Elliptic Curves

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ISBN: 978-0-387-95490-5 (Print) 978-0-387-21577-8 (Online)

Table of contents (21 chapters)

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  1. No Access

    Book Chapter

    Pages 1-22

    Introduction to Rational Points on Plane Curves

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    Book Chapter

    Pages 23-43

    Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve

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    Book Chapter

    Pages 45-63

    Plane Algebraic Curves

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    Book Chapter

    Pages 65-84

    Elliptic Curves and Their Isomorphisms

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    Book Chapter

    Pages 85-102

    Families of Elliptic Curves and Geometric Properties of Torsion Points

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    Book Chapter

    Pages 103-123

    Reduction mod p and Torsion Points

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    Book Chapter

    Pages 125-142

    Proof of Mordell’s Finite Generation Theorem

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    Book Chapter

    Pages 143-156

    Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields

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    Book Chapter

    Pages 157-166

    Descent and Galois Cohomology

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    Book Chapter

    Pages 167-187

    Elliptic and Hypergeometric Functions

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    Book Chapter

    Pages 189-207

    Theta Functions

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    Book Chapter

    Pages 209-231

    Modular Functions

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    Book Chapter

    Pages 233-252

    Endomorphisms of Elliptic Curves

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    Book Chapter

    Pages 253-273

    Elliptic Curves over Finite Fields

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    Book Chapter

    Pages 275-289

    Elliptic Curves over Local Fields

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    Book Chapter

    Pages 291-308

    Elliptic Curves over Global Fields and ℓ-Adic Representations

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    Book Chapter

    Pages 309-324

    L-Function of an Elliptic Curve and Its Analytic Continuation

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    Book Chapter

    Pages 325-332

    Remarks on the Birch and Swinnerton-Dyer Conjecture

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    Book Chapter

    Pages 333-343

    Remarks on the Modular Elliptic Curves Conjecture and Fermat’s Last Theorem

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    Book Chapter

    Pages 345-381

    Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties

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