Number of points on elliptic curve

Have you heard of Sage?

Sage includes Pari, which is an open source package for number theory. Pari has an implementation of SEA.

From http://wstein.org/papers/2008-bordeaux/sphinx/elliptic_curves.html#schoof-elkies-atkin-point-counting:

sage: k = GF(next_prime(10^20))
sage: E = EllipticCurve(k.random_element())
sage: E.cardinality()                   # less than a second
100000000005466254167