Contents

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Chapter 1. Elliptic curves 1
4. Chapter 2. Elliptic curves over the complex numbers 33
5. Chapter 3. Elliptic curves over finite fields 63
6. Chapter 4. Elliptic curves over local fields 87
7. Chapter 5. The Mordell-Weil theorem and heights 103
8. Chapter 6. Torsion group 147
9. Chapter 7. The rank 198
10. Chapter 8. Basis 242
11. Chapter 9. S-integral points 263
12. Appendix A. Algorithmic theory of diophantine equations 294
13. Appendix B. Multiquadratic number fields 316
14. Backmatter 351