d40-8ba8-e45398dfda8b_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
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    <link:label id="lab_us-gaap_SpecialMentionMember_019e2363-9f61-7a47-af0a-0343bd99bb4b_terseLabel_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Special mention</link:label>
    <link:label id="lab_us-gaap_SpecialMentionMember_label_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Special Mention [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SpecialMentionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SpecialMentionMember"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Four, Originated, Three Years before Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff"/>
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    <link:label id="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember_019e2363-9f61-7a0e-8098-39e18286512e_terseLabel_en-US" xlink:label="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Farmer Mac Guaranteed Securities and USDA Securities</link:label>
    <link:label id="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember_label_en-US" xlink:label="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Farmer Mac and USDA Guaranteed Securities [Member]</link:label>
    <link:label id="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember_documentation_en-US" xlink:label="lab_agm_FarmerMacAndUsdaGuaranteedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Farmer Mac and USDA Guaranteed Securities [Member]</link:label>
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    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019e2363-9ecc-7240-a0f7-ad799325323c_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable (includes $14,696 and $15,795, respectively, related to consolidated trusts)</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019e2363-9ecc-7e26-bd30-5e7efe6b26b9_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable - consolidated trusts amount</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
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    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_019e2363-9f61-7991-bf35-5bbccebba649_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">5.750% Non-Cumulative Preferred Stock, Series E</link:label>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_019e2363-9f61-73fc-bc35-b2de8c0d3d76_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series E</link:label>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series E Preferred Stock [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesEPreferredStockMember" xlink:to="lab_us-gaap_SeriesEPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecuritiesTextBlock_019e2363-9ecc-70ec-8f3a-5f813368e608_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Farmer Mac Investment Securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesTextBlock_label_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MarketableSecuritiesTextBlock"/>
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    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_019e2363-9f61-7231-8877-52fa6ec770b7_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Liability)</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:to="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherReceivables_019e2363-9ecc-7caf-bcc7-069881e4ac7e_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment fees receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherReceivables_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherReceivables"/>
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    <link:label id="lab_us-gaap_EquityComponentDomain_019e2363-9ecc-7fc4-8757-759c8259a52a_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_019e2363-9ecc-79de-850b-8cb69a4c1493_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_019e2363-9ff0-7aba-a46c-c0ef68942b2b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized (losses)/gains included in Income</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1"/>
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    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_019e2363-9ecc-76e3-965a-9143594b1fd9_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:to="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTaxCredit_019e2363-9ecd-7276-a799-55ed25292440_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTaxCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Renewable energy investment tax credits, purchased amount</link:label>
    <link:label id="lab_us-gaap_InvestmentTaxCredit_label_en-US" xlink:label="lab_us-gaap_InvestmentTaxCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Tax Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTaxCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentTaxCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTaxCredit" xlink:to="lab_us-gaap_InvestmentTaxCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract_019e2363-9ecc-7d78-8609-f3e68733da3f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, before Allowance for Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:to="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_019e2363-9f61-76f6-be16-ce0518fd6c74_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAverageRemainingMaturity1_019e2363-9f61-7b98-b5d2-f2c42f76ce48_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageRemainingMaturity1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Remaining Term (in&#160;years)</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageRemainingMaturity1_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageRemainingMaturity1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Remaining Maturity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageRemainingMaturity1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAverageRemainingMaturity1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAverageRemainingMaturity1" xlink:to="lab_us-gaap_DerivativeAverageRemainingMaturity1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_019e2363-9ff0-7b60-89c4-ab1319c10b44_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments of stock issuance costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Stock Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfStockIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain_019e2363-9df4-7e4f-b89d-9024f5c4cc17_terseLabel_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees [Domain]</link:label>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain_label_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded maximum potential exposure on guarantees [Domain]</link:label>
    <link:label id="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain_documentation_en-US" xlink:label="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Domain] for Unrecorded maximum potential exposure on guarantees, pertinent information about guarantee obligations issued [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:href="agm-20260630.xsd#agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:to="lab_agm_UnrecordedMaximumPotentialExposureOnGuaranteesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_019e2363-9f61-7b28-9791-559614dca6d5_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019e2363-9f61-7669-9769-158a8897c039_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GUARANTEES AND COMMITMENTS</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_019e2363-9f61-70e6-b447-215f38b1181d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty_019e2363-9f61-7b16-99e9-4b6133d4643f_terseLabel_en-US" xlink:label="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, additional net exposure to counterparty</link:label>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty_label_en-US" xlink:label="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Collateral Exceeding Derivative Position, Additional Net Exposure To Counterparty</link:label>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty_documentation_en-US" xlink:label="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative, Collateral Exceeding Derivative Position, Additional Net Exposure To Counterparty</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty" xlink:href="agm-20260630.xsd#agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty" xlink:to="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_019e2363-9ecc-7cac-900e-fc157d29dd07_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019e2363-9f61-7e05-82a9-65ba2d2046b4_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubstandardMember_019e2363-9f61-7a1a-bad5-a60f6f5cb7fe_terseLabel_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Substandard</link:label>
    <link:label id="lab_us-gaap_SubstandardMember_label_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Substandard [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubstandardMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubstandardMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubstandardMember" xlink:to="lab_us-gaap_SubstandardMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_019e2363-9f61-7242-9786-2869c901da03_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019e2363-9ecc-757d-bff7-876396e2d29f_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_019e2363-9f61-7219-90be-7a98ee8adcf8_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax asset, net</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:to="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements_019e2363-9f61-7a46-80f6-5928835ec7ff_terseLabel_en-US" xlink:label="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SARs and restricted stock units (in dollars per share)</link:label>
    <link:label id="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements_label_en-US" xlink:label="lab_agm_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, On Incremental Common Shares Attributable to Share-based Payment Arrangements</link:label>
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    <link:label id="lab_dei_CityAreaCode_019e2363-9ff0-7e01-b8c1-213dd2671c50_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
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    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
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    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
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    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_019e2363-9ecd-749b-82c5-4b99f31a8fd1_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_019e2363-9ecc-742d-bd21-6976bc2d1a7a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Receivable, Recorded Investment, Credit Quality Indicator [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10"/>
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    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities_019e2363-9f61-7776-8153-bebd54b77b34_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Other Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndOtherAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAndOtherAccruedLiabilities"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_019e2363-9f61-77dc-ace7-d5ee9bf27646_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class C Common Stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear5Through10"/>
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    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_019e2363-9f61-79d5-9d6c-08f8fa1b3fb2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
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    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_019e2363-9ff1-7c77-9ea9-0e3e2c212a76_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts offset in the Consolidated Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Liability Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetFairValueGrossLiability"/>
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    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_019e2363-9f61-7a01-8217-1570607cf761_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repurchase of Class C Common Stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_019e2363-9f61-7bec-8d7b-9c597fed9546_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase of Class C Common Stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased and Retired During Period, Shares</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfLoansHeldForInvestment_019e2363-9ecc-7fe3-a97e-dd37ca3f00bc_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of loans previously classified as held for investment</link:label>
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    <link:label id="lab_us-gaap_Investments_019e2363-9ecd-7c2e-b1f6-6b0293a623b0_totalLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Investment Securities</link:label>
    <link:label id="lab_us-gaap_Investments_label_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Investments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Investments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Investments" xlink:to="lab_us-gaap_Investments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassCMember_019e2363-9f61-7553-8b0f-3748c515ce10_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class C non-voting common stock</link:label>
    <link:label id="lab_us-gaap_CommonClassCMember_label_en-US" xlink:label="lab_us-gaap_CommonClassCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class C [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassCMember" xlink:to="lab_us-gaap_CommonClassCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_019e2363-9f61-7638-bc20-e6753fb3f480_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due within one year</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff_019e2363-9f61-79fe-ae6a-6292a9052b5e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Revolving, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestRevolvingWriteoff"/>
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    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_019e2363-9ecc-76c5-98f5-2480017fe398_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-Sale Securities</link:label>
    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Available-for-Sale, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:to="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_019e2363-9ecc-7cbc-a3b3-36fb3e426cd7_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019e2363-9ecc-7477-9b4f-980cd850cf58_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019e2363-9ecc-7c25-a511-caa3866a6be4_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
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    <link:label id="lab_agm_UnallocatedAssets_019e2363-9ecc-72a5-a369-18a4a1653e47_terseLabel_en-US" xlink:label="lab_agm_UnallocatedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unallocated assets</link:label>
    <link:label id="lab_agm_UnallocatedAssets_label_en-US" xlink:label="lab_agm_UnallocatedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unallocated Assets</link:label>
    <link:label id="lab_agm_UnallocatedAssets_documentation_en-US" xlink:label="lab_agm_UnallocatedAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unallocated Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnallocatedAssets" xlink:href="agm-20260630.xsd#agm_UnallocatedAssets"/>
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    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnAmt"/>
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    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust_019e2363-9ff0-7449-a7f7-0a553dc504e8_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for investment in consolidated trusts, at amortized cost</link:label>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust_label_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss, Held In Trust</link:label>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust_documentation_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss, Held In Trust</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:href="agm-20260630.xsd#agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust"/>
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    <link:label id="lab_agm_LongTermDebtHedgingAdjustments_label_en-US" xlink:label="lab_agm_LongTermDebtHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-term Debt, Hedging Adjustments</link:label>
    <link:label id="lab_agm_LongTermDebtHedgingAdjustments_documentation_en-US" xlink:label="lab_agm_LongTermDebtHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-term Debt, Hedging Adjustments</link:label>
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    <link:label id="lab_agm_ClearedDerivativesMember_019e2363-9ecc-739e-9f81-3cd203aa81fa_terseLabel_en-US" xlink:label="lab_agm_ClearedDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cleared derivatives</link:label>
    <link:label id="lab_agm_ClearedDerivativesMember_label_en-US" xlink:label="lab_agm_ClearedDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cleared Derivatives [Member]</link:label>
    <link:label id="lab_agm_ClearedDerivativesMember_documentation_en-US" xlink:label="lab_agm_ClearedDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cleared Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ClearedDerivativesMember" xlink:href="agm-20260630.xsd#agm_ClearedDerivativesMember"/>
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    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_019e2363-9f61-7384-9844-0bfd1b43d2ec_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CashFlowHedgingMember_019e2363-9f61-7f7a-a495-b5729c46f008_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flow hedges:</link:label>
    <link:label id="lab_us-gaap_CashFlowHedgingMember_label_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow Hedging [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowHedgingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashFlowHedgingMember"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_019e2363-9f61-715e-bc74-5c807e6fd594_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Three years</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_019e2363-9f61-7504-851c-16cb2075c140_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableModifiedWeightedAverageTermIncreaseFromModification_019f6a25-f1dd-7aa1-b887-25b494ca7700_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableModifiedWeightedAverageTermIncreaseFromModification" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Effect</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableModifiedWeightedAverageTermIncreaseFromModification_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableModifiedWeightedAverageTermIncreaseFromModification" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Modified, Weighted-Average Term Increase from Modification</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableModifiedWeightedAverageTermIncreaseFromModification" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableModifiedWeightedAverageTermIncreaseFromModification"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableModifiedWeightedAverageTermIncreaseFromModification" xlink:to="lab_us-gaap_FinancingReceivableModifiedWeightedAverageTermIncreaseFromModification" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019e2363-9f61-7b4b-a5f2-93409d1abe47_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember_019e2363-9ecc-753a-8dd9-2ca301fad366_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Three years</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPeriodThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019e2363-9f61-7bac-a401-33df3b781f37_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract_019e2363-9f61-7928-b6d3-1849b6cd3479_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year Five</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Four Years before Latest Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Four Years before Latest Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:href="agm-20260630.xsd#agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract_019e2363-9f61-7b79-a7ab-61aa85c1aac5_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision (Benefit)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossTaxAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_019e2363-9f61-7d58-94fb-bcef76a4e692_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Five, Originated, Four Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_019e2363-9f61-7f59-ab9c-102eb70be030_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives, at fair value</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_019e2363-9f61-7db4-a4c5-8557225a73d5_netLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Fair value, asset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_019e2363-9f61-7ac5-a6fb-ea28e01e9fd1_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_019e2363-9f61-73f1-ac14-d80e814713f5_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated Fair Value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_019e2363-9f61-7703-a5bd-b2309331ec08_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class C Common Stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockMember_019e2363-9ecc-7371-978a-89cf68d65c90_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockMember_label_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockMember" xlink:to="lab_us-gaap_PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019e2363-9f61-7075-aef0-ec30ec6ff6ce_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax_019e2363-9f61-7a3b-bcdd-3058db01b801_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized (losses)/gains on available-for-sale securities</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Gain (Loss), after Adjustment, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod_019e2363-9f61-7ad1-9ade-4ab702091982_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Modified in Period, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForLoanLeaseAndOtherLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:to="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
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    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months"/>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurements, Recurring and Nonrecurring [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock"/>
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    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
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    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_019e2363-9ecc-7c29-a28e-59c25a5ae89b_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Year Two Through Five, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Year Two Through Five, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield" xlink:href="agm-20260630.xsd#agm_AvailableForSaleSecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield"/>
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    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
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    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_019e2363-9f61-7ce8-90e3-c1c7a62cc2d1_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal"/>
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    <link:label id="lab_us-gaap_DerivativeLineItems_019e2363-9ecc-7773-b54f-808833872418_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLineItems"/>
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    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
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    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_019e2363-9f61-79a0-a52a-5113c3d13b76_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock dividends per common share (in dollars per share)</link:label>
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    <link:label id="lab_dei_EntityFileNumber_019e2363-9ecd-7e1c-a763-ec7b617ceda3_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
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    <link:label id="lab_agm_RuralInfrastructureFinanceRenewableEnergySegmentMember_019e2363-9f61-7139-be5e-f1345d228419_terseLabel_en-US" xlink:label="lab_agm_RuralInfrastructureFinanceRenewableEnergySegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Renewable Energy</link:label>
    <link:label id="lab_agm_RuralInfrastructureFinanceRenewableEnergySegmentMember_label_en-US" xlink:label="lab_agm_RuralInfrastructureFinanceRenewableEnergySegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rural Infrastructure Finance, Renewable Energy Segment [Member]</link:label>
    <link:label id="lab_agm_RuralInfrastructureFinanceRenewableEnergySegmentMember_documentation_en-US" xlink:label="lab_agm_RuralInfrastructureFinanceRenewableEnergySegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Infrastructure Finance, Renewable Energy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_RuralInfrastructureFinanceRenewableEnergySegmentMember" xlink:href="agm-20260630.xsd#agm_RuralInfrastructureFinanceRenewableEnergySegmentMember"/>
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    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_019e2363-9f61-788f-87de-cdb1fba6da1e_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-Sale Securities Maturities</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleMeasurementInput"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_019e2363-9f61-77dc-ba34-0538a7f0a7cc_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Consolidation of Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019e2363-9f61-7d7f-9664-6649da067139_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LiabilitiesHeldInTrust_019e2363-9f61-79c1-8a96-9fc792d777a1_terseLabel_en-US" xlink:label="lab_agm_LiabilitiesHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities of consolidated trusts held by third parties</link:label>
    <link:label id="lab_agm_LiabilitiesHeldInTrust_label_en-US" xlink:label="lab_agm_LiabilitiesHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities Held in Trust</link:label>
    <link:label id="lab_agm_LiabilitiesHeldInTrust_documentation_en-US" xlink:label="lab_agm_LiabilitiesHeldInTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liabilities Held in Trust</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LiabilitiesHeldInTrust" xlink:href="agm-20260630.xsd#agm_LiabilitiesHeldInTrust"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LiabilitiesHeldInTrust" xlink:to="lab_agm_LiabilitiesHeldInTrust" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassAMember_019e2363-9f61-7190-b325-5e2e37b6197e_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Class A voting common stock</link:label>
    <link:label id="lab_us-gaap_CommonClassAMember_label_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class A [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassAMember" xlink:to="lab_us-gaap_CommonClassAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019e2363-9f61-7a93-a113-576c5d73556f_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_019e2363-9ecc-70eb-b52d-1433e2404f81_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_019e2363-9f61-7e72-afa0-57a06f088199_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair&#160; Value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019e2363-9ecd-764f-a52f-c85723772c2a_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour_019e2363-9f61-7410-83da-14b12bef3e70_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, After Year Four</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:href="agm-20260630.xsd#agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019e2363-9ecc-703e-9c20-d0435efd9745_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12gTitle_019e2363-9ecd-73b6-989b-62ea9a9e90b1_terseLabel_en-US" xlink:label="lab_dei_Security12gTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(g) Security</link:label>
    <link:label id="lab_dei_Security12gTitle_label_en-US" xlink:label="lab_dei_Security12gTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(g) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12gTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12gTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12gTitle" xlink:to="lab_dei_Security12gTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeWeightedAverageForwardPrice_019e2363-9f61-7ff6-954f-aa4b81ccaf16_terseLabel_en-US" xlink:label="lab_agm_DerivativeWeightedAverageForwardPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted- Average Forward Price (in dollars per share)</link:label>
    <link:label id="lab_agm_DerivativeWeightedAverageForwardPrice_label_en-US" xlink:label="lab_agm_DerivativeWeightedAverageForwardPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Weighted-Average Forward Price</link:label>
    <link:label id="lab_agm_DerivativeWeightedAverageForwardPrice_documentation_en-US" xlink:label="lab_agm_DerivativeWeightedAverageForwardPrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative, Weighted-Average Forward Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeWeightedAverageForwardPrice" xlink:href="agm-20260630.xsd#agm_DerivativeWeightedAverageForwardPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeWeightedAverageForwardPrice" xlink:to="lab_agm_DerivativeWeightedAverageForwardPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_019e2363-9ecc-74c1-a043-c97c7271cfe5_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseNet" xlink:to="lab_us-gaap_InterestIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019e2363-9ecc-7f37-99d3-12ba28ad2862_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue_019e2363-9ff0-71e0-bb95-ce57351a549d_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_019e2363-9f61-7a96-bad2-1700873ca027_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest_019e2363-9ecc-795d-95cc-28cc745c379c_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Allowance for losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Allowance for Credit Loss, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_019e2363-9ecd-7a06-a25b-a46d4f8d2a40_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour_019e2363-9f61-7a42-ae03-a0ff90c432c8_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Four</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:href="agm-20260630.xsd#agm_LongTermDebtWithInterestRateResetMaturityYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InterestRateSwapReceiveFixedNonCallableMember_019e2363-9ff0-7d93-8c17-cecc1ed1b520_terseLabel_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receive fixed non-callable</link:label>
    <link:label id="lab_agm_InterestRateSwapReceiveFixedNonCallableMember_label_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Receive Fixed Non-Callable [Member]</link:label>
    <link:label id="lab_agm_InterestRateSwapReceiveFixedNonCallableMember_documentation_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Receive Fixed Non-Callable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:href="agm-20260630.xsd#agm_InterestRateSwapReceiveFixedNonCallableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:to="lab_agm_InterestRateSwapReceiveFixedNonCallableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_019e2363-9f61-7c9a-8ec0-166a577554c5_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019e2363-9f61-7c73-a0eb-8b90abe9be2f_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuarantyLiabilities_019e2363-9f61-7c3a-920e-29eb6d6d1984_terseLabel_en-US" xlink:label="lab_us-gaap_GuarantyLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantee and commitment obligation</link:label>
    <link:label id="lab_us-gaap_GuarantyLiabilities_label_en-US" xlink:label="lab_us-gaap_GuarantyLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guaranty Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuarantyLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GuarantyLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuarantyLiabilities" xlink:to="lab_us-gaap_GuarantyLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent_019e2363-9ecc-7e86-8851-03beac2e5ec1_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive loss before tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgedStatusDomain_019e2363-9f61-7830-aaa7-40fb73c532f2_terseLabel_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:label id="lab_us-gaap_PledgedStatusDomain_label_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PledgedStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgedStatusDomain" xlink:to="lab_us-gaap_PledgedStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019e2363-9f61-7cea-ba4b-06b202dbad05_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019e2363-9f61-7e7c-81de-4fd0eb572ab7_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies (Note 5)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShorttermDebtAverageOutstandingAmount_019e2363-9f61-7bc5-8d64-92ea1060c447_terseLabel_en-US" xlink:label="lab_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average Outstanding, Amount</link:label>
    <link:label id="lab_us-gaap_ShorttermDebtAverageOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Average Outstanding Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShorttermDebtAverageOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:to="lab_us-gaap_ShorttermDebtAverageOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_019e2363-9ecc-7074-8dbb-69587af30bbd_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentRedemptionPeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_019e2363-9ecc-7cab-b50a-9c066b3ff254_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxContingencyTable_019e2363-9f61-7400-ac25-b41b026435df_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxContingencyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Contingency [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxContingencyTable_label_en-US" xlink:label="lab_us-gaap_IncomeTaxContingencyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Contingency [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxContingencyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxContingencyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxContingencyTable" xlink:to="lab_us-gaap_IncomeTaxContingencyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax_019e2363-9f61-7ef9-8bd4-45e960d6f04d_terseLabel_en-US" xlink:label="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net changes in held-to-maturity securities</link:label>
    <link:label id="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax_label_en-US" xlink:label="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Held-To-Maturity Securities, Before Tax</link:label>
    <link:label id="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax_documentation_en-US" xlink:label="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Held-To-Maturity Securities, Before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:href="agm-20260630.xsd#agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:to="lab_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_019e2363-9ecc-75e5-91d0-a70036b7aa03_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and Equity:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OtherAssetMeasurementInput_019e2363-9ff0-7e66-9628-3ea0bf50df56_terseLabel_en-US" xlink:label="lab_agm_OtherAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other asset, measurement input</link:label>
    <link:label id="lab_agm_OtherAssetMeasurementInput_label_en-US" xlink:label="lab_agm_OtherAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Asset, Measurement Input</link:label>
    <link:label id="lab_agm_OtherAssetMeasurementInput_documentation_en-US" xlink:label="lab_agm_OtherAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Asset, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OtherAssetMeasurementInput" xlink:href="agm-20260630.xsd#agm_OtherAssetMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OtherAssetMeasurementInput" xlink:to="lab_agm_OtherAssetMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_019e2363-9ecc-7b6d-843e-3842856b4486_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_019e2363-9f61-7765-9175-44a30c8b2b46_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net effects of cash flow hedges</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
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    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_019e2363-9f61-7b68-bff3-b404734cfd7e_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flow Hedges</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:to="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract_019e2363-9ff0-7342-84ff-2f52f5050a8e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial liabilities:</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Financial Liabilities, Balance Sheet Groupings [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:to="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingOtherItemAmount_019e2363-9ecc-787f-83f1-e45d63374524_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unallocated (expenses)/income</link:label>
    <link:label id="lab_us-gaap_SegmentReportingOtherItemAmount_label_en-US" xlink:label="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Other Segment Item, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingOtherItemAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingOtherItemAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingOtherItemAmount" xlink:to="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019e2363-9f61-7fe2-a67a-3f5cb9f50f5f_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_019e2363-9ecc-7d90-856e-de84d0b0d92f_terseLabel_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Past Due Financing Receivables</link:label>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PastDueFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_019e2363-9f61-74a5-a9fb-4c4f4f13efda_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities and cash equivalents</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Securities, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestAndDividendIncomeSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:to="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_019e2363-9f61-768c-9cd4-1d83863d2b19_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current</link:label>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Not Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialAssetNotPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:to="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_019e2363-9f61-74be-b478-be104fa1c2e5_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized (losses)/gains on cash flow hedges</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_019e2363-9ecd-720d-886e-dfaccc6f1e95_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:to="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear_019e2363-9ecd-7a15-b667-320dc0657b06_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Reminder Of The Fiscal Year</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Reminder Of The Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:href="agm-20260630.xsd#agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear"/>
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    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_019e2363-9f61-72fb-9fbf-ea0e48c51016_negatedLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends, Income Statement Impact</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockDividendsIncomeStatementImpact"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:to="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty_019e2363-9ecc-7c1c-aab4-71a280595a8f_terseLabel_en-US" xlink:label="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, additional net exposure from counterparty</link:label>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty_label_en-US" xlink:label="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Collateral Exceeding Derivative Position, Additional Net Exposure From Counterparty</link:label>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty_documentation_en-US" xlink:label="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative, Collateral Exceeding Derivative Position, Additional Net Exposure From Counterparty</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty" xlink:href="agm-20260630.xsd#agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty"/>
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    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019e2363-9ecc-7233-b42a-3f702fabeccf_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
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    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableRevolvingAbstract_019e2363-9ff1-7527-8c2e-f5152c6a24c8_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Loans - Amortized Cost Basis</link:label>
    <link:label id="lab_agm_FinancingReceivableRevolvingAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Revolving [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableRevolvingAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableRevolvingAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Revolving</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableRevolvingAbstract" xlink:href="agm-20260630.xsd#agm_FinancingReceivableRevolvingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableRevolvingAbstract" xlink:to="lab_agm_FinancingReceivableRevolvingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019e2363-9f61-7786-b359-b8d83e8036ee_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_019e2363-9ecd-7d8c-b737-62d60727c5d8_verboseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019e2363-9f61-70e4-80fb-99997566dee7_terseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation and employee benefits</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_label_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor and Related Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LaborAndRelatedExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LaborAndRelatedExpense" xlink:to="lab_us-gaap_LaborAndRelatedExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_IncomeTaxEffectRelatedToReconcilingItems_019e2363-9f61-780b-870a-83eab473b970_terseLabel_en-US" xlink:label="lab_agm_IncomeTaxEffectRelatedToReconcilingItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax effect related to reconciling items</link:label>
    <link:label id="lab_agm_IncomeTaxEffectRelatedToReconcilingItems_label_en-US" xlink:label="lab_agm_IncomeTaxEffectRelatedToReconcilingItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Effect Related To Reconciling Items</link:label>
    <link:label id="lab_agm_IncomeTaxEffectRelatedToReconcilingItems_documentation_en-US" xlink:label="lab_agm_IncomeTaxEffectRelatedToReconcilingItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Tax Effect Related To Reconciling Items</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_IncomeTaxEffectRelatedToReconcilingItems" xlink:href="agm-20260630.xsd#agm_IncomeTaxEffectRelatedToReconcilingItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_IncomeTaxEffectRelatedToReconcilingItems" xlink:to="lab_agm_IncomeTaxEffectRelatedToReconcilingItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019e2363-9f61-7d89-a617-e7aa90b973b2_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic earnings per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019e2363-9f61-7f04-ac6e-4be16717a724_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common stockholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_019e2363-9ecc-7a87-9bb6-f814f71f0834_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtMaturityAfterYearFour_019e2363-9ecd-7ca5-bd6a-4c9ea418c859_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_agm_LongTermDebtMaturityAfterYearFour_label_en-US" xlink:label="lab_agm_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Four</link:label>
    <link:label id="lab_agm_LongTermDebtMaturityAfterYearFour_documentation_en-US" xlink:label="lab_agm_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtMaturityAfterYearFour" xlink:href="agm-20260630.xsd#agm_LongTermDebtMaturityAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtMaturityAfterYearFour" xlink:to="lab_agm_LongTermDebtMaturityAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OtherNonInterestIncomeExpenseAdjusted_019e2363-9f61-7e0b-a1d5-f746fa0ca8ba_terseLabel_en-US" xlink:label="lab_agm_OtherNonInterestIncomeExpenseAdjusted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income/(expense)</link:label>
    <link:label id="lab_agm_OtherNonInterestIncomeExpenseAdjusted_label_en-US" xlink:label="lab_agm_OtherNonInterestIncomeExpenseAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Non-Interest Income (Expense), Adjusted</link:label>
    <link:label id="lab_agm_OtherNonInterestIncomeExpenseAdjusted_documentation_en-US" xlink:label="lab_agm_OtherNonInterestIncomeExpenseAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Non-Interest Income (Expense), Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_OtherNonInterestIncomeExpenseAdjusted" xlink:href="agm-20260630.xsd#agm_OtherNonInterestIncomeExpenseAdjusted"/>
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    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_019e2363-9f61-7a6f-9986-dce367e4041f_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total due after one year</link:label>
    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Excluding Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtNoncurrent" xlink:to="lab_us-gaap_LongTermDebtNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease_019e2373-f390-727e-99e8-f19005863582_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cumulative amount of fair value hedging adjustments, hedged liabilities</link:label>
    <link:label id="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Liability, Fair Value Hedge, Cumulative Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease"/>
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    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield_019e2363-9f61-7248-9700-6f272579c0e5_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total, weighted-average yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:href="agm-20260630.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:to="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
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    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_019e2363-9ecc-788d-90f2-a2a5bd8dce38_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Recovery</link:label>
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    <link:label id="lab_us-gaap_ExcessCapital_019e2363-9ecc-7345-aa23-942eaa4688ec_terseLabel_en-US" xlink:label="lab_us-gaap_ExcessCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess capital</link:label>
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    <link:label id="lab_us-gaap_HedgingRelationshipDomain_019e2363-9ecc-70de-8303-a7b9f5ed070e_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_label_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
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    <link:label id="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease_019e2363-9f61-73fb-b6db-d0299780afbc_terseLabel_en-US" xlink:label="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cumulative amount of fair value hedging adjustments, hedged assets</link:label>
    <link:label id="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Asset, Fair Value Hedge, Cumulative Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:to="lab_us-gaap_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_019e2363-9f61-7f4f-8b00-ab774f62fe43_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity:</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_019e2363-9f61-73e2-92ff-fa6a3ffa47ad_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtNetOfHedgingAdjustments_019e2363-9ecc-7f1b-a25f-dd379f99cf48_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes payable</link:label>
    <link:label id="lab_agm_LongTermDebtNetOfHedgingAdjustments_019e2363-9ecc-7ec4-8a5f-7f7d43752b0c_totalLabel_en-US" xlink:label="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_agm_LongTermDebtNetOfHedgingAdjustments_label_en-US" xlink:label="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-term Debt, Net of Hedging Adjustments</link:label>
    <link:label id="lab_agm_LongTermDebtNetOfHedgingAdjustments_documentation_en-US" xlink:label="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-term Debt, Net of Hedging Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtNetOfHedgingAdjustments" xlink:href="agm-20260630.xsd#agm_LongTermDebtNetOfHedgingAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtNetOfHedgingAdjustments" xlink:to="lab_agm_LongTermDebtNetOfHedgingAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable_019e2363-9f61-7cd1-9392-f145a7f50b99_terseLabel_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Table]</link:label>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable_label_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Table]</link:label>
    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable_documentation_en-US" xlink:label="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale and Trading Securities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:href="agm-20260630.xsd#agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:to="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_019e2363-9ecc-787d-b8fc-c37b52d27ca0_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationAdditionalInformationAbstract_019e2363-9ecc-7386-9e88-000ace3647a8_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationAdditionalInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation to net income:</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationAdditionalInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationAdditionalInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Other Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationAdditionalInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingInformationAdditionalInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationAdditionalInformationAbstract" xlink:to="lab_us-gaap_SegmentReportingInformationAdditionalInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_019e2363-9f61-730d-9e9b-72d12c8e8c3c_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgingDesignationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationDomain" xlink:to="lab_us-gaap_HedgingDesignationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_019e2363-9f61-7988-a70f-67916003999a_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_019e2363-9f61-77ea-abf7-77645cf7408f_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember_019e2363-9f61-7809-9dc5-245d0209555d_terseLabel_en-US" xlink:label="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate AgFinance</link:label>
    <link:label id="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember_019e2363-9f61-7721-9687-f0405febad50_verboseLabel_en-US" xlink:label="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Corporate AgFinance</link:label>
    <link:label id="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember_019e2363-9f61-7a79-a0f1-c1e9a98d08b9_netLabel_en-US" xlink:label="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Agricultural Finance - Corporate AgFinance loans</link:label>
    <link:label id="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember_label_en-US" xlink:label="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agriculture Finance, Corporate AgFinance Segment [Member]</link:label>
    <link:label id="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember_documentation_en-US" xlink:label="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agriculture Finance, Corporate AgFinance Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:href="agm-20260630.xsd#agm_AgricultureFinanceCorporateAgFinanceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:to="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsMember_019e2363-9ecd-7069-9690-491dfd31060e_terseLabel_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Standby Purchase Commitments</link:label>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsMember_label_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Standby Purchase Commitments [Member]</link:label>
    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsMember_documentation_en-US" xlink:label="lab_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Standby Purchase Commitments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:href="agm-20260630.xsd#agm_LongTermStandbyPurchaseCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:to="lab_agm_LongTermStandbyPurchaseCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_019e2363-9ecc-718b-8044-461d464972fb_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">INCOME TAXES</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_019e2363-9ecc-7be8-9491-272a02d517c4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_019e2363-9f61-7f92-a7b3-c4860b9c54cb_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Income/(Expense) Recognized</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivatives Instruments Statements of Financial Performance and Financial Position, Location [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell_019e2363-9ecc-74de-9ea0-f74360b02f02_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives, net payable position</link:label>
    <link:label id="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell_label_en-US" xlink:label="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Purchased under Agreements to Resell</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesPurchasedUnderAgreementsToResell"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:to="lab_us-gaap_SecuritiesPurchasedUnderAgreementsToResell" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019e2363-9f61-7769-ae7a-1c23db324e42_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities_019e2363-9ecc-7e60-b501-9438e0fadfce_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of debt securities of consolidated trusts</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Trust Preferred Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfTrustPreferredSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_019e2363-9ecc-7698-a561-fe7aa538959b_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Offsetting Liabilities</link:label>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod_019e2363-9ecc-7590-aa64-6a40018c0f4a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average Outstanding, Weighted - average rate (as a percent)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:to="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_019e2363-9ecc-7855-94ea-15afa58c2416_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gains/(losses) on financial derivatives</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_019e2363-9ecc-77d7-9e63-143a6fc2c5de_netLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Gains/(losses) on financial derivatives</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments, Net, Pretax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnDerivativeInstrumentsNetPretax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_019e2363-9ecc-72b8-8f19-587fdb537004_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesPeriodPastDueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NondesignatedMember_019e2363-9f61-7d8a-8ec2-8b60ae835e5c_verboseLabel_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">No hedge designation</link:label>
    <link:label id="lab_us-gaap_NondesignatedMember_label_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Not Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NondesignatedMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NondesignatedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NondesignatedMember" xlink:to="lab_us-gaap_NondesignatedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract_019e2363-9f61-7e34-bc75-628925215233_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year Four</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Three Years before Latest Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Three Years before Latest Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:href="agm-20260630.xsd#agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:to="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_019e2363-9ecd-7912-bea1-f400a3a17730_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:to="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_SegmentCoreEarnings_019e2363-9ecc-7112-bf39-277cac216556_totalLabel_en-US" xlink:label="lab_agm_SegmentCoreEarnings" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Segment core earnings</link:label>
    <link:label id="lab_agm_SegmentCoreEarnings_label_en-US" xlink:label="lab_agm_SegmentCoreEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Core Earnings</link:label>
    <link:label id="lab_agm_SegmentCoreEarnings_documentation_en-US" xlink:label="lab_agm_SegmentCoreEarnings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Segment core earnings - net income (loss) available to common shareholders, basic, adjusted for reconciling items related to segment reporting</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_SegmentCoreEarnings" xlink:href="agm-20260630.xsd#agm_SegmentCoreEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_SegmentCoreEarnings" xlink:to="lab_agm_SegmentCoreEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne_019e2363-9ecc-750b-8e53-a5db99bc6605_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne_label_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year One</link:label>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne_documentation_en-US" xlink:label="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt With Interest Rate Reset, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:href="agm-20260630.xsd#agm_LongTermDebtWithInterestRateResetMaturityYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_019e2363-9ecc-7ca7-96f4-9e6aacdf56fd_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_019e2363-9f61-75bf-a0f1-ba3bb941fb6d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherLoansAndLeasesHeldForInvestment_019e2363-9ecc-79d6-863b-fd9686a0c931_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherLoansAndLeasesHeldForInvestment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of defaulted loans</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherLoansAndLeasesHeldForInvestment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherLoansAndLeasesHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Acquisition, Loan and Lease, Other, Held-for-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireOtherLoansAndLeasesHeldForInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireOtherLoansAndLeasesHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireOtherLoansAndLeasesHeldForInvestment" xlink:to="lab_us-gaap_PaymentsToAcquireOtherLoansAndLeasesHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield_019e2363-9ecc-7ae0-8175-2529b83eeb29_terseLabel_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield_label_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Available-for-sale Securities, Debt Maturities, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:href="agm-20260630.xsd#agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:to="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InterestRateSwapPayFixedNonCallableMember_019e2363-9f61-7c0b-bce0-5e92c331537e_terseLabel_en-US" xlink:label="lab_agm_InterestRateSwapPayFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay fixed non-callable</link:label>
    <link:label id="lab_agm_InterestRateSwapPayFixedNonCallableMember_label_en-US" xlink:label="lab_agm_InterestRateSwapPayFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Pay Fixed Non-Callable [Member]</link:label>
    <link:label id="lab_agm_InterestRateSwapPayFixedNonCallableMember_documentation_en-US" xlink:label="lab_agm_InterestRateSwapPayFixedNonCallableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Pay Fixed Non-Callable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InterestRateSwapPayFixedNonCallableMember" xlink:href="agm-20260630.xsd#agm_InterestRateSwapPayFixedNonCallableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InterestRateSwapPayFixedNonCallableMember" xlink:to="lab_agm_InterestRateSwapPayFixedNonCallableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019e2363-9f61-73b0-96a7-d40619e24449_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives, at fair value</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019e2363-9f61-77ea-a5a1-6daa57312c52_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Fair value, liability</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019e2363-9f61-734d-847e-83c361883db4_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquired_019e2363-9ff0-7c9b-b8e7-f0d4e2ab11d1_terseLabel_en-US" xlink:label="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans acquired through non-cash transactions</link:label>
    <link:label id="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquired_label_en-US" xlink:label="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Or Part Noncash Acquisition, Loans Acquired</link:label>
    <link:label id="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquired_documentation_en-US" xlink:label="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquired" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncash Or Part Noncash Acquisition, Loans Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_NoncashOrPartNoncashAcquisitionLoansAcquired" xlink:href="agm-20260630.xsd#agm_NoncashOrPartNoncashAcquisitionLoansAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_NoncashOrPartNoncashAcquisitionLoansAcquired" xlink:to="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019e2363-9ecc-76aa-a4a4-034aba3fe3ec_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract_019e2363-9f61-7c00-b374-ea3a52315998_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Maturity, Allocated and Single Maturity Date, Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019e2363-9ecc-78ba-b139-3356cf93e2ba_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesHPreferredStockMember_019e2363-9f61-77a9-9a5d-8faf1c545c37_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesHPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">6.500% Non-Cumulative Preferred Stock, Series H</link:label>
    <link:label id="lab_us-gaap_SeriesHPreferredStockMember_019e2363-9f61-7c29-bcd9-a2c1f6b3aa6b_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesHPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Series H</link:label>
    <link:label id="lab_us-gaap_SeriesHPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesHPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series H Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesHPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeriesHPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesHPreferredStockMember" xlink:to="lab_us-gaap_SeriesHPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueHedgingMember_019e2363-9f61-7acb-9360-72691039d161_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value hedges:</link:label>
    <link:label id="lab_us-gaap_FairValueHedgingMember_label_en-US" xlink:label="lab_us-gaap_FairValueHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hedging [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueHedgingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueHedgingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueHedgingMember" xlink:to="lab_us-gaap_FairValueHedgingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnclearedSwapsMember_019e2363-9ff0-7ad0-8d6b-8e5af31f13bd_terseLabel_en-US" xlink:label="lab_agm_UnclearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Uncleared Swaps</link:label>
    <link:label id="lab_agm_UnclearedSwapsMember_label_en-US" xlink:label="lab_agm_UnclearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Uncleared Swaps [Member]</link:label>
    <link:label id="lab_agm_UnclearedSwapsMember_documentation_en-US" xlink:label="lab_agm_UnclearedSwapsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Uncleared Swaps</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_UnclearedSwapsMember" xlink:href="agm-20260630.xsd#agm_UnclearedSwapsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnclearedSwapsMember" xlink:to="lab_agm_UnclearedSwapsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_019e2363-9ff0-740f-9414-e54a39a129ba_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomePolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:to="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueYearOneMember_019e2363-9ecc-7414-a87b-999c67285e04_terseLabel_en-US" xlink:label="lab_agm_DueYearOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year one</link:label>
    <link:label id="lab_agm_DueYearOneMember_label_en-US" xlink:label="lab_agm_DueYearOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due Year One [Member]</link:label>
    <link:label id="lab_agm_DueYearOneMember_documentation_en-US" xlink:label="lab_agm_DueYearOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Due Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DueYearOneMember" xlink:href="agm-20260630.xsd#agm_DueYearOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DueYearOneMember" xlink:to="lab_agm_DueYearOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019e2363-9f61-7ef6-8f00-6d65b0fc28ca_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff_019e2363-9f61-711d-a959-0bf158ecaa16_negatedLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff_019e2363-9f61-7b99-bac7-ee51fbfbeac3_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract_019e2363-9f61-7224-8240-81b924e95a92_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Derivative Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingDerivativeLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:to="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_019e2363-9f61-7a42-b5e6-17d6e3c642f5_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated VIE</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_019e2363-9ff0-7783-8875-64076c7d0d18_terseLabel_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_label_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AOCIAttributableToParentNetOfTaxRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:to="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoanRestructuringModificationDomain_019f6a25-f1dd-750f-a469-1833ca769c24_terseLabel_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:label id="lab_us-gaap_LoanRestructuringModificationDomain_label_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoanRestructuringModificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoanRestructuringModificationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoanRestructuringModificationDomain" xlink:to="lab_us-gaap_LoanRestructuringModificationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_019e2363-9f61-7a75-8081-d290d7532560_terseLabel_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, After Ten Years, Weighted-Average Yield</link:label>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_documentation_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, After Ten Years, Weighted-Average Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:href="agm-20260630.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:to="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_019e2363-9ecd-7064-aed8-07fea9d0f781_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted cash flow</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:to="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019e2363-9f61-7d4c-8727-8ddb031c1d0a_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
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