UID:
edocfu_9958353763402883
Format:
1 online resource (376p.)
ISBN:
9783110198010
Series Statement:
De Gruyter Studies in Mathematics, 31
Content:
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.
Note:
Frontmatter --
,
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 --
,
Backmatter
,
In English.
Additional Edition:
ISBN 978-3-11-916163-3
Additional Edition:
ISBN 978-3-11-016808-2
Language:
English
DOI:
10.1515/9783110198010
URL:
https://doi.org/10.1515/9783110198010
