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Fungrim entry: 44a529

j ⁣(τ)=256(1λ ⁣(τ)+(λ ⁣(τ))2)3(λ ⁣(τ))2(1λ ⁣(τ))2j\!\left(\tau\right) = 256 \frac{{\left(1 - \lambda\!\left(\tau\right) + {\left(\lambda\!\left(\tau\right)\right)}^{2}\right)}^{3}}{{\left(\lambda\!\left(\tau\right)\right)}^{2} {\left(1 - \lambda\!\left(\tau\right)\right)}^{2}}
Assumptions:τH\tau \in \mathbb{H}
TeX:
j\!\left(\tau\right) = 256 \frac{{\left(1 - \lambda\!\left(\tau\right) + {\left(\lambda\!\left(\tau\right)\right)}^{2}\right)}^{3}}{{\left(\lambda\!\left(\tau\right)\right)}^{2} {\left(1 - \lambda\!\left(\tau\right)\right)}^{2}}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ModularJj ⁣(τ)j\!\left(\tau\right) Modular j-invariant
Powab{a}^{b} Power
ModularLambdaλ ⁣(τ)\lambda\!\left(\tau\right) Modular lambda function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("44a529"),
    Formula(Equal(ModularJ(tau), Mul(256, Div(Pow(Add(Sub(1, ModularLambda(tau)), Pow(ModularLambda(tau), 2)), 3), Mul(Pow(ModularLambda(tau), 2), Pow(Sub(1, ModularLambda(tau)), 2)))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-09-16 21:17:18.797188 UTC