The Arithmetic of Elliptic Curves [Paperback]

Algebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of an Elliptic Curve.- Elliptic Curves over Finite Fields.- Elliptic Curves over C.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields.- Integral Points on Elliptic Curves.- Computing the Mordell#x2013;Weil Group.- Algorithmic Aspects of Elliptic Curves.

From the reviews of the second edition:

This well-written book covers the basic facts about the geometry and arithmetic of elliptic curves, and is sure to become the standard reference in the subject. It meets the needs of at least three groups of people: students interested in doing research in Diophantine geometry, mathematicians needing a reference for standard facts about elliptic curves, and computer scientists interested in algorithms and needing an introduction to elliptic curves... -- MATHEMATICAL REVIEWS

The book under review is the second, revised, enlarged, and updated edition of J. Silvermans meanwhile classical primer of the arithmetic of elliptic curves. & All together, this enlarged and updated version of J. Silvermans classic The Arithmetic of Elliptic Curves significantly increases the unchallenged value of this modern primer as a standard textbook in the field. & This makes the entire text a perfect source for teachers and students, for courses and self-study, and for further studies in the arithmetic of elliptic curves likewise. (Werner Kleinert, Zentralblatt MATH, Vol. 1194, 2010)

For the second edition of his masterly book, the author considerably updated and improved several results and proofs. & book contains a great many exercises, many of which develop or complement the results from the main body of the book. & The reference list contains 317 items and reflects both classical and recent achievements on the topic. Notes on the exercises are an aid to the reader. & Summarizing, this is an excellent book & . usefullã7