Here is the derivative. (This also verifies the defining differential equation.)
This is the integral.
WeierstrassZeta takes as a second argument the coefficients of the equation of the elliptic curve under consideration (in Weierstrass normal form). If instead we know the periods of the curve, we start by using WeierstrassInvariants.
The Weierstrass zeta function satisfies the following quasiperiodicity condition: if is any element of the lattice generated by the periods and , then for all , where is a constant depending on . For , we have . Here is an example, with :
This unsets the variables.