Rational Points on Elliptic Curves

See our review of the first edition of this excellent book. The two main changes for this edition are a new section on elliptic curve cryptography and an explanation of how elliptic curves played a role in the proof of Fermat’s Last Theorem.

When I arrived at Harvard in 1983, everyone was talking about elliptic curves. I had never heard of them, so I needed to learn fast. What everyone recommended were “Tate’s Haverford lectures.” Naïve as I was, I asked Tate for a copy. He told me he didn’t have one. As I found out, the lecture notes circulated only in samizdat form, badly photocopied from a previous bad photocopy.

No need for that any more: those lectures, expanded and improved, form the first three and a half chapters of this book. The remaining chapters offer a glimpse of other topics in the theory. And, perhaps most importantly, there are exercises.

This is probably still the best place to start learning about elliptic curves.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME. He now knows a little more about elliptic curves.