# Fungrim entry: a0dff6

$E_{6}^{2}\!\left(\tau\right) = \frac{1}{8} \left({\left({a}^{8} + {b}^{8} + {c}^{8}\right)}^{3} - 54 {\left(a b c\right)}^{8}\right)\; \text{ where } a = \theta_{2}\!\left(0 , \tau\right),\,b = \theta_{3}\!\left(0 , \tau\right),\,c = \theta_{4}\!\left(0 , \tau\right)$
Assumptions:$\tau \in \mathbb{H}$
TeX:
E_{6}^{2}\!\left(\tau\right) = \frac{1}{8} \left({\left({a}^{8} + {b}^{8} + {c}^{8}\right)}^{3} - 54 {\left(a b c\right)}^{8}\right)\; \text{ where } a = \theta_{2}\!\left(0 , \tau\right),\,b = \theta_{3}\!\left(0 , \tau\right),\,c = \theta_{4}\!\left(0 , \tau\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), Where(Mul(Div(1, 8), Sub(Pow(Add(Add(Pow(a, 8), Pow(b, 8)), Pow(c, 8)), 3), Mul(54, Pow(Mul(Mul(a, b), c), 8)))), Equal(a, JacobiTheta(2, 0, tau)), Equal(b, JacobiTheta(3, 0, tau)), Equal(c, JacobiTheta(4, 0, tau))))),
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.

2019-08-19 14:38:23.809000 UTC