The Arithmetic of Elliptic Curves

Graduate Texts in Mathematics #106

by Joseph H. Silverman

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel's theorem and explicit computations for the curve Y^2 = X^3 + DX. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics.

Genres: Mathematics, Geometry, Algebra, Reference, Number Theory, Theory, Number

Hardcover

First published October 14, 1985

Reviews

[Will · Rating 5 out of 5]

The character development was excellent, but the plot was a little threadbare.

[Dan · Rating 4 out of 5]

I used this book for a term paper I was writing.

Joseph Silverman is a good author to learn from. His books are easier to read and more user friendly than Serge Lang's.

[Wissam Raji · Rating 5 out of 5]

A classic and one of the most famous introductory books to the theory of elliptic curves. The treatment of the topics in elliptic curves is very clear. The book is self-contained and well-written. There is another book that deals with advanced topics. This book can be read by advanced undergraduate students who are interested in the theory of elliptic curves and the geometric aspects of the theory.

[Satyaki]

https://www.youtube.com/playlist?list...

[Didier "Dirac Ghost" Gaulin · Rating 3 out of 5]

Great little reference book, perfect for a beginner who is studying cryptography, for the mathematicians, not so much, as many proofs are omitted.