For any pair of complex numbers $g_2,g_3\in \mathbb{C}$, we can find a lattice $L={\omega }_1\mathbb{Z}+{\omega }_2\mathbb{Z}$ such that $g_2=60\sum _{\omega \ne 0}\frac{1}{{\omega }^4}$ and $g_3=\sum _{\omega \ne 0}\frac{1}{{\omega }^6}$. Furthermore, the Weierstrauss $\mathrm{\wp }$-function for this lattice satisfies the differential equation:
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The general solution for this differential equation looks like $\mathrm{\wp }(z+a)$ for some constant $a\in \mathbb{C}$.