The Arithmetic of Elliptic Curves
Joseph H. Silverman(Author)
Springer (Publisher)
198th Edition
Published on 31. December 1986
Book
Hardback
400 pages
978-3-540-96203-8 (ISBN)
Article exhausted; check for reprint
Description
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 algebraic-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 Siegels Theorem and explicit computations for the curve Y2=X3+DX.
More details
Series
Edition
198., Corr. 3rd printing
Language
German
Place of publication
Berlin
Germany
Target group
College/higher education
Illustrations
13 figs. XII,400 pages.
Dimensions
Height: 216 mm
Width: 138 mm
Weight
730 gr
ISBN-13
978-3-540-96203-8 (9783540962038)
Schweitzer Classification
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Joseph H. Silverman
The Arithmetic of Elliptic Curves
Book
05/2009
2nd Edition
Springer
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Content
Algebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of Elliptic Curves.- 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 Weil Group.- Appendix A: Elliptic Curves in Characteristics.-Appendix B: Group Cohomology (H0 and H1).