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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:automorphismGroup
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gptkb:modular_group
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gptkbp:canBe
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compactified
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gptkbp:canBeDefinedOver
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rational numbers
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gptkbp:compact
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adding cusps
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gptkbp:definedIn
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complex numbers
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gptkbp:example
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X(N)
X_0(N)
X_1(N)
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gptkbp:field
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gptkb:mathematics
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gptkbp:genus
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depends on level N
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gptkbp:hasSubfield
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gptkb:algebraic_geometry
number theory
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gptkbp:isQuotientOf
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upper half-plane by congruence subgroup
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gptkbp:parameterize
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isomorphism classes of elliptic curves with level structure
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gptkbp:relatedTo
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gptkb:modular_abelian_varieties
gptkb:modularity_theorem
gptkb:moduli_space
gptkb:modular_function
Hecke operators
modular forms
elliptic curves
Galois representations
Jacobians of modular curves
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gptkbp:studiedBy
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gptkb:Yutaka_Taniyama
gptkb:André_Weil
gptkb:Jean-Pierre_Serre
gptkb:Goro_Shimura
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gptkbp:usedIn
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proof of Fermat's Last Theorem
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gptkbp:bfsParent
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gptkb:Klein_quartic
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gptkbp:bfsLayer
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5
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https://www.w3.org/2000/01/rdf-schema#label
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modular curves
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