# Fungrim entry: 44a529

$j\!\left(\tau\right) = 256 \frac{{\left(1 - \lambda\!\left(\tau\right) + {\left(\lambda\!\left(\tau\right)\right)}^{2}\right)}^{3}}{{\left(\lambda\!\left(\tau\right)\right)}^{2} {\left(1 - \lambda\!\left(\tau\right)\right)}^{2}}$
Assumptions:$\tau \in \mathbb{H}$
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
ModularJ$j\!\left(\tau\right)$ Modular j-invariant
Pow${a}^{b}$ Power
ModularLambda$\lambda\!\left(\tau\right)$ Modular lambda function
HH$\mathbb{H}$ 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)))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-16 21:17:18.797188 UTC