Chapters in this book

1. Frontmatter i
2. CONTENTS vii
3. List of Figures x
4. List of Tables x
5. Preface xi
6. Standard Notation xv
7. Elliptic Curves 1
8. I. Overview 3
9. II. Curves in Projective Space 19
10. III. Cubic Curves in Weierstrass Form 50
11. IV. Mordell's Theorem 80
12. V. Torsion Subgroup of E(Q) 130
13. VI. Complex Points 151
14. VII. Dirichlet's Theorem 189
15. VIII. Modular Forms for SL(2,ℤ) 221
16. IX. Modular Forms for Hecke Subgroups 256
17. X. L Function of an Elliptic Curve 290
18. XI. Eichler-Shimura Theory 302
19. XII. Taniyama-Weil Conjecture 386
20. Notes 401
21. References 409
22. Index of Notation 419
23. Index 423