Let $g_2,g_3\in \mathbb{C}$ be two complex numbers, and by the previous proposition let $L={\omega }_1\mathbb{Z}+{\omega }_2\mathbb{Z}$ be the associated lattice, $\mathrm{\wp }(z)$ the associated $\mathrm{\wp }$ function. We define the cubic curve, given $g_2,g_3$ as 1;;$\gamma =\{(y,w)\in \mathbb{C}\times \mathbb{C}|w^2=4y^3-g_{2}y-g_3\}$. We further remark that $(\mathrm{\wp }(z),{\mathrm{\wp }}^{\prime }(z))$ parametrizes this curve in a 1-1 correspondence, if we mod out by the Lattice. So we have a bijective map: