Modular Forms Software - HECKE can be used to compute basis of q-expansions and Hecke operators on fairly general spaces of modular forms.TECC - Tiny Elliptic Curve Calculator, by Masanari Kida. Requires KASH 2.2.
MWRANK - Mordell-Weil rank of elliptic curves over the rationals, by John Cremona.
The CAGE Project - Classes for Algebraic Geometry and Ellliptic Curves, implemented in C++.
APECS - FTP site for Ian McConnell's MAPLE programs.
ECPC Demonstration - Harley's implementation of Satoh's ECPC algorithm is offered here as a demonstration for Linux PCs.
Heegner Tools - Peter Green's Heegner Points package. Requires Linux and Pari/GP 2.1.1 or higher.