Book contents
- Frontmatter
- Contents
- 0 Introduction
- 1 Curves of genus 0. Introduction
- 2 p-adic numbers
- 3 The local-global principle for conies
- 4 Geometry of numbers
- 5 Local-global principle. Conclusion of proof
- 6 Cubic curves
- 7 Non-singular cubics. The group law
- 8 Elliptic curves. Canonical form
- 9 Degenerate laws
- 10 Reduction
- 11 The p-adic case
- 12 Global torsion
- 13 Finite basis theorem. Strategy and comments
- 14 A 2-isogeny
- 15 The weak finite basis theory
- 16 Remedial mathematics. Resultants
- 17 Heights. Finite basis Theorem
- 18 Local-global for genus 1
- 19 Elements of Galois cohomology
- 20 Construction of the jacobian
- 21 Some abstract nonsense
- 22 Principal homogeneous spaces and Galois cohomology
- 23 The Tate-Shafarevich group
- 24 The endomorphism group
- 25 Points over finite fields
- 26 Factorizing using elliptic curves
- Formulary
- Further Reading
- Index
10 - Reduction
Published online by Cambridge University Press: 05 June 2012
Book contents
- Frontmatter
- Contents
- 0 Introduction
- 1 Curves of genus 0. Introduction
- 2 p-adic numbers
- 3 The local-global principle for conies
- 4 Geometry of numbers
- 5 Local-global principle. Conclusion of proof
- 6 Cubic curves
- 7 Non-singular cubics. The group law
- 8 Elliptic curves. Canonical form
- 9 Degenerate laws
- 10 Reduction
- 11 The p-adic case
- 12 Global torsion
- 13 Finite basis theorem. Strategy and comments
- 14 A 2-isogeny
- 15 The weak finite basis theory
- 16 Remedial mathematics. Resultants
- 17 Heights. Finite basis Theorem
- 18 Local-global for genus 1
- 19 Elements of Galois cohomology
- 20 Construction of the jacobian
- 21 Some abstract nonsense
- 22 Principal homogeneous spaces and Galois cohomology
- 23 The Tate-Shafarevich group
- 24 The endomorphism group
- 25 Points over finite fields
- 26 Factorizing using elliptic curves
- Formulary
- Further Reading
- Index
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- LMSST: 24 Lectures on Elliptic Curves , pp. 42 - 45Publisher: Cambridge University PressPrint publication year: 1991