The arithmetic of elliptic curves：橢圓曲線算術（第2版）

Preface to the Second Edition
Preface to the First Edition
Introduction
CHAPTER 1
Algebraic Varieties
1. Affine Varieties
2. Projective Varieties
3. Maps Between Varieties
Exercises

CHAPTER 2
Algebraic Curves
1. Curves
2. Maps Between Curves
3. Divisors
4. Differentials
5. The Riemarm-Roch Theorem
Exercises

CHAPTER 3
The Geometry of Elliptic Curves
1. Weierstrass Equations
2. The Group Law
3. Elliptic Curves
4. Isogenies
5. The Invariant Differential
6. The Dual Isogeny
7. The Tate Module
8. The Weil Pairing
9. The Endomorphism Ring
10. The Automorphism Group
Exercises

CHAPTER 4
The Formal Group of an Elliptic Curve
1. Expansion Around O
2. Formal Groups
3. Groups Associated to Formal Groups
4. The Invariant Differential
5. The Formal Logarithm
6. Formal Groups over Discrete Valuation Rings
7. Formal Groups in Characteristic p
Exercises

CHAPTER 5
Elliptic Curves over Finite Fields
1. Number of Rational Points
2. The Weil Conjectures
3. The Endomorphism Ring
4. Calculating the Hasse Invariant
Exercises

CHAPTER 6
Elliptic Curves over C
1. Elliptic Integrals
2. Elliptic Functions
3. Construction of Elliptic Functions
4. Maps Analytic and Maps Algebraic
5. Uniformization
6. The Lefschetz Principle
Exercises

CHAPTER 7
Computing the Mordell-Weil Group
CHAPTER 8
Algorithmic Aspects of Elliptic Curves
APPENDIX