Elliptic curves : a computational approach / Susanne Schmitt, Horst G. Zimmer ; with an appendix by Attila Petho.

Format:

Book

Author/Creator:

Schmitt, Susanne.

Contributor:

Zimmer, Horst G.

Series:

Gruyter studies in mathematics ; 31.

De Gruyter studies in mathematics ; 31

Language:

English

Subjects (All):

Curves, Elliptic.

Physical Description:

1 online resource (377 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; New York : Walter de Gruyter, c2003.

Language Note:

English

Summary:

The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available.

Contents:

Front matter

Contents

Chapter 1. Elliptic curves

Chapter 2. Elliptic curves over the complex numbers

Chapter 3. Elliptic curves over finite fields

Chapter 4. Elliptic curves over local fields

Chapter 5. The Mordell-Weil theorem and heights

Chapter 6. Torsion group

Chapter 7. The rank

Chapter 8. Basis

Chapter 9. S-integral points

Appendix A. Algorithmic theory of diophantine equations

Appendix B. Multiquadratic number fields

Back matter

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [351]-363) and index.

ISBN:

9786612194283

9781282194281

1282194283

9783110198010

3110198010

OCLC:

232160036