EllipticExp[u, a, b] is the inverse for EllipticLog. It produces a list x, y such that u == EllipticLog[x, y, a, b].
EllipticExp gives the generalized exponential associated with the elliptic curve .
EllipticExp is the basis for computing Weierstrass functions in Mathematica.
See The Mathematica Book: Section 3.2.11.