Fungrim entry: 664b4c

j\!\left(\tau\right) = {\left({\left(\frac{\eta\!\left(\tau\right)}{\eta\!\left(2 \tau\right)}\right)}^{8} + {2}^{8} {\left(\frac{\eta\!\left(2 \tau\right)}{\eta\!\left(\tau\right)}\right)}^{16}\right)}^{3}

Assumptions:

\tau \in \mathbb{H}

TeX:

j\!\left(\tau\right) = {\left({\left(\frac{\eta\!\left(\tau\right)}{\eta\!\left(2 \tau\right)}\right)}^{8} + {2}^{8} {\left(\frac{\eta\!\left(2 \tau\right)}{\eta\!\left(\tau\right)}\right)}^{16}\right)}^{3}

\tau \in \mathbb{H}

Definitions:

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

Source code for this entry:

Entry(ID("664b4c"),
    Formula(Equal(ModularJ(tau), Pow(Add(Pow(Div(DedekindEta(tau), DedekindEta(Mul(2, tau))), 8), Mul(Pow(2, 8), Pow(Div(DedekindEta(Mul(2, tau)), DedekindEta(tau)), 16))), 3))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Modular j-invariant