Fungrim entry: dc8251

j(\tau) = \frac{E_{4}^{3}\!\left(\tau\right)}{\eta^{24}\!\left(\tau\right)}

Assumptions:

\tau \in \mathbb{H}

TeX:

j(\tau) = \frac{E_{4}^{3}\!\left(\tau\right)}{\eta^{24}\!\left(\tau\right)}

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`ModularJ`	$j(\tau)$	Modular j-invariant
`Pow`	${a}^{b}$	Power
`EisensteinE`	$E_{k}\!\left(\tau\right)$	Normalized Eisenstein series
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("dc8251"),
    Formula(Equal(ModularJ(tau), Div(Pow(EisensteinE(4, tau), 3), Pow(DedekindEta(tau), 24)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Modular j-invariant

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

2021-03-15 19:12:00.328586 UTC