What is in These Tables?

Most of the standard arithmetic invariants of each curve. This data gives very strong corroboration for the famous conjecture of Birch and Swinnerton-Dyer, which ties these invariants together. (There is no known provably-correct algorithm to compute all the invariants appearing in the conjecture, but we usually succeed in practice.)
If there is a "homomorphism" from E onto F, we say that E and F are isogenous (isogeny is an equivalence relation). The curves are divided up into isogeny classes, and the structure of the isogenies is given.
Gave evidence for the Shimura-Taniyama conjecture (before it was proved by Taylor, Wiles, Breuil, Conrad, and Diamond).

If there is a "homomorphism" from E onto F, we say that E and F are isogenous (isogeny is an equivalence relation). The curves are divided up into isogeny classes, and the structure of the isogenies is given.