A Landen-type Method for Computation of Weierstrass Functions

We establish a version of the Landen transformation forWeierstrass functions and invariants that is applicable to generallattices in the complex plane. Using it we present an effectivemethod for computing the Weierstrass functions, their periods, andelliptic integral in the Weierstrass form given Weierstrassinvariants \(g_{2}\) and \(g_{3}\) of an elliptic curve. Similarly to theclassical Landen method, our algorithm has quadratic rate ofconvergence.