Lectures on elliptic curves - Cassels, J. W. S. (Cambridge Cambridge University Press, 1995)
1. Curves of genus 0. Introduction 3 -- 2. p-adic numbers 6 -- 3. Local-global principle for conics 13 -- 4. Geometry of numbers 17 -- 5. Local-global principle - Conclusion of proof 20 -- 6. Cubic curves 23 -- 7. Non-singular cubics - The group law 27 -- 8. Elliptic curves- Canonical form 32 -- 9. Degenerate laws 39 -- 10. Reduction 42 -- 11. P-adic case 46 -- 12. Global torsion 50 -- 13. Finite basis theorem. Strategy and comments 54 -- 14. A 2-isogeny 58 -- 15. Weak finite basis theory 66 -- 16. Remedial mathematics. Resultants 75 -- 17. Heights - Finite basis Theorem 78 -- 18. Local-global for genus 1 85 -- 19. Elements of Galois cohomology 89 -- 20. Construction of the jacobian 92 -- 21. Some abstract nonsense 98 -- 22. Principal homogeneous spaces and Galois cohomology 104 -- 23. Tate-Shafarevich group 108 -- 24. Endomorphism group 114 -- 25. Points over finite fields 118 -- 26. Factorizing using elliptic curves 124.
Includes bibliographical references (page 135) and index.
Keywords: Curves, Elliptic