This page was prepared for a workshop at the Workshop on Modular Forms: Arithmetic and Computation, BIRS (Banff, Canada) 3-8 June 2007.
Magma has a huge amount of functionality for working with elliptic curves over Q, number fields, finite fields, and general fields.
It includes the database of all elliptic curves over Q with conductor less than 130000 (but none of the data in the database is made available apart from the curves themselves).
Pari/GP has a many functions for working with elliptic curves over Q, and a few fir general fields. There are also some add-on packages (e.g. mine for group structure over F_{p} and for analytic rank).
An optional extra database has all elliptic curves of conductor up to 130000, together with ranks and generators mod torsion.
Has all Pari/GP functionality and access to mwrank and my other elliptic curve programs, but currently there is a lot not yet available (unless you also have Magma installed)