# Fungrim entry: a0dff6

$E_{6}^{2}\!\left(\tau\right) = \frac{1}{8} \left({\left(\theta_{2}^{8}\!\left(0, \tau\right) + \theta_{3}^{8}\!\left(0, \tau\right) + \theta_{4}^{8}\!\left(0, \tau\right)\right)}^{3} - 54 {\left(\theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right)\right)}^{8}\right)$
Assumptions:$\tau \in \mathbb{H}$
TeX:
E_{6}^{2}\!\left(\tau\right) = \frac{1}{8} \left({\left(\theta_{2}^{8}\!\left(0, \tau\right) + \theta_{3}^{8}\!\left(0, \tau\right) + \theta_{4}^{8}\!\left(0, \tau\right)\right)}^{3} - 54 {\left(\theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right)\right)}^{8}\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
EisensteinE$E_{k}\!\left(\tau\right)$ Normalized Eisenstein series
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("a0dff6"),
Formula(Equal(Pow(EisensteinE(6, tau), 2), Mul(Div(1, 8), Sub(Pow(Add(Add(Pow(JacobiTheta(2, 0, tau), 8), Pow(JacobiTheta(3, 0, tau), 8)), Pow(JacobiTheta(4, 0, tau), 8)), 3), Mul(54, Pow(Mul(Mul(JacobiTheta(2, 0, tau), JacobiTheta(3, 0, tau)), JacobiTheta(4, 0, tau)), 8)))))),
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.

2021-03-15 19:12:00.328586 UTC