The Arithmetic of Elliptic Curves

• Main Author: Silverman, Joseph H. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Graduate Texts in Mathematics, 106
• Subjects: Mathematics.; Algebra.; Geometry, algebraic.; Number theory.; Algebraic Geometry.; Number Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-09494-6

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 b...

Table of Contents:

• Preface to the Second Edition
• Preface to the First Edition
• Introduction
• 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 MordellWeil Group
• Algorithmic Aspects of Elliptic Curves
• Appendix A: Elliptic Curves in Characteristics 2 and 3
• Appendix B: Group Cohomology (H0 and H1)
• Appendix C: Further Topics: An Overview
• Notes on Exercises
• Bibliography
• List of Notation
• References
• Index.