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    <link:label id="lab_agm_InterestRateSwapReceiveFixedCallableMember_label_en-US" xlink:label="lab_agm_InterestRateSwapReceiveFixedCallableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swap, Receive Fixed Callable [Member]</link:label>
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    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesMember_019caf6e-900c-7b34-99b4-c2136d0c8714_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_019caf6e-900c-76dd-8219-9a2f063b7e11_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
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    <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/2025/ecd-2025.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_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>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract_019caf6e-908a-79c0-83f9-cac2f02e4cf7_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" 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_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAbstract"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery_019caf6e-900c-74ce-90ff-0b3a3aa08b02_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recovery</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery"/>
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    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_019caf6e-9089-7213-a6a4-35ff5669133f_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/2025/elts/us-gaap-2025.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_FinancingReceivableBeforeAllowanceForCreditLossAbstract_019caf6e-8f6f-7085-a6f0-1e6b6d3c3acc_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/2025/elts/us-gaap-2025.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_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive_019caf6e-900c-7d44-bf6f-87ad6fe2b1ae_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive" 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_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive" 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, after Year One through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughFive"/>
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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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAmt"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_019caf6e-900c-7496-92b8-47bc3973a92c_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
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    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019caf6e-9089-718b-9678-7c2708888da0_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/2025/elts/us-gaap-2025.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_ShareBasedCompensation_019caf6e-900c-71ee-a6ac-2281b04285aa_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/2025/elts/us-gaap-2025.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_DerivativeAssetNotionalAmount_019caf6e-9089-7bd8-b077-d040fedb20a9_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Notional amount</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetNotionalAmount_019caf6e-9089-7fcd-bdf1-549c51afc016_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional Amount</link:label>
    <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/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetNotionalAmount"/>
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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/2025/elts/us-gaap-2025.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_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_019caf6e-9089-7fb2-963e-6b43b005964e_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
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    <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/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsCommonStockCash"/>
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    <link:label id="lab_us-gaap_StockholdersEquity_019caf6e-9089-7613-a895-36149414248d_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_019caf6e-9089-7f0b-8fbd-652676c3da05_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_019caf6e-9089-71d7-ab21-c58ab4a0ff08_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>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_019caf6e-900c-7dc9-a00f-ed7652715986_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/2025/elts/us-gaap-2025.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_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_019caf6e-908a-7d7c-a95f-59c97751727c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">After Tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" 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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <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"/>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_019caf6e-900c-7eb3-bc8e-d8e1b269be3e_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/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:to="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_019caf6e-900d-7b49-987d-0a23eeedc421_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/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_019caf6e-9089-7532-8fc5-ad3de838db0a_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/2025/elts/us-gaap-2025.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_us-gaap_MediumTermNotesMember_019caf6e-900c-7227-95f1-bd992b9b5c5f_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/2025/elts/us-gaap-2025.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_dei_CoverAbstract_019caf6e-9089-74ad-b60f-ff384218aff5_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover page.</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_019caf6e-90f8-71c7-9fe6-2d242755b145_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:to="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_019caf6e-900c-7711-b4ee-58dccbcb9778_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <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/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019caf6e-90f8-734a-8ce5-043dd2a58b3a_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_019caf6e-900c-7409-a948-576a1003b817_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost"/>
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    <link:label id="lab_us-gaap_IncomeTaxContingencyLineItems_019caf6e-9089-7b73-9e5c-edab4988b77d_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/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxContingencyLineItems"/>
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    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <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/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019caf6e-900c-7861-9b60-d157677cdbbf_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/2025/elts/us-gaap-2025.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_HedgedItemsinFairValueHedgingRelationshipTable_019caf6e-9089-7eb4-93b1-1be232961837_terseLabel_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">HedgedItemsinFairValueHedgingRelationship [Table]</link:label>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable_label_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">HedgedItemsinFairValueHedgingRelationship [Table]</link:label>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable_documentation_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hedged Items in Fair Value Hedging Relationship [Table]</link:label>
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    <link:label id="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount_019caf6e-900c-7f74-966e-6d01efd67992_terseLabel_en-US" xlink:label="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum amount of discount notes outstanding at any month end</link:label>
    <link:label id="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_ShorttermDebtMaximumMonthendOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Maximum Month-end Outstanding Amount</link:label>
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    <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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable"/>
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    <link:label id="lab_us-gaap_OtherAssetsMember_019caf6e-8f6f-71aa-986f-e1e4ea903fa1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsMember" xlink:to="lab_us-gaap_OtherAssetsMember" xlink:type="arc" order="1"/>
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    <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>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019caf6e-9089-7e70-af74-380aa33773f4_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>
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    <link:label id="lab_dei_EntityShellCompany_019caf6e-908a-73de-8692-d0c90b9b34b0_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>
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    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilities_019caf6e-900c-777e-9e7f-11493df64ede_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/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableAndOtherAccruedLiabilities"/>
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    <link:label id="lab_us-gaap_DebtInstrumentTable_019caf6e-9089-736d-8665-b67a17d444d9_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/2025/elts/us-gaap-2025.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_StatementOfStockholdersEquityAbstract_019caf6e-908a-79c6-a946-fe30194e4857_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>
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    <link:label id="lab_us-gaap_OperatingSegmentsMember_019caf6e-900c-7ac4-b947-4aa134a07e3b_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/2025/elts/us-gaap-2025.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"/>
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    <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/2025/ecd-2025.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_FinancingReceivableExcludingAccruedInterestNonaccrual_019caf6e-900c-796c-863f-8ba7cd35b942_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/2025/elts/us-gaap-2025.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_agm_VariableInterestEntityConsolidatedFairValueDisclosureLiabilities_019caf6e-900c-7d9d-a7b5-e80ce756772d_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-20260331.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_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss_019caf6e-900c-71e5-9c1b-ab8c81770b6a_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">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/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <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/2025/elts/us-gaap-2025.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_us-gaap_HedgingRelationshipDomain_019caf6e-900c-742f-866b-85c82383d8f7_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingRelationshipDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingRelationshipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingRelationshipDomain" xlink:to="lab_us-gaap_HedgingRelationshipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019caf6e-9089-7127-9d74-b7978f653ac3_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/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019caf6e-900d-79af-aa52-f5366d22b0ec_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>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_019caf6e-900c-799f-9a23-e20bce1fd0eb_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-20260331.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_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_019caf6e-900c-76a0-8bc1-bd107c9c6f07_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueWithinOneYearMember_019caf6e-908a-7608-bdf3-afe0ea2b932c_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-20260331.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_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/2025/ecd-2025.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_IncomeStatementLocationDomain_019caf6e-900d-789b-8d3d-c92668629897_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement Location [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationDomain" xlink:to="lab_us-gaap_IncomeStatementLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019caf6e-900c-73fd-a74b-30adeab98b72_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/2025/dei-2025.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_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_019caf6e-900c-796f-8a40-c2a0bf092caa_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_019caf6e-900c-7228-ab37-53b4ebc44855_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>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_DerivativeCollateralRightToReclaimCash_019caf6e-908a-7f1b-a0fd-e4a4e73b2b8f_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/2025/elts/us-gaap-2025.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_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>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueYearFourMember_019caf6e-90f8-7044-9e83-d564ac710a33_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-20260331.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_NoninterestIncome_019caf6e-900c-73ca-b18b-0d6735f8b628_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/2025/elts/us-gaap-2025.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_us-gaap_CommonClassCMember_019caf6e-900d-761b-beca-cb39544f875a_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassCMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonClassCMember"/>
    <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_CommonStockSharesOutstanding_019caf6e-9089-7be1-98fc-2734c6d73562_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecuritiesTextBlock_019caf6e-900c-7261-b470-d1d4e0588f4d_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/2025/elts/us-gaap-2025.xsd#us-gaap_MarketableSecuritiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecuritiesTextBlock" xlink:to="lab_us-gaap_MarketableSecuritiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss_019caf6e-90f8-7ae0-8b2b-781373e1d036_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/2025/elts/us-gaap-2025.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_OtherAssetsFairValueDisclosure_019caf6e-8f6f-72fd-bc3d-d67d05b6bc60_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsFairValueDisclosure" xlink:to="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestExpenseAbstract_019caf6e-900c-75c8-a73b-37637dc139ad_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses:</link:label>
    <link:label id="lab_us-gaap_NoninterestExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestExpenseAbstract" xlink:to="lab_us-gaap_NoninterestExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_019caf6e-908a-7840-b197-0d47ee95ee18_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:type="arc" order="1"/>
    <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>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue_019caf6e-9089-7d83-ae51-b65d06d8c11e_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/2025/elts/us-gaap-2025.xsd#us-gaap_GuaranteeObligationsCurrentCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:to="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_019caf6e-9089-77ec-a416-0e7d177b0e90_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_019caf6e-900c-784c-925e-462bda06d70c_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/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MaturitiesOfLongTermDebtAbstract_019caf6e-9089-71aa-ab16-50b6ef7d8b8a_terseLabel_en-US" xlink:label="lab_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Medium-term notes due in:</link:label>
    <link:label id="lab_us-gaap_MaturitiesOfLongTermDebtAbstract_label_en-US" xlink:label="lab_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maturities of Long-Term Debt [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MaturitiesOfLongTermDebtAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:to="lab_us-gaap_MaturitiesOfLongTermDebtAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgedStatusDomain_019caf6e-900c-7938-b90d-d01c82bb2773_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/2025/elts/us-gaap-2025.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_dei_EntityAddressPostalZipCode_019caf6e-900c-7530-908a-8d399ce1a10f_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/2025/dei-2025.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_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/2025/ecd-2025.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_019caf6e-9089-7c55-a6ac-b52ef95a6fa0_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_019caf6e-9089-70ba-8cd5-7cde26252137_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest Income Investments 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/2025/elts/us-gaap-2025.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_IncomeTaxExpenseBenefit_019caf6e-9089-7028-b9e8-9dd0269d96e1_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/2025/elts/us-gaap-2025.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_CommonClassBMember_019caf6e-900d-7fff-be51-e525fc1bd636_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/2025/elts/us-gaap-2025.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_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019caf6e-908a-7b38-84eb-8c89dc71cc23_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_019caf6e-908a-7e15-8b29-a4e64086826d_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/2025/elts/us-gaap-2025.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_us-gaap_PreferredStockSharesIssued_019caf6e-8f6f-70fe-8566-e03ee40ca47f_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_019caf6e-900d-7107-ae7e-15158ecc1648_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DesignatedAsHedgingInstrumentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:to="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_UnsecuritizedMember_019caf6e-900c-7f63-8e15-f55f28f05bc8_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-20260331.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_FairValueByFairValueHierarchyLevelAxis_019caf6e-900c-7f97-ab94-f29eebfc430c_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_019caf6e-900c-7141-8930-c815977f3514_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue_019caf6e-900c-74da-9190-59fa56e7d2a5_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/2025/elts/us-gaap-2025.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_agm_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_019caf6e-900c-70f3-9e56-49f90b9b5bfa_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_019caf6e-900c-752e-8bb4-4e6b2cbd0f6b_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-20260331.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_us-gaap_ScheduleOfGuaranteeObligationsTable_019caf6e-9089-746f-a88e-35161d9b8bc9_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/2025/elts/us-gaap-2025.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_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueAfterYearFourMember_019caf6e-900c-7015-ad6b-5252b5b5b5c2_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-20260331.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_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <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/2025/ecd-2025.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"/>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" 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/2025/ecd-2025.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_PreferredStockDividendsIncomeStatementImpact_019caf6e-900c-7d78-a0df-19519f4b9a87_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/2025/elts/us-gaap-2025.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_us-gaap_NoninterestIncomeOtherOperatingIncome_019caf6e-900c-7bbd-acd0-a6db7083ca00_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/2025/elts/us-gaap-2025.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_CommitmentsAndContingenciesDisclosureAbstract_019caf6e-900c-7ab8-a74b-782a3335f67c_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <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/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems_019caf6e-900c-7f16-946c-906ec78faafb_terseLabel_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">HedgedItemsinFairValueHedgingRelationship [Line Items]</link:label>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems_label_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">HedgedItemsinFairValueHedgingRelationship [Line Items]</link:label>
    <link:label id="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems_documentation_en-US" xlink:label="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for HedgedItemsinFairValueHedgingRelationship [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:href="agm-20260331.xsd#agm_HedgedItemsinFairValueHedgingRelationshipLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:to="lab_agm_HedgedItemsinFairValueHedgingRelationshipLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019caf6e-900c-703d-970d-986dcd0ee50d_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/2025/elts/us-gaap-2025.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_DebtInstrumentTerm_019caf6e-9089-70ad-8779-aa0d2c898fd4_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/2025/elts/us-gaap-2025.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_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019caf6e-9089-780f-8bbc-a3e2cbf75bf3_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 $14,269,843 and $13,813,551, respectively)</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019caf6e-9089-7f82-af6e-06be060611e2_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_019caf6e-9089-742d-9ff1-60c334d454a8_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/2025/elts/us-gaap-2025.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_us-gaap_ProceedsFromSaleOfOtherRealEstate_019caf6e-900c-772d-9617-831f72dd2f91_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of real estate owned</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Other Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:to="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_019caf6e-900c-7e1c-b387-2ecb2e8de34c_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_019caf6e-9089-727b-b47c-597506f47ad1_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_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/2025/ecd-2025.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_LongtermDebtTypeAxis_019caf6e-908a-79a6-a34c-35876120579a_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/2025/elts/us-gaap-2025.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_us-gaap_DebtInstrumentRedemptionPeriodThreeMember_019caf6e-908a-76dc-a5b9-c43721199e9c_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/2025/elts/us-gaap-2025.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_DerivativeFairValueOfDerivativeLiability_019caf6e-900c-7502-a862-a53c5dc83acf_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/2025/elts/us-gaap-2025.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_GainLossOnDerivativeInstrumentsMember_019caf6e-90f8-7fbd-ab9d-6ac064a91c53_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsMember" 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_GainLossOnDerivativeInstrumentsMember_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnDerivativeInstrumentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019caf6e-900c-7a7f-9709-205b08ed8408_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/2025/elts/us-gaap-2025.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_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_019caf6e-9089-73cb-8342-406d25da74c7_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" 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_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" 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</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AuctionRateSecuritiesMember_019caf6e-8f6f-77c8-a903-d7acfe285d64_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_us-gaap_NumberOfReportableSegments_019caf6e-900c-77f7-ae32-78386f89990e_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfOrdinaryDividends_019caf6e-9089-7b2e-825b-1daedf8493f2_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/2025/elts/us-gaap-2025.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_CommercialRealEstateMember_019caf6e-900c-712a-9616-a3207d4bcc5d_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Real Estate</link:label>
    <link:label id="lab_us-gaap_CommercialRealEstateMember_label_en-US" xlink:label="lab_us-gaap_CommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Real Estate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialRealEstateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommercialRealEstateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialRealEstateMember" xlink:to="lab_us-gaap_CommercialRealEstateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019caf6e-900c-7f8d-9267-a6f160373f5f_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/2025/dei-2025.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_SubstandardMember_019caf6e-900c-7ae8-a468-b7113c829040_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/2025/elts/us-gaap-2025.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_InterestAndDividendIncomeOperating_019caf6e-908a-7488-9831-cd68f7608254_totalLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_019caf6e-908a-73d5-9dbf-e978ce935a83_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndDividendIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SpecialMentionMember_019caf6e-9089-7ef5-97be-6aa1d14a5d84_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/2025/elts/us-gaap-2025.xsd#us-gaap_SpecialMentionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SpecialMentionMember" xlink:to="lab_us-gaap_SpecialMentionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_019caf6e-900c-7c16-8816-b4e427309562_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/2025/elts/us-gaap-2025.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_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_019caf6e-9089-7ff6-a394-63f3c6622e85_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_019caf6e-900c-7d20-9692-66d9c13ccb27_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/2025/elts/us-gaap-2025.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_agm_PremiumDiscountRecognizedOnHedgedInstrument_019caf6e-900c-7518-b6ca-df04067e419f_negatedLabel_en-US" xlink:label="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Premium/discount amortization recognized on hedged items</link:label>
    <link:label id="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument_label_en-US" xlink:label="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium (Discount), Recognized on Hedged Instrument</link:label>
    <link:label id="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument_documentation_en-US" xlink:label="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Premium (Discount), Recognized on Hedged Instrument</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:href="agm-20260331.xsd#agm_PremiumDiscountRecognizedOnHedgedInstrument"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_PremiumDiscountRecognizedOnHedgedInstrument" xlink:to="lab_agm_PremiumDiscountRecognizedOnHedgedInstrument" 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/2025/ecd-2025.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_IncreaseDecreaseInOtherReceivables_019caf6e-9089-7e09-bdc9-efa140918d45_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/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitiesTable_019caf6e-9089-71e1-b5c1-d9e6c4f8717d_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/2025/dei-2025.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_us-gaap_VariableInterestEntityEntityMaximumLossExposureAmount_019caf6e-9089-7cd7-8fb0-ce6df2702cf6_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_dei_EntityInteractiveDataCurrent_019caf6e-9089-720e-83d5-18298b9aec91_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/2025/dei-2025.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_agm_RuralInfrastructureBroadbandInfrastructureSegmentMember_019caf6e-900c-7bc4-991c-f27097618a25_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-20260331.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_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleList_019caf6e-908a-7752-a1af-db22ecd94752_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/2025/elts/us-gaap-2025.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_InterestAndDividendIncomeOperatingAbstract_019caf6e-9089-70bc-a4b9-7e1c8fc8fef1_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/2025/elts/us-gaap-2025.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_TreasuryFundingSegmentMember_019caf6e-900c-7e3e-8625-ee2ec77ef478_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-20260331.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_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_019caf6e-900c-7112-b0ea-e674e3fb2158_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-20260331.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_NoninterestIncomeAbstract_019caf6e-900c-76a8-b17f-79da63793bb0_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/2025/elts/us-gaap-2025.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_agm_DebtInstrumentRedemptionAfterPeriodFiveMember_019caf6e-900c-745c-9ccc-ed778df82609_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-20260331.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_SeriesDPreferredStockMember_019caf6e-900c-73d5-8910-2cbb75c777b3_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5.700% Non-Cumulative Preferred Stock, Series D</link:label>
    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_019caf6e-900c-74d2-9198-b88aa9bc050c_verboseLabel_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Series D</link:label>
    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesDPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesDPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesDPreferredStockMember" xlink:to="lab_us-gaap_SeriesDPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted_019caf6e-900c-7d31-9dcf-bb6e10201beb_terseLabel_en-US" xlink:label="lab_agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted" 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_agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted_label_en-US" xlink:label="lab_agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted" 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, Adjusted</link:label>
    <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-20260331.xsd#agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted" xlink:to="lab_agm_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissionsAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019caf6e-9089-79d8-ac86-bb1062b9720c_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/2025/dei-2025.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_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/2025/ecd-2025.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" 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/2025/ecd-2025.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_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_019caf6e-9089-790c-956b-8bcff99dfe58_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract_019caf6e-900c-7324-9f37-4935f869befa_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-20260331.xsd#agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:to="lab_agm_AvailableforsaleSecuritiesDebtMaturitiesWeightedAverageYieldSingleMaturityDateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_019caf6e-900c-7639-b8f8-c9ed91e9b32c_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/2025/elts/us-gaap-2025.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_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019caf6e-900c-7ccc-9fa4-707673a85454_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">Schedule of Segment Reporting Information, by Segment [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">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <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/2025/ecd-2025.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019caf6e-900c-757a-8fe7-6c5b1d852dca_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/2025/dei-2025.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_ClassOfStockDomain_019caf6e-9089-791d-8fbf-b6853f75bd8f_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/2025/elts/us-gaap-2025.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_HedgedAssetFairValueHedgeCumulativeIncreaseDecrease_019caf6e-9089-7505-a5f0-672e6fcc93e9_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 included in the carrying amount of 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/2025/elts/us-gaap-2025.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_LongTermDebtNoncurrent_019caf6e-900c-755f-9463-b3a6aa93c762_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/2025/elts/us-gaap-2025.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_BalanceSheetLocationAxis_019caf6e-9089-7dd8-aa69-558b3521d40b_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BalanceSheetLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationAxis" xlink:to="lab_us-gaap_BalanceSheetLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtCurrentAndNoncurrentAbstract_019caf6e-8f6f-730d-9eb3-d08473bdc543_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/2025/elts/us-gaap-2025.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_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax_019caf6e-90f8-7d50-9ec5-4b7453ffb5ec_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/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" xlink:to="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax" 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/2025/ecd-2025.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_dei_EntityAddressAddressLine1_019caf6e-900c-7762-972a-a3f389864d84_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/2025/dei-2025.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_dei_EntityAddressAddressLine2_019caf6e-900c-7045-b722-4c511d078959_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/2025/dei-2025.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_AccumulatedOtherComprehensiveIncomeMember_019caf6e-900d-7827-84e9-8fcc6bc06d88_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_019dd870-c2ad-74e5-9d85-12e81c8c3e6e_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/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_019caf6e-900c-7aae-ac46-d1db8655470d_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InternalCreditAssessmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InternalCreditAssessmentAxis" xlink:to="lab_us-gaap_InternalCreditAssessmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_019caf6e-9089-7723-99ec-60475a7224ed_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/2025/elts/us-gaap-2025.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_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019caf6e-9089-7539-8c9f-9b79f1d9acdf_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/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_019caf6e-900c-79bb-b606-cc48d4e65ae0_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/2025/elts/us-gaap-2025.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_ScheduleOfDebtInstrumentsTextBlock_019caf6e-900c-7523-a103-4779a9725bf3_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>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019caf6e-9089-7a7f-999d-d9fa76850283_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/2025/elts/us-gaap-2025.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_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_019caf6e-900c-7c23-9be8-448d48420be0_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SARs and restricted stock units (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Share-Based Payment Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements"/>
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    <link:label id="lab_dei_DocumentQuarterlyReport_019caf6e-9089-78b4-b7e2-1800d5964300_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>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_TreasuryInvestmentsSegmentMember_019caf6e-900c-761a-a0fb-200056516ef9_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>
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    <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>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" 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</link:label>
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    <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>
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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_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember_019caf6e-900d-7fa4-9bc8-6ab17f3deeff_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:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:to="lab_us-gaap_USGovernmentSponsoredEnterprisesDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncomeMember_019caf6e-9089-7a0c-9f90-4fa1ddd866cb_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncomeMember" 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_OtherIncomeMember_label_en-US" xlink:label="lab_us-gaap_OtherIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncomeMember" xlink:to="lab_us-gaap_OtherIncomeMember" 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>
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    <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_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome_019caf6e-9089-73d3-b571-80cd21b6885c_totalLabel_en-US" xlink:label="lab_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome" xlink:href="agm-20260331.xsd#agm_TotalAmountsOfLineItemsPresentedInTheConsolidatedStatementOfIncome"/>
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    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_019caf6e-9089-7f0b-bb63-638c76c75559_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>
    <link:label id="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield_label_en-US" xlink:label="lab_agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Held-To-Maturity Securities, Debt Maturities, Next Twelve Months, Weighted-Average Yield</link:label>
    <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-20260331.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesNextTwelveMonthsWeightedAverageYield"/>
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    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalAdjusted_019caf6e-908a-7487-945e-eb2654873aeb_negatedTerseLabel_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalAdjusted" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Provision for)/release of losses</link:label>
    <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-20260331.xsd#agm_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalAdjusted"/>
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    <link:label id="lab_us-gaap_Investments_019caf6e-8f6f-7e2b-8863-a852e0567c19_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/2025/elts/us-gaap-2025.xsd#us-gaap_Investments"/>
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    <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>
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    <link:label id="lab_agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss_019caf6e-900c-7382-b24a-e98c25c21577_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-20260331.xsd#agm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetAllowanceForCreditLoss"/>
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    <link:label id="lab_us-gaap_NotesReceivableNetAbstract_019caf6e-900c-758f-9754-a4accaf4ad2c_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>
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    <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>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.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_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_019caf6e-908a-7878-8bbb-271471eecb49_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/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_019caf6e-9089-7860-b1a3-9596124713be_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/2025/elts/us-gaap-2025.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_us-gaap_OffsettingAssetsTableTextBlock_019caf6e-90f8-70af-9e22-f1e21dfdbb8a_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Assets</link:label>
    <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/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:to="lab_us-gaap_OffsettingAssetsTableTextBlock" 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/2025/elts/us-gaap-2025.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_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_019caf6e-8f6f-799e-8e12-630cbe02c3a9_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_agm_MediumTermNotesCalledDuringThePeriod_019caf6e-90f8-7d60-94d1-a53534881ba8_terseLabel_en-US" xlink:label="lab_agm_MediumTermNotesCalledDuringThePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Medium term notes called during the period</link:label>
    <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-20260331.xsd#agm_MediumTermNotesCalledDuringThePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_MediumTermNotesCalledDuringThePeriod" xlink:to="lab_agm_MediumTermNotesCalledDuringThePeriod" 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/2025/ecd-2025.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_us-gaap_DebtInstrumentNameDomain_019caf6e-9089-7fcf-ac90-4e2173264f39_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ProvisionForLoanLeaseAndOtherLossesNoncash_019ddaac-dc20-708f-a3e4-5f623913d688_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>
    <link:loc xlink:type="locator" xlink:label="loc_agm_ProvisionForLoanLeaseAndOtherLossesNoncash" xlink:href="agm-20260331.xsd#agm_ProvisionForLoanLeaseAndOtherLossesNoncash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ProvisionForLoanLeaseAndOtherLossesNoncash" xlink:to="lab_agm_ProvisionForLoanLeaseAndOtherLossesNoncash" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.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_us-gaap_EstimateOfFairValueFairValueDisclosureMember_019caf6e-8f6f-77c4-ab9b-08e993101d2b_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_019caf6e-90f8-7567-8492-d7c0bf755449_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/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
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    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems_019caf6e-90f8-7110-880d-4991bb2c24d4_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Recorded Investment, Past Due [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_019caf6e-9089-7fe8-b9fa-e178793ccb49_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/2025/elts/us-gaap-2025.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_DerivativeLiabilityNotOffsetPolicyElectionDeduction_019caf6e-9089-7246-a43c-7995ede39723_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:to="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019caf6e-900c-7d53-96d7-b26ffefa908d_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
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    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019caf6e-900c-75d7-912d-f781fc9c2d65_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/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue_019caf6e-900c-7bb9-aeb2-08336eb06d8b_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>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_019caf6e-9089-71b2-84a5-be312b5facce_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/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_019caf6e-900d-7490-8701-c9ebe0894c64_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
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    <link:label id="lab_us-gaap_PerformanceSharesMember_019caf6e-9089-7519-a355-4c38e1637c5c_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformanceSharesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PerformanceSharesMember"/>
    <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_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock_019caf6e-900c-78b7-a93d-a8c65702d42e_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-20260331.xsd#agm_ScheduleOfLongTermStandbyPurchaseCommitmentsTableTextBlock"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_019caf6e-9089-78e7-826f-5702a673dcd2_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">Expense recognized on 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/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax"/>
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    <link:label id="lab_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment_019caf6e-90f8-7d9f-baf7-84e24634c8cb_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment" 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 investment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPrincipalRepaymentsOnLoansAndLeasesHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Principal Repayment, Loan and Lease, Held-for-Investment</link:label>
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    <link:label id="lab_srt_MinimumMember_019caf6e-900c-73db-b5ed-1fe4d11c5dc9_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
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    <link:label id="lab_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_019caf6e-908a-7d14-8caa-c012dc4aa40d_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss"/>
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    <link:label id="lab_us-gaap_RepaymentsOfNotesPayable_019caf6e-8f6f-7c72-93ad-9629f1c3c84f_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/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfNotesPayable"/>
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    <link:label id="lab_agm_DerivativeLiabilityIncludingNotSubjectToMasterNettingArrangementAfterOffsetAndDeductionNetAmount_019caf6e-900c-7d0f-bdb6-84885672f38b_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>
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    <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>
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    <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>
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    <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>
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    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacy_019caf6e-900c-74fb-a7b6-6e55b5e4ffaf_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/2025/elts/us-gaap-2025.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_DebtDisclosureTextBlock_019caf6e-9089-7fb6-8c5c-5f041223e9e2_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019caf6e-900c-7f3c-98a2-3e140583a918_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/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralDomain_019caf6e-908a-7370-88cd-ebb78565de9b_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CollateralDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralDomain" xlink:to="lab_us-gaap_CollateralDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019caf6e-900c-7f06-8c0f-3059a73d7d69_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/2025/elts/us-gaap-2025.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_agm_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsWeightedAverageYield_019caf6e-900c-7d6b-84e4-30ebe316b0c6_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-20260331.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_WeightedAverageNumberOfDilutedSharesOutstanding_019caf6e-908a-718a-9312-5fa19273c3f0_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/2025/elts/us-gaap-2025.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_ShortTermDebtWeightedAverageInterestRate_019caf6e-900c-70e5-a62e-13e38054ea38_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding, Weighted - average rate</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate_019caf6e-900c-7999-81ee-97ed3f2a5f54_verboseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Short-term debt, weighted average rate</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Weighted Average Interest Rate, at Point in Time</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtWeightedAverageInterestRate"/>
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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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
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    <link:label id="lab_us-gaap_DerivativeTable_019caf6e-900c-72ac-9e5c-eeb256803b5f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearThree_019caf6e-900c-7081-b17b-2a455a2025b4_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>
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    <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>
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    <link:label id="lab_agm_ClearedSwapsMember_019caf6e-9089-7f33-b938-de70111ebdee_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>
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    <link:label id="lab_dei_EntitySmallBusiness_019caf6e-900c-7fdf-ae8c-dee4b316f556_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/2025/dei-2025.xsd#dei_EntitySmallBusiness"/>
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    <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/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
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    <link:label id="lab_agm_PaymentsToAcquireTaxCredits_019caf6e-900c-7bd5-b90a-52d0beb0ca48_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-20260331.xsd#agm_PaymentsToAcquireTaxCredits"/>
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    <link:label id="lab_us-gaap_DerivativeAverageRemainingMaturity1_019caf6e-9089-76ec-9f5a-abb785d603e4_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/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAverageRemainingMaturity1"/>
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    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_019caf6e-900c-7e52-9bdc-998a2e78c0e4_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesOutstanding"/>
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    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition_019caf6e-9089-71c7-82d5-1b6840e4cdc6_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other stock-based award activity</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Other, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationOtherLongtermIncentivePlansRequisiteServicePeriodRecognition"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_019caf6e-9089-7d39-aa06-f2913cc2032e_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>
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    <link:label id="lab_us-gaap_LongTermDebtMember_019caf6e-9089-74de-83cb-0bc9da783481_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMember" 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_LongTermDebtMember_019caf6e-9089-7d1b-b75f-836a2bdf9213_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Current portion of medium-term notes</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMember_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt [Member]</link:label>
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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_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>
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    <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_EquityComponentDomain_019caf6e-900c-78ce-86b9-fecb76eb3b2e_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>
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    <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_dei_DocumentPeriodEndDate_019caf6e-9089-7c1b-aa4c-63c4aebcd02f_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>
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    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_019caf6e-900c-7e12-b41e-add518f2b3be_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/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_CommonClassAMember_019caf6e-900c-70c7-a7c0-24013d36a0cc_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>
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    <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>
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    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_019caf6e-900c-7367-9075-e7d638d229b2_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net amount</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Including Not Subject to Master Netting Arrangement, after Offset and Deduction</link:label>
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    <link:label id="lab_agm_StockAppreciationRightsAndRestrictedStockMember_019caf6e-8f6f-777d-94cb-1518ecac4c2d_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>
    <link:label id="lab_agm_StockAppreciationRightsAndRestrictedStockMember_documentation_en-US" xlink:label="lab_agm_StockAppreciationRightsAndRestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights and Restricted Stock</link:label>
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    <link:label id="lab_dei_DocumentType_019caf6e-90f8-7a4d-a2e6-2358bf2686b0_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>
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    <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>
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    <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>
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    <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/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
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    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_label_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StockRepurchaseProgramAuthorizedAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:to="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff_019caf6e-9089-7594-ad3a-7def2d2cfe4d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" 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_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Two, Originated, Fiscal Year before Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff"/>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_019caf6e-900c-7294-b085-a4401d04073f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" 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/2025/ecd-2025.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_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_019caf6e-900c-7633-88b1-1bda4f764c95_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/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
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    <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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019caf6e-900c-7019-8865-1b930047acaa_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_019caf6e-900c-79d4-ae4c-f88df3aa2d09_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/2025/elts/us-gaap-2025.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_dei_EntityInformationLineItems_019caf6e-9089-7def-947b-ecd20c782fbc_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/2025/dei-2025.xsd#dei_EntityInformationLineItems"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019caf6e-900d-76c1-bce8-ad0649a59833_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)/income net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019caf6e-900d-71cb-b931-a0015fc4c2e6_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, 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/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
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    <link:label id="lab_agm_NetEffectiveSpread_019caf6e-9089-7086-995a-09144f965246_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-20260331.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_019caf6e-908a-7326-9a96-9a9a01fe54e7_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-20260331.xsd#agm_RuralInfrastructurePowerUtilitiesSegmentMember"/>
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    <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/2025/elts/us-gaap-2025.xsd#us-gaap_GuaranteeObligationsNatureDomain"/>
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    <link:label id="lab_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted_019caf6e-9089-76dc-a419-b4df102e085a_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-20260331.xsd#agm_NoninterestExpenseExcludingLoanLeaseAndOtherLossesAdjusted"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditEnergyRelatedAmount_019cf735-622a-75b4-b860-473011e60971_negatedLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditEnergyRelatedAmount" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Renewable energy investment tax credits</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/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditEnergyRelatedAmount"/>
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    <link:label id="lab_agm_OffBalanceSheetProgramAssets_019caf6e-8f6f-7f93-8002-105c58292e35_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-20260331.xsd#agm_OffBalanceSheetProgramAssets"/>
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    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019caf6e-900c-7daf-8503-e89c5f8170db_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/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
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    <link:label id="lab_us-gaap_SharesOutstanding_019caf6e-90f8-7484-bd73-b2257be70a74_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>
    <link:label id="lab_us-gaap_SharesOutstanding_019caf6e-90f8-7eb7-95e8-bb76d18e67e7_periodEndLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesOutstanding_label_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesOutstanding" xlink:to="lab_us-gaap_SharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_RegulatoryFees_019caf6e-900c-75d0-8a19-77149910a45a_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-20260331.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_019caf6e-9089-7861-b0c9-227ac0c1588d_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-20260331.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_agm_NoninterestExpenseExcludingLoanLeaseAndOtherLosses_019caf6e-900c-75ec-9eea-b43be9807fe3_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-20260331.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_us-gaap_IncreaseDecreaseInAccruedLiabilities_019caf6e-900c-7277-bef6-b559807432f5_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/2025/elts/us-gaap-2025.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_EarningsPerShareDiluted_019caf6e-900c-7c68-9959-b54ee2cb4e7a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted earnings per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019caf6e-900c-7248-ba03-a7d17c35a354_totalLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Diluted EPS (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InConsolidatedTrustsMember_019caf6e-900c-7239-a634-dac3115987c6_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-20260331.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_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019caf6e-900c-7ab3-9926-51ec2800d9a0_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/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_019caf6e-908a-7400-a6d6-64dd8d0a7f56_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/2025/elts/us-gaap-2025.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_FinancingReceivableExcludingAccruedInterestModifiedPeriod_019caf6e-900c-760f-956f-2a9952581667_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">Loans modified</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/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_019caf6e-8f6f-7f20-9cef-7a31c4baa369_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/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPreferredStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPreferredStockCash" xlink:to="lab_us-gaap_DividendsPreferredStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsWeightedAverageYield_019caf6e-90f8-72a5-8b70-804299519789_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-20260331.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_srt_ConsolidationItemsDomain_019caf6e-900c-7704-a9b7-3934445b2c22_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/2025/elts/srt-2025.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_InvestmentsDebtAndEquitySecuritiesAbstract_019caf6e-900c-7269-9a3b-b513e117e6d4_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/2025/elts/us-gaap-2025.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_us-gaap_PaymentsToAcquireLoansHeldForInvestment_019caf6e-9089-709e-aa8a-cf19ff895c3e_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/2025/elts/us-gaap-2025.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_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_019caf6e-900c-773c-a756-277c0c5510e5_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/2025/elts/us-gaap-2025.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_StockRepurchasedAndRetiredDuringPeriodValue_019caf6e-900c-7ba9-8610-20b0aa4ac01b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repurchase of Class C Common Stock</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_019dd504-6fd5-7715-beff-8d671a6d4952_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase of Class C Common Stock</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased and Retired During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:to="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_019caf6e-900c-7f7a-89e9-a083f779348f_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>
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    <link:label id="lab_us-gaap_TransactionDomain_label_en-US" xlink:label="lab_us-gaap_TransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction [Domain]</link:label>
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    <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>
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    <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/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_019caf6e-900c-7aeb-b294-d33e3f137989_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" 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_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_019caf6e-900c-79c8-8cb0-b7e2c4bf0ce9_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
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    <link:label id="lab_us-gaap_CollateralPledgedMember_019caf6e-900c-760c-b328-510ab7850b25_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>
    <link:label id="lab_us-gaap_CollateralPledgedMember_label_en-US" xlink:label="lab_us-gaap_CollateralPledgedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateral Pledged [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralPledgedMember" xlink:to="lab_us-gaap_CollateralPledgedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_019caf6e-900c-7c0e-a48d-38669f2f6404_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/2025/elts/us-gaap-2025.xsd#us-gaap_PastDueFinancingReceivablesTableTextBlock"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019caf6e-9089-78d8-8fb5-d8cb334573d6_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/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
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    <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/2025/ecd-2025.xsd#ecd_MeasureAxis"/>
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    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019caf6e-900c-7188-b583-1a9495e2b007_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/2025/elts/us-gaap-2025.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_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_019caf6e-900c-7c7a-ac38-ff727f8deb20_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/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1"/>
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    <link:label id="lab_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems_019caf6e-9089-7dda-a945-210e709b7154_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-20260331.xsd#agm_ScheduleOfAvailableForSaleAndTradingSecuritiesLineItems"/>
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    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_019caf6e-900d-738f-b5ff-ba2632acb226_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/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock"/>
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    <link:label id="lab_agm_FairValueAssetsAndLiabilitiesFairValueAsPercentOfTotalAssets_019caf6e-908a-7509-a4c2-2e9dd923d4b3_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>
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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>
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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>
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    <link:label id="lab_dei_EntityTaxIdentificationNumber_019caf6e-8f6f-7c3f-accf-9ae335090b86_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>
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    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_019caf6e-908a-7322-b483-83c5b6d61fd1_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>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff_019caf6e-9089-7b8c-b964-7a79abca7979_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Charge-offs</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_019caf6e-9089-7aed-b72b-80bdebfa1b48_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>
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    <link:label id="lab_us-gaap_SegmentReportingInformationAdditionalInformationAbstract_019caf6e-9089-723e-94b8-258c2ce7bd46_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 Information, Additional Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationAdditionalInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_019caf6e-9089-7917-890e-42f5f506a789_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" 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_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_019caf6e-9089-7383-b1fc-6eb11c6851c2_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ReserveForLosses_019caf6e-900c-72ea-9c89-a6610c9f9aa8_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-20260331.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_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_019caf6e-9089-7870-9903-4304a8599e34_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/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:to="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019caf6e-9089-7411-9379-c9c9c46ef090_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/2025/elts/us-gaap-2025.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_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DueYearThreeMember_019caf6e-900c-7da2-9b72-45fa93d575e9_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-20260331.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_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/2025/ecd-2025.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_019caf6e-900c-74f9-8e18-36afbbafac01_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_019caf6e-900c-7db4-86a0-4a7072e61cc6_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesEPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesEPreferredStockMember"/>
    <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_dei_SecurityExchangeName_019caf6e-9089-7abf-8f6a-857dc399307b_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/2025/dei-2025.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_SecuritiesPurchasedUnderAgreementsToResell_019caf6e-9089-79e7-85b4-425d5c72c134_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/2025/elts/us-gaap-2025.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_us-gaap_MortgageBackedSecuritiesMember_019caf6e-900c-7920-8069-2d52ded02e6c_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/2025/elts/us-gaap-2025.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_us-gaap_DerivativeAssetFairValueNetAbstract_019caf6e-9089-7765-9d46-16eaaab1c256_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueNetAbstract" 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_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetFairValueNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:to="lab_us-gaap_DerivativeAssetFairValueNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesTextBlock_019caf6e-900d-7f59-b817-b4cb2817bce6_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesTextBlock" xlink:to="lab_us-gaap_FinancingReceivablesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019caf6e-9089-7587-b630-a417cde6bf1f_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/2025/elts/us-gaap-2025.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_agm_LongTermDebtWithInterestRateResetMaturityYearTwo_019caf6e-900c-7ec0-aa6d-18d670d5b7c0_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-20260331.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_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_019caf6e-900c-7ec4-a9f1-0e44db91266f_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/2025/elts/us-gaap-2025.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_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1_019caf6e-908a-7644-8e3d-c107dc815106_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/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1" xlink:type="arc" order="1"/>
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    <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>
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    <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>
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    <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_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>
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    <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>
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    <link:label id="lab_agm_NetEffectsOfDerivativesAndTradingSecurities_019caf6e-9089-7a60-98c2-d2e09696476a_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>
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    <link:label id="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_019caf6e-9089-7f96-9153-35d9a4bd11cb_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>
    <link:label id="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems_label_en-US" xlink:label="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:to="lab_us-gaap_ReclassificationAdjustmentOutOfAccumulatedOtherComprehensiveIncomeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent_019caf6e-908a-78d0-9bda-507b5c346811_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_019caf6e-908a-7dcd-9b7b-7b825f34d222_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/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAociCurrentPeriodNetOfTaxAttributableToParent"/>
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    <link:label id="lab_us-gaap_OffsettingDerivativeAssetsAbstract_019caf6e-9089-7fbe-97be-4bf979d00e95_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingDerivativeAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:to="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities_019caf6e-900c-730f-a84e-424ff1aa070f_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/2025/elts/us-gaap-2025.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_AccountingPoliciesAbstract_019caf6e-908a-7ed2-a08b-b177c8dacd8c_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/2025/elts/us-gaap-2025.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_agm_NumberOfSubsidiaries_019caf6e-908a-7d1d-90f2-9782bbdf6772_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-20260331.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_us-gaap_PaymentsToAcquireOtherInvestments_019caf6e-908a-745d-bf54-1de1b53b5f6c_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/2025/elts/us-gaap-2025.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_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_019caf6e-90f8-7e28-bdcb-df6eae0c40c1_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/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear"/>
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    <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/2025/ecd-2025.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_USGovernmentAgenciesDebtSecuritiesMember_019caf6e-9089-7f44-b283-41bc33072bbe_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/2025/elts/us-gaap-2025.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_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_019caf6e-900c-769d-acb1-7e345b7ba40e_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/2025/elts/us-gaap-2025.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_LiabilitiesAbstract_019caf6e-900c-7ce6-87b7-db4ab479bfa9_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/2025/elts/us-gaap-2025.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_agm_HedgedItemNetInterestSettlements_019caf6e-90f8-71d2-a880-a13ab87d639f_terseLabel_en-US" xlink:label="lab_agm_HedgedItemNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognized on hedged items</link:label>
    <link:label id="lab_agm_HedgedItemNetInterestSettlements_label_en-US" xlink:label="lab_agm_HedgedItemNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedged Item Net Interest Settlements</link:label>
    <link:label id="lab_agm_HedgedItemNetInterestSettlements_documentation_en-US" xlink:label="lab_agm_HedgedItemNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hedged Item Net Interest Settlements (Interest Accruals)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_HedgedItemNetInterestSettlements" xlink:href="agm-20260331.xsd#agm_HedgedItemNetInterestSettlements"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019caf6e-9089-72a8-82c7-c028086530db_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/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
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    <link:label id="lab_agm_DerivativeNetInterestSettlements_019caf6e-9089-72ad-9dca-cb62ae7a9a83_terseLabel_en-US" xlink:label="lab_agm_DerivativeNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognized on derivatives</link:label>
    <link:label id="lab_agm_DerivativeNetInterestSettlements_label_en-US" xlink:label="lab_agm_DerivativeNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Net Interest Settlements</link:label>
    <link:label id="lab_agm_DerivativeNetInterestSettlements_documentation_en-US" xlink:label="lab_agm_DerivativeNetInterestSettlements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Net Interest Settlements (Interest Accruals)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeNetInterestSettlements" xlink:href="agm-20260331.xsd#agm_DerivativeNetInterestSettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeNetInterestSettlements" xlink:to="lab_agm_DerivativeNetInterestSettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_019caf6e-900c-7926-8abb-b8533d495cc2_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/2025/elts/us-gaap-2025.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"/>
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    <link:label id="lab_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1_label_en-US" xlink:label="lab_us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Unrealized Gain (Loss) on Hedged Item in Fair Value Hedge</link:label>
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    <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-20260331.xsd#agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:to="lab_agm_WeightedAverageRemainingMaturityLoansUnderlyingGuaranteesNotHeldByTransferor" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_019caf6e-9089-75de-bd53-68dc45f47685_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/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
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    <link:label id="lab_us-gaap_LongTermDebtCurrent_019caf6e-9089-7d91-b8b8-8559599f39cb_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/2025/elts/us-gaap-2025.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_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_019caf6e-90f8-7c21-ae6f-a51475720881_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/2025/elts/us-gaap-2025.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_StatementOfCashFlowsAbstract_019caf6e-900c-7b53-af48-c5d006ead5d5_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff_019caf6e-9089-78fc-85b0-ea50f1860702_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" 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_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Originated, More than Five Years before Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff"/>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019caf6e-90f8-7391-9f00-06463c957cb3_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/2025/elts/us-gaap-2025.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_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember_019caf6e-90f8-790d-8a92-8e05d0e646c2_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>
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    <link:loc xlink:type="locator" xlink:label="loc_agm_AOCIAccumulatedGainLossDebtSecuritiesHeldToMaturityParentMember" xlink:href="agm-20260331.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_MeasurementInputTypeAxis_019caf6e-9089-7b3e-b21f-eb465afec9b3_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/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeAxis"/>
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    <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>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_019caf6e-9089-7c6e-a6ac-c05eafa360bd_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent_019caf6e-90f8-757e-8196-bbf41dfd87c0_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)/income 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>
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    <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>
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    <link:label id="lab_us-gaap_LongTermDebt_019caf6e-9089-7227-9813-13e823491332_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:label id="lab_us-gaap_Assets_019caf6e-900c-7f50-a8b7-937220682107_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>
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    <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>
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    <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/2025/elts/us-gaap-2025.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_agm_HeldToMaturitySecuritiesDebtMaturitiesYearTwoThroughFiveWeightedAverageYield_019caf6e-900c-795d-9c00-da2765ecaea9_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>
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    <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-20260331.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_agm_LongTermDebtWithInterestRateReset_019caf6e-90f8-780b-9417-c199661582d6_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-20260331.xsd#agm_LongTermDebtWithInterestRateReset"/>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_019caf6e-90f8-736a-b4d3-704be9011609_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/2025/elts/us-gaap-2025.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_agm_IncomeExpenseInterestSettlementsFairValueHedges_019caf6e-9089-75da-a067-719d6211caa3_totalLabel_en-US" xlink:label="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income/(expense) related to interest settlements on fair value hedging relationships</link:label>
    <link:label id="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges_label_en-US" xlink:label="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Expense, Interest Settlements, Fair Value Hedges</link:label>
    <link:label id="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges_documentation_en-US" xlink:label="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Expense, Interest Settlements, Fair Value Hedges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:href="agm-20260331.xsd#agm_IncomeExpenseInterestSettlementsFairValueHedges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:to="lab_agm_IncomeExpenseInterestSettlementsFairValueHedges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019caf6e-90f8-77dc-9f9c-b35231557dc6_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/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
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    <link:label id="lab_agm_FinanceReceivableAccruedInterestPayable_019caf6e-908a-7f00-9bec-59faa0b7d82d_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-20260331.xsd#agm_FinanceReceivableAccruedInterestPayable"/>
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    <link:label id="lab_us-gaap_SegmentReportingOtherItemAmount_019caf6e-900c-78bd-9608-e12d9596ac3a_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/2025/elts/us-gaap-2025.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_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract_019caf6e-90f8-75ab-9742-090971fde46d_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/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesClassifiedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:to="lab_us-gaap_HeldToMaturitySecuritiesClassifiedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_019caf6e-908a-77bb-bb4d-363a8651f6d1_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/2025/elts/us-gaap-2025.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_VariableInterestEntityLineItems_019caf6e-900c-76d0-9889-2a6948fe69d9_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction_019caf6e-9089-70b2-a58c-17af423bed7d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Financial instruments pledged</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Deduction of Financial Instrument Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:to="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_019caf6e-900c-7410-9909-d2f22168139b_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>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
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    <link:label id="lab_us-gaap_OtherInvestments_019caf6e-900c-763d-9fc5-fe276ebae9c8_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/2025/elts/us-gaap-2025.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_dei_EntityCommonStockSharesOutstanding_019caf6e-900c-7220-9924-4409e759d847_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding"/>
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    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_019caf6e-908a-7bf5-baa7-29281a6e6c56_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/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
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    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019caf6e-908a-7fd3-b113-95c1438022a4_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/2025/elts/us-gaap-2025.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"/>
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    <link:label id="lab_agm_MarketableSecuritiesFairValueDisclosure_019caf6e-900c-7f35-b256-aa2fcf91ba17_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>
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    <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>
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    <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>
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    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_019caf6e-908a-7dcd-90fb-bca6bb7c29f3_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_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/2025/elts/us-gaap-2025.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_IncreaseDecreaseInOperatingCapitalAbstract_019caf6e-900c-72e1-95c2-b9b451a3dcce_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_agm_UnrecordedMaximumPotentialExposureOnGuaranteesAxis_019caf6e-900c-78bc-a367-691b552202aa_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>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_019caf6e-900c-70ac-ab8e-5f0beeb18311_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_IncomeStatementAbstract_019caf6e-908a-7c65-950a-5fd299eeda1b_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/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract"/>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019caf6e-9089-7d95-b696-fe42089c716b_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 $27,338 and $24,475, respectively)</link:label>
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    <link:label id="lab_us-gaap_DerivativeAssets_019caf6e-900c-7731-ae08-8aa57c3b6269_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_019caf6e-900c-7373-9648-bb8bb8972de2_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_019caf6e-900c-7966-ba9e-46331d9a1703_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>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_019caf6e-900c-74df-b65a-714c3c68ba3e_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>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" 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</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger"/>
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    <link:label id="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_019caf6e-9089-773b-82e5-ec25c47f656f_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>
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    <link:label id="lab_agm_DueAfterFourYearsMember_019caf6e-900c-767c-85c4-eabad6ebf95a_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>
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    <link:label id="lab_agm_FinancingReceivableOriginatedInCurrentFiscalYearAbstract_019caf6e-9089-7217-bfb4-23c44fc62196_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-20260331.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_srt_ProductsAndServicesDomain_019caf6e-9089-7e52-9407-7b248bfd84f3_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/2025/elts/srt-2025.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_AvailableForSaleSecuritiesAbstract_019caf6e-9089-75e3-8cd4-68004faa4269_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AFS Securities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesAbstract" 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/2025/ecd-2025.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_LiabilitiesFairValueDisclosure_019caf6e-900c-7cc3-ba4f-3c4ec233c92e_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/2025/elts/us-gaap-2025.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_agm_AgriculturalFinanceMember_019caf6e-900c-782c-ada6-09773c26605d_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_019caf6e-900c-7f16-9f9e-e5204b0ec4f5_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-20260331.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_us-gaap_SeriesHPreferredStockMember_019caf6e-900d-76fc-a9e1-a556de90ad5e_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_019caf6e-900d-737d-87d2-c29ed6e4ff16_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/2025/elts/us-gaap-2025.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_agm_InvestmentTaxCreditPricePerCredit_019caf6e-9089-7204-a8ba-d00d378adbf4_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-20260331.xsd#agm_InvestmentTaxCreditPricePerCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InvestmentTaxCreditPricePerCredit" xlink:to="lab_agm_InvestmentTaxCreditPricePerCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving_019caf6e-900c-7390-881e-e2e71bd493f8_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/2025/elts/us-gaap-2025.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_dei_Security12gTitle_019caf6e-900c-72ff-b77c-d832cc08fde8_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/2025/dei-2025.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_dei_CityAreaCode_019caf6e-900d-7c82-a0d7-6333dff9c3d9_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>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_019caf6e-90f8-7d28-a26a-fd8f56280448_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_BasisSwapMember_019caf6e-900d-7ee8-9428-0e43a5fbf4a5_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/2025/elts/us-gaap-2025.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_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts_019caf6e-9089-79db-8c4f-d069ac108ddf_negatedTerseLabel_en-US" xlink:label="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments to third parties on debt securities of consolidated trusts</link:label>
    <link:label id="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts_label_en-US" xlink:label="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments To Third Parties On Debt Securities Of Consolidated Trusts</link:label>
    <link:label id="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts_documentation_en-US" xlink:label="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The cash outflows associated with consolidated trusts where Farmer Mac is determined to be the primary beneficiary but trusts are owned by third parties.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:href="agm-20260331.xsd#agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:to="lab_agm_PaymentsToThirdPartiesOnDebtSecuritiesOfConsolidatedTrusts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019caf6e-900c-75e5-bcd2-bfda3272d2cf_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" 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 [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_019caf6e-900c-7a04-902e-92fd3854aded_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities_019caf6e-8f6f-7f25-9eb0-b2f045540644_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from repayment of held-to-maturity investment securities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale and Maturity of Held-to-Maturity Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities" xlink:to="lab_us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_019caf6e-9089-7e2d-bedf-9c9b08f46d7c_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 $25,874 and $40,945, respectively, related to consolidated trusts)</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_019caf6e-9089-7f01-b06b-3da2627d1aec_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/2025/elts/us-gaap-2025.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_us-gaap_FairValueHedgingMember_019caf6e-908a-7399-9b38-252204d90eb9_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/2025/elts/us-gaap-2025.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_us-gaap_CashFlowHedgingMember_019caf6e-900c-79be-a51a-d030eebf4cf5_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/2025/elts/us-gaap-2025.xsd#us-gaap_CashFlowHedgingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowHedgingMember" xlink:to="lab_us-gaap_CashFlowHedgingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateLoanMember_019caf6e-9089-77e0-8e2f-af275a099663_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Loan</link:label>
    <link:label id="lab_us-gaap_RealEstateLoanMember_label_en-US" xlink:label="lab_us-gaap_RealEstateLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Loan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateLoanMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateLoanMember" xlink:to="lab_us-gaap_RealEstateLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure_019caf6e-908a-799b-9b8b-b5e33fb3fdcb_totalLabel_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total loans</link:label>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" 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 And Loans Held-For-Sale Fair Value Disclosure</link:label>
    <link:label id="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure_documentation_en-US" xlink:label="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" 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 And Loans Held-For-Sale Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:href="agm-20260331.xsd#agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:to="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossAndLoansHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_InterestRevenueExpenseNetMember_019caf6e-900c-7db8-9a38-79c1be9a7f1c_terseLabel_en-US" xlink:label="lab_agm_InterestRevenueExpenseNetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Income Investments and Cash Equivalents</link:label>
    <link:label id="lab_agm_InterestRevenueExpenseNetMember_label_en-US" xlink:label="lab_agm_InterestRevenueExpenseNetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Revenue (Expense), Net [Member]</link:label>
    <link:label id="lab_agm_InterestRevenueExpenseNetMember_documentation_en-US" xlink:label="lab_agm_InterestRevenueExpenseNetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Revenue (Expense), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_InterestRevenueExpenseNetMember" xlink:href="agm-20260331.xsd#agm_InterestRevenueExpenseNetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_InterestRevenueExpenseNetMember" xlink:to="lab_agm_InterestRevenueExpenseNetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuarantyAssets_019caf6e-908a-76db-a009-b94cdb86559b_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_019caf6e-908a-725a-b619-4a5ce1efba9d_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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"/>
    <link:label id="lab_us-gaap_MeasurementInputConstantPrepaymentRateMember_019caf6e-900d-726c-aa51-285600f90b3c_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/2025/elts/us-gaap-2025.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_DerivativeInstrumentRiskAxis_019caf6e-900c-79a9-ae09-9ad13047ebfc_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, by Nature [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCash_019caf6e-900c-7202-8693-ecea87d1706e_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/2025/elts/us-gaap-2025.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_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract_019caf6e-900c-7b77-a2de-a498b82afaa7_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/2025/elts/us-gaap-2025.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_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet_019caf6e-900c-7487-8d42-1f1201b132ab_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-20260331.xsd#agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:to="lab_agm_ReconcilingAdjustmentsFromNetInterestIncomeToNetEffectiveSpreadNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableUnamortizedLoanCommitmentOriginationFeeAndPremiumDiscount_019caf6e-9089-749c-8392-0bcfc8efb9b2_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/2025/elts/us-gaap-2025.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_us-gaap_InvestmentsAbstract_019caf6e-8f6f-7b93-a994-7b42970ec83b_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/2025/elts/us-gaap-2025.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_NetCashProvidedByUsedInInvestingActivities_019caf6e-9089-7416-8560-fcff8276a4b8_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019caf6e-900c-74a2-a4ae-d6974fbde052_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/2025/elts/us-gaap-2025.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_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty_019caf6e-9089-7c3e-ab55-4a8604866366_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-20260331.xsd#agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureToCounterparty"/>
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    <link:label id="lab_dei_LocalPhoneNumber_019caf6e-908a-74cf-b403-f3b480c998cf_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/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
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    <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>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_019caf6e-9089-7ad2-8ad3-37bb002ef1cc_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive"/>
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    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_019caf6e-8f6f-7ae9-867d-0b446486fe38_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_019dd503-edea-7dc0-aef0-b55a749482da_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_SeriesFPreferredStockMember_019caf6e-900c-7987-9ff1-9eae2511ba0e_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>
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    <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_us-gaap_AssetsAbstract_019caf6e-908a-7c18-a1f8-65bbbabe2efa_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/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax_019caf6e-900c-7926-b12d-a8c68ef78b6a_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/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax"/>
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    <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>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.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_EarningsPerShareOnIncrementalCommonSharesAttributableToShareBasedPaymentArrangements_019caf6e-900c-7c20-b9e2-98669b6c02f9_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_us-gaap_DebtInstrumentAxis_019caf6e-900d-727f-8006-c61fed39f26b_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>
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    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019caf6e-90f8-766a-a624-c261f0ff0d5b_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>
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    <link:label id="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet_019caf6e-900c-74a3-9966-fb4fc07a4ac5_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain expected to be reclassified from AOCI to earnings over next 12 months</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivables30To59DaysPastDueMember_019caf6e-900c-7b55-9eec-834a43e98ee3_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>
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    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_019caf6e-900c-7ecf-a3d6-ac81b3d1da54_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amount Recognized</link:label>
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    <link:label id="lab_dei_EntityRegistrantName_019caf6e-900c-7179-8aca-1f9890467691_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>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.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_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_019caf6e-9089-7f9a-8ff0-1be9e5dd8ba5_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/2025/elts/us-gaap-2025.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_us-gaap_AssetsFairValueDisclosure_019caf6e-908a-78a0-8523-6ae5d759048f_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/2025/elts/us-gaap-2025.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_us-gaap_ProvisionForLoanLeaseAndOtherLosses_019ddaab-5de7-78b0-8606-ac1235d82a67_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Provision for losses</link:label>
    <link:label id="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses_label_en-US" xlink:label="lab_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Provision for Loan, Lease, and Other Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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"/>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_019caf6e-90f8-7de3-b067-5de9b44fb7ba_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/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialAssetPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetPastDueMember" xlink:to="lab_us-gaap_FinancialAssetPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_019caf6e-900c-7d31-a20e-10f6e856f2b7_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments"/>
    <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_AccretionAmortizationOfDiscountsAndPremiumsInvestments_019caf6e-9089-7337-9900-dac936622e5e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net amortization of deferred gains, premiums, and discounts on loans, investments, Farmer Mac Guaranteed Securities, and USDA Securities</link:label>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_label_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:to="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_019caf6e-9089-7e0c-8ad1-586583ee6810_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/2025/elts/us-gaap-2025.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_MaterialReconcilingItemsMember_019caf6e-9089-750c-878b-656186ee29e1_terseLabel_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciling Adjustments</link:label>
    <link:label id="lab_us-gaap_MaterialReconcilingItemsMember_label_en-US" xlink:label="lab_us-gaap_MaterialReconcilingItemsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Excluding Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MaterialReconcilingItemsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MaterialReconcilingItemsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MaterialReconcilingItemsMember" xlink:to="lab_us-gaap_MaterialReconcilingItemsMember" 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/2025/ecd-2025.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_AccumulatedOtherComprehensiveIncomeLossTable_019caf6e-900c-7f1e-8d63-ffdf378777da_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/2025/elts/us-gaap-2025.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_us-gaap_GuarantyLiabilities_019caf6e-900c-7111-b0e8-7e004dd45600_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/2025/elts/us-gaap-2025.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_agm_UnallocatedAssets_019caf6e-8f6f-7094-9953-bb24ea054d03_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-20260331.xsd#agm_UnallocatedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_UnallocatedAssets" xlink:to="lab_agm_UnallocatedAssets" 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/2025/ecd-2025.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_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust_019caf6e-9089-75d5-8f4f-e70259a99eca_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-20260331.xsd#agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:to="lab_agm_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossHeldInTrust" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtHedgingAdjustments_019caf6e-9089-7aa8-8147-b5969138f056_terseLabel_en-US" xlink:label="lab_agm_LongTermDebtHedgingAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging adjustments</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_agm_LongTermDebtHedgingAdjustments" xlink:href="agm-20260331.xsd#agm_LongTermDebtHedgingAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtHedgingAdjustments" xlink:to="lab_agm_LongTermDebtHedgingAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_ClearedDerivativesMember_019caf6e-9089-7da3-b231-b78ae8bd28ac_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-20260331.xsd#agm_ClearedDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_ClearedDerivativesMember" xlink:to="lab_agm_ClearedDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotionalAmountOfDerivativesAbstract_019caf6e-900c-7526-8a4c-9081a2ff1678_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/2025/elts/us-gaap-2025.xsd#us-gaap_NotionalAmountOfDerivativesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:to="lab_us-gaap_NotionalAmountOfDerivativesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_019caf6e-900d-7d91-83ce-2117c6791b29_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/2025/elts/us-gaap-2025.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_us-gaap_PreferredStockMember_019caf6e-900c-727a-a38b-2ff6be0fa75b_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>
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    <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>
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    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_019caf6e-9089-7120-a27c-9d59dbc2f28c_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_019caf6e-9089-7a57-967e-9b5669dc0d68_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/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityFairValueGrossAsset"/>
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    <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/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt"/>
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    <link:label id="lab_us-gaap_PreferredStockValue_019caf6e-9089-7d36-8da8-8728c1a80268_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/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockValue"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_019caf6e-9089-792a-84c2-a438e5b89969_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/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract"/>
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    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019caf6e-9089-79f7-8e08-365371d5f391_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/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear_019caf6e-900d-7e73-baf7-81bc529ccee8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear"/>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract_019caf6e-900c-785e-a798-a7b80aab0886_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/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValueAbstract"/>
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    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_019caf6e-9089-7df5-85ad-3654842391b3_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/2025/elts/us-gaap-2025.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_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllExecutiveCategoriesMember"/>
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    <link:label id="lab_us-gaap_CommonStockValue_019caf6e-900c-7562-aac4-abd036a37b2a_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/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue"/>
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    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_019caf6e-908a-7e37-bef3-626351fecccc_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_019caf6e-908a-73d7-8212-bdb5e459d12d_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest Income 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, Loans and Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1_019caf6e-900c-7363-9795-3f8051019ee1_terseLabel_en-US" xlink:label="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Losses)/gains on fair value hedging relationships, recognized on derivatives</link:label>
    <link:label id="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1_label_en-US" xlink:label="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Unrealized Gain (Loss) on Fair Value Hedging Instruments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019caf6e-9089-70e1-ad51-5954e0c5d581_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" 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 [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" 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]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
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    <link:label id="lab_agm_RuralInfrastructureFinanceRenewableEnergySegmentMember_019caf6e-908a-70f5-a6a1-c033e2109576_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>
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    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019caf6e-900c-7998-a88b-93dc0fef0f74_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/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff"/>
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    <link:label id="lab_us-gaap_ExchangeClearedMember_019caf6e-90f8-7a52-9506-5b40480ab22a_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/2025/elts/us-gaap-2025.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_agm_LiabilitiesHeldInTrust_019caf6e-900d-7543-a85e-3e54db78ec8e_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-20260331.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_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease_019caf6e-900c-7ea8-8ce5-ca8d845e64c0_terseLabel_en-US" xlink:label="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cumulative amount of fair value hedging adjustments included in the carrying amount of 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/2025/elts/us-gaap-2025.xsd#us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" xlink:to="lab_us-gaap_HedgedLiabilityFairValueHedgeCumulativeIncreaseDecrease" 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/2025/ecd-2025.xsd#ecd_PeoActuallyPaidCompAmt"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_019caf6e-900d-7f9b-8d17-be7fc1a5a646_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/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour_019caf6e-9089-7809-b417-5549a764da98_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-20260331.xsd#agm_LongTermDebtWithInterestRateResetMaturityAfterYearFour"/>
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    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_019caf6e-900c-78a8-aa2b-b6cb6b21835d_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/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDilutedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:to="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember_019caf6e-9089-7d3e-b934-4b1b126e9bdf_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/2025/elts/us-gaap-2025.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_019caf6e-900c-7507-b29a-b72e804e1d37_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/2025/elts/us-gaap-2025.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_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_019caf6e-900d-7f55-98d7-9c9788520954_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/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock"/>
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    <link:label id="lab_agm_DerivativeWeightedAverageForwardPrice_019caf6e-90f8-7159-b93e-b0e224792317_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-20260331.xsd#agm_DerivativeWeightedAverageForwardPrice"/>
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    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_019caf6e-900c-72d3-a42c-e04963553a23_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/2025/elts/us-gaap-2025.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_us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable_019caf6e-900c-7c14-ba28-597328380c1b_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/2025/elts/us-gaap-2025.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_ProceedsFromIssuanceOfCommonStock_019caf6e-900c-7244-9b9b-9a9f8fff4ee2_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from common stock issuance</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10_019caf6e-900c-7421-a771-76e5cbe526a9_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10" 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_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10" 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, after Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateAfterYear10"/>
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    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_019caf6e-900c-7d3d-8dea-6b00d6bd354c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Amount of Hedged Assets/(Liabilities)</link:label>
    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_label_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Amount of Hedged Item</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAmountOfHedgedItem" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAmountOfHedgedItem"/>
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    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <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/2025/ecd-2025.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_agm_LongTermDebtWithInterestRateResetMaturityYearFour_019caf6e-908a-7fc0-8ea1-db1865522686_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-20260331.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_us-gaap_LongtermDebtTypeDomain_019caf6e-900c-73b4-b924-5652fa978eb0_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/2025/elts/us-gaap-2025.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_agm_InterestRateSwapReceiveFixedNonCallableMember_019caf6e-9089-7316-b0e7-8621f55ec81d_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-20260331.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_FairValueDisclosuresAbstract_019caf6e-9089-7db9-8aa1-a602a467e963_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <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>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_019caf6e-900c-73f7-89b9-383edadede21_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/2025/elts/us-gaap-2025.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_agm_OtherComprehensiveIncomeLossHeldToMaturitySecuritiesBeforeTax_019caf6e-900c-7727-bcc3-d7662c4ef575_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-20260331.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_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_019caf6e-9089-7255-99cb-18660b09ac1f_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" 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_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" 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, Amortized Cost [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff_019caf6e-908a-7584-a6a8-93aada8be47f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" 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_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" 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, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_019caf6e-900c-7940-b50c-a65972024514_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments in Statement of Financial Position</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativeInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_019caf6e-8f6f-73bd-b54f-1d98571ad06b_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_us-gaap_DerivativeAverageFixedInterestRate_019caf6e-900c-7231-a062-12104be2f206_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/2025/elts/us-gaap-2025.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_us-gaap_DerivativeLiabilitiesAbstract_019caf6e-9089-7f44-b39e-8e39ece314c7_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/2025/elts/us-gaap-2025.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_us-gaap_TransactionTypeAxis_019caf6e-908a-74d1-92a9-ff3b7799f882_terseLabel_en-US" xlink:label="lab_us-gaap_TransactionTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction Type [Axis]</link:label>
    <link:label id="lab_us-gaap_TransactionTypeAxis_label_en-US" xlink:label="lab_us-gaap_TransactionTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransactionTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransactionTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransactionTypeAxis" xlink:to="lab_us-gaap_TransactionTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OtherAssetMeasurementInput_019caf6e-90f8-7c79-a252-835926e122b0_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-20260331.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_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/2025/ecd-2025.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_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <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/2025/ecd-2025.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"/>
    <link:label id="lab_dei_Security12bTitle_019caf6e-900c-75d4-9202-19f1625404af_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>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_019caf6e-908a-752b-b803-fe432d42f81c_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/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019caf6e-908a-708c-b745-a453358006a6_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>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear_019caf6e-900c-73ea-b355-51c7127703bb_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-20260331.xsd#agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:to="lab_agm_LongTermDebtWithInterestRateResetMaturityReminderOfTheFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty_019caf6e-9089-777a-b0a9-81feab8da76c_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-20260331.xsd#agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty" xlink:to="lab_agm_DerivativeCollateralExceedingDerivativePositionAdditionalNetExposureFromCounterparty" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableRevolvingAbstract_019caf6e-900c-7ef8-ae6c-e59ec082818d_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-20260331.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_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff_019caf6e-900c-7b3b-b57a-a856a474a118_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" 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_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" 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, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnFairValueHedgesRecognizedInEarnings_019caf6e-9089-7b6a-ab99-6cd75e6de635_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">(Losses)/gains on 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/2025/elts/us-gaap-2025.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_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_019caf6e-9089-772a-bb86-bc046509a0cf_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/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_IncomeTaxEffectRelatedToReconcilingItems_019caf6e-900c-70f9-9071-7a21207393af_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-20260331.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_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_019caf6e-9089-7ed7-ad52-a90f1afceacc_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/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_019caf6e-908a-7312-8d7c-84a5dbc0d760_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/2025/elts/us-gaap-2025.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_agm_DebtSecuritiesAvailableForSaleMember_019caf6e-8f6f-74a8-b829-b9246e8b4695_verboseLabel_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Investment securities, Available-for-Sale, at fair value</link:label>
    <link:label id="lab_agm_DebtSecuritiesAvailableForSaleMember_label_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-For-Sale [Member]</link:label>
    <link:label id="lab_agm_DebtSecuritiesAvailableForSaleMember_documentation_en-US" xlink:label="lab_agm_DebtSecuritiesAvailableForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-For-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtSecuritiesAvailableForSaleMember" xlink:href="agm-20260331.xsd#agm_DebtSecuritiesAvailableForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_DebtSecuritiesAvailableForSaleMember" xlink:to="lab_agm_DebtSecuritiesAvailableForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtMaturityAfterYearFour_019caf6e-9089-79e1-b6f0-609db1a39646_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-20260331.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_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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_OtherNonInterestIncomeExpenseAdjusted_019caf6e-900c-7821-8d6c-de11d3e8ffe5_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-20260331.xsd#agm_OtherNonInterestIncomeExpenseAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_agm_OtherNonInterestIncomeExpenseAdjusted" xlink:to="lab_agm_OtherNonInterestIncomeExpenseAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019caf6e-900c-7a72-84a3-88844715f68d_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/2025/elts/us-gaap-2025.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_agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield_019caf6e-9089-77c7-84e3-a2bd468734b3_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>
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    <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-20260331.xsd#agm_HeldToMaturitySecuritiesDebtMaturitiesWeightedAverageYield"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_019caf6e-90f8-77d6-9af0-57362426cf2b_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/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
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    <link:label id="lab_us-gaap_DebtInstrumentInterestRateDuringPeriod_019caf6e-9089-781a-8700-6ade4cfce6e1_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/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateDuringPeriod"/>
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    <link:label id="lab_us-gaap_NetIncomeLoss_019caf6e-900c-7b83-a5e8-cfb283ea3e28_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>
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    <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_SegmentReportingInformationLineItems_019caf6e-9089-7193-873f-7ce312858cfd_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 Information [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 Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_019caf6e-8f6f-7b88-aa94-1689e80c4ed4_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/2025/elts/us-gaap-2025.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_PaymentsForRepurchaseOfCommonStock_019caf6e-900c-70fe-8ea5-b179dbd709b0_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/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
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    <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>
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    <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_ScheduleOfFinancingReceivablesPastDueTable_019caf6e-900c-726d-9e1f-49e53be30911_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/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivablesPastDueTable"/>
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    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_019caf6e-9089-7b75-92b5-c032b47e38b0_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">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/2025/elts/us-gaap-2025.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_RetainedEarningsAccumulatedDeficit_019caf6e-9089-7a45-9c76-6b0d45226c9a_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/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract_019caf6e-908a-77ed-8d67-ad7bea4fa671_terseLabel_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract_label_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Five or More Years before Latest Fiscal Year [Abstract]</link:label>
    <link:label id="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract_documentation_en-US" xlink:label="lab_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Originated Five or More Years before Latest Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract" xlink:href="agm-20260331.xsd#agm_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYearAbstract"/>
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    <link:label id="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem_019caf6e-900c-7d7d-942a-f753d6a0b670_negatedTerseLabel_en-US" xlink:label="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Recognized on hedged items</link:label>
    <link:label id="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem_label_en-US" xlink:label="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Net Hedge Ineffectiveness Gain Loss Component Recognized On Hedged Item</link:label>
    <link:label id="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem_documentation_en-US" xlink:label="lab_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Net Hedge Ineffectiveness Gain Loss Component Recognized On Hedged Item</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem" xlink:href="agm-20260331.xsd#agm_DerivativeNetHedgeIneffectivenessGainLossComponentRecognizedOnHedgedItem"/>
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    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
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    <link:label id="lab_agm_DebtInstrumentRedemptionAfterOneYearMember_019caf6e-8f6f-798e-8210-0e126f5591ff_terseLabel_en-US" xlink:label="lab_agm_DebtInstrumentRedemptionAfterOneYearMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total due after one year</link:label>
    <link:label id="lab_agm_DebtInstrumentRedemptionAfterOneYearMember_label_en-US" xlink:label="lab_agm_DebtInstrumentRedemptionAfterOneYearMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, After One Year [Member]</link:label>
    <link:label id="lab_agm_DebtInstrumentRedemptionAfterOneYearMember_documentation_en-US" xlink:label="lab_agm_DebtInstrumentRedemptionAfterOneYearMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, After One Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_agm_DebtInstrumentRedemptionAfterOneYearMember" xlink:href="agm-20260331.xsd#agm_DebtInstrumentRedemptionAfterOneYearMember"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireHeldToMaturitySecurities_019caf6e-8f6f-7fdc-bb1f-ef6d9230e6c3_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/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireHeldToMaturitySecurities"/>
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    <link:label id="lab_us-gaap_StatementClassOfStockAxis_019caf6e-908a-799f-87b5-61eff7f77f8e_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/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis"/>
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    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_019caf6e-900c-76a6-a9e0-ae7796a401a2_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019caf6e-9089-7b39-82f3-e74c6e999a3d_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019caf6e-900c-74d8-8737-891d4f7aad85_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income to net cash provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" 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 [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_agm_LongTermDebtNetOfHedgingAdjustments_019caf6e-90f8-7027-8577-cca3e00ba16c_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_019caf6e-90f8-7b77-a7e6-7ecdbd580966_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-20260331.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_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019caf6e-900c-7779-b0e4-5f2697c4c148_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/2025/elts/us-gaap-2025.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_agm_ScheduleOfAvailableForSaleAndTradingSecuritiesTable_019caf6e-900c-7360-9903-30b24d0b9877_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-20260331.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_ProceedsFromCollectionOfLoansHeldForSale_019caf6e-9089-77ba-8d56-6044756864c4_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/2025/elts/us-gaap-2025.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_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019caf6e-900c-7d37-9cc0-d4aefec04830_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/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
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    <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/2025/ecd-2025.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_dei_AmendmentFlag_019caf6e-908a-7acf-9d48-1191948ef099_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss_019caf6e-900c-7196-a79c-0d3527cfd324_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/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss"/>
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    <link:label id="lab_agm_AgricultureFinanceCorporateAgFinanceSegmentMember_019caf6e-900c-7bff-8aba-d6727d09dd49_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_019caf6e-900c-772d-84b1-b8e419b04126_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_019caf6e-900c-7b98-8b21-1dc01ead06bd_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-20260331.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_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" 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/2025/ecd-2025.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_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019caf6e-9089-735d-b5ec-d303f178ea54_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_019caf6e-9089-7301-91fb-0fc8ad64b0be_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_019caf6e-9089-7d05-b019-924d5d7b17f8_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_019caf6e-9089-787b-89bb-f2614e7fb61a_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/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne_019caf6e-9089-72dc-97f3-9349b7d4a6ac_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/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateYearOne"/>
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    <link:label id="lab_agm_LongTermStandbyPurchaseCommitmentsMember_019caf6e-8f6f-7480-ba06-2b9898a1e7c2_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-20260331.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_LoansAndFinanceReceivablesMember_019caf6e-9089-7949-8b8f-3655fc8a3a6b_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndFinanceReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Income Loans</link:label>
    <link:label id="lab_us-gaap_LoansAndFinanceReceivablesMember_label_en-US" xlink:label="lab_us-gaap_LoansAndFinanceReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Finance Receivables [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndFinanceReceivablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndFinanceReceivablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndFinanceReceivablesMember" xlink:to="lab_us-gaap_LoansAndFinanceReceivablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019caf6e-900c-7c2e-a3aa-205acd135c0a_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/2025/elts/us-gaap-2025.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_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019caf6e-900c-7676-82d3-3887c11a6c2e_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement_019caf6e-9089-7e94-9d6d-85f5e82274e0_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Amount Presented in the Consolidated Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Gross Asset Including Not Subject to Master Netting Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeAssetFairValueGrossAssetIncludingNotSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_019caf6e-9089-7e71-bb7d-4ea3ee5f58f7_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_019caf6e-900c-78de-b770-7499a64de5a4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <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/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax_019caf6e-90f8-7f49-9180-23a3f4765967_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>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from AOCI, Current Period, Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAociCurrentPeriodTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:to="lab_us-gaap_ReclassificationFromAociCurrentPeriodTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_019caf6e-908a-7fe4-a6e9-a8e3884f9ddb_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>
    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from AOCI, Current Period, before Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent"/>
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    <link:label id="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract_019caf6e-900c-7b9a-997b-49a1b5751820_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/2025/elts/us-gaap-2025.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_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/2025/ecd-2025.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_CommonStockParOrStatedValuePerShare_019caf6e-908a-785a-ad5f-b015a88a3391_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
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    <link:label id="lab_srt_ConsolidatedEntitiesAxis_019caf6e-900d-779f-a5ab-51cb5fa770a4_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis"/>
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    <link:label id="lab_agm_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYearAbstract_019caf6e-900c-7f68-ad37-abad4de3af48_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>
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    <link:label id="lab_agm_SegmentCoreEarnings_019caf6e-900c-7196-af87-333728b3e9b9_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-20260331.xsd#agm_SegmentCoreEarnings"/>
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    <link:label id="lab_agm_LongTermDebtWithInterestRateResetMaturityYearOne_019caf6e-900c-7f85-a8fa-adcfe8c4ec39_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-20260331.xsd#agm_LongTermDebtWithInterestRateResetMaturityYearOne"/>
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    <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-20260331.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_019caf6e-900c-7ec4-aee3-eb2690c4b62c_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-20260331.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_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements_019caf6e-9089-779c-ada9-a037de07ba62_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Settlements</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" 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, Settlements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements"/>
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    <link:label id="lab_us-gaap_GuaranteeObligationsByNatureAxis_019caf6e-900c-73ca-849d-11dfe719aa9c_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsByNatureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Nature [Axis]</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsByNatureAxis_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsByNatureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Nature [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsByNatureAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GuaranteeObligationsByNatureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsByNatureAxis" xlink:to="lab_us-gaap_GuaranteeObligationsByNatureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Capital_019caf6e-900c-7a85-a452-ce9b87b59ff7_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/2025/elts/us-gaap-2025.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_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_019caf6e-9089-7e05-9830-6a9c19c41dca_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/(expense) related to other comprehensive (loss)/income</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_019caf6e-9089-74b4-b899-e67510c54d29_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/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1"/>
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    <link:label id="lab_agm_NoncashOrPartNoncashAcquisitionLoansAcquired_019caf6e-900c-78f6-9929-f2ce7adc0829_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-20260331.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_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_019caf6e-90f8-7d61-8017-d77dfb03f826_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value Measurements</link:label>
    <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/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_019caf6e-9089-766a-a211-87067038b771_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" 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_DerivativeAssetFairValueGrossLiability_019caf6e-9089-7e8a-bab8-81cc1917610c_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/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetFairValueGrossLiability"/>
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    <link:label id="lab_agm_UnclearedSwapsMember_019caf6e-90f8-79b3-881a-fc0798cd6894_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-20260331.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_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/2025/ecd-2025.xsd#ecd_InsiderTradingArrLineItems"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_019caf6e-900c-7e61-914b-e62f1bb495a0_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" 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_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Originated, More than Five Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear"/>
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    <link:label id="lab_agm_DueYearOneMember_019caf6e-900c-740c-aca0-6628a3a1ddc7_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-20260331.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_FinancialAssetNotPastDueMember_019caf6e-90f8-7fdd-b6c2-67a3a54f0bf5_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/2025/elts/us-gaap-2025.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_DebtSecuritiesAvailableForSaleAmortizedCostAllowanceForCreditLossExcludingAccruedInterest_019caf6e-900c-7645-be24-79d0618d3420_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/2025/elts/us-gaap-2025.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_Liabilities_019caf6e-900c-7c16-b09d-ca198e48dbfa_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_019caf6e-900c-7d85-8853-75324ac36ec3_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">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/2025/elts/us-gaap-2025.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_us-gaap_AntidilutiveSecuritiesNameDomain_019caf6e-900c-70a4-ac06-df4f1a9b90df_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/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember_019caf6e-9089-72e3-baca-cf825745a4f5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Five years</link:label>
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