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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:alsoKnownAs
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modular invariant
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gptkbp:class
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isomorphism classes of elliptic curves over C
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gptkbp:definedIn
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gptkb:elliptic_curve
gptkb:Hilbert_class_polynomial
modular polynomial
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gptkbp:field
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gptkb:algebraic_geometry
gptkb:mathematics
complex analysis
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gptkbp:function
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modular parameter tau
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gptkbp:hasApplication
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cryptography
class field theory
complex multiplication
moduli spaces
moonshine theory
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gptkbp:hasExplicitFormula
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j(τ) = 1728 g_2^3 / (g_2^3 - 27 g_3^2)
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gptkbp:hasFourierExpansion
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j(τ) = q^{-1} + 744 + 196884q + ...
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gptkbp:hasInvariant
|
isomorphism of elliptic curves
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gptkbp:hasPoleAt
|
infinity
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https://www.w3.org/2000/01/rdf-schema#label
|
j-invariant
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gptkbp:isAlgebraicInteger
|
for CM elliptic curves
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gptkbp:isAlgebraicOver
|
Q for CM points
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gptkbp:isHauptmodulFor
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gptkb:modular_curve_X(1)
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gptkbp:isHolomorphicExceptAt
|
infinity
|
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gptkbp:isMeromorphicOn
|
upper half-plane
|
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gptkbp:isModularFunctionFor
|
gptkb:SL(2,_Z)
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gptkbp:isRationalFunctionOf
|
g_2 and g_3
|
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gptkbp:isSurjectiveOnto
|
C
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gptkbp:isTranscendentalFor
|
non-CM points
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gptkbp:mapType
|
complex number
|
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gptkbp:namedAfter
|
gptkb:Felix_Klein
|
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gptkbp:notation
|
j
j(τ)
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gptkbp:q
|
e^{2πiτ}
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gptkbp:usedIn
|
modular forms
number theory
elliptic curves
|
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gptkbp:bfsParent
|
gptkb:modular_group
gptkb:elliptic_curve
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gptkbp:bfsLayer
|
5
|