Elliptic Curves

Table of Contents

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   Book Overview
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   Chapter 1 Introduction to Rational Points on Plane Curves
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   Chapter 2 Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve
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   Chapter 3 Plane Algebraic Curves
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   Chapter 4 Elliptic Curves and Their Isomorphisms
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   Chapter 5 Families of Elliptic Curves and Geometric Properties of Torsion Points
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   Chapter 6 Reduction mod p and Torsion Points
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   Chapter 7 Proof of Mordell’s Finite Generation Theorem
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   Chapter 8 Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields
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    Chapter 9 Descent and Galois Cohomology
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    Chapter 10 Elliptic and Hypergeometric Functions
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    Chapter 11 Theta Functions
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    Chapter 12 Modular Functions
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    Chapter 13 Endomorphisms of Elliptic Curves
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    Chapter 14 Elliptic Curves over Finite Fields
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    Chapter 15 Elliptic Curves over Local Fields
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    Chapter 16 Elliptic Curves over Global Fields and ℓ-Adic Representations
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    Chapter 17 L -Function of an Elliptic Curve and Its Analytic Continuation
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    Chapter 18 Remarks on the Birch and Swinnerton-Dyer Conjecture
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    Chapter 19 Remarks on the Modular Elliptic Curves Conjecture and Fermat’s Last Theorem
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    Chapter 20 Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties
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    Chapter 21 Families of Elliptic Curves