Elliptic functions (awaiting review)

The first example is through the theory of elliptic functions, and the closely related elementary theory of elliptic curves over $\C$: in this context, the functions that arise naturally are the Eisenstein series $E_k$ (or their alternately normalized counterparts $F_k$ and $G_k$), the quasi-modular Eisenstein series $E_2$, the discriminant function $\Delta$ and the elliptic modular invariant $j$.