WeierstrassPPrime 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.
If and for some complex number , the pair satisfies the defining equation for the curve, .
The derivative of is an even elliptic function with poles only at the origin (in the fundamental parallelogram), so it must be expressible in terms of .
This plot illustrates that has periods and (here and ).