Invariant (Elliptic Function)

The invariants of a Weierstraß Elliptic Function are defined by

$$\begin{eqnarray*} g_2&\equiv& 60\Sigma' {\Omega_{mn}}^{-4}\\ g_3&\equiv& 140\Sigma' {\Omega_{mn}}^{-6}. \end{eqnarray*}$$

Here,

$$\Omega_{mn}\equiv 2m\omega_1-2n\omega_2,$$

where $\omega_1$ and $\omega_2$ are the periods of the Elliptic Function.