To "play" with symbolic math software.

Click on the download link at the Pari website ( http://pari.math.u-bordeaux.fr/ ) at the math department of the University of Bordeaux in France, for Pari, a free symbolic calculator similar to ones used by number theory scientists like Henri Darmon. The Pari download includes an excellent user manual and a 46 page tutorial to get you started experimenting with numbers. Be sure to look at the tutorial right away. It gives examples of things to type into Pari to immediately discover what it can do. Functions exist for number fields and elliptic curves among many other number theory tools.