Arithmetic of elliptic curves

Includes index

Includes bibliographical references

Chapter I: Algebraic Varieties
Chapter II: Algebraic Curves
Chapter III: The Geometry of Elliptic Curves
Chapter IV: The Formal Group of an Elliptic Curve
Chapter V: Elliptic Curves over Finite Fields
Chapter VI: Elliptic Curves over ℂ
Chapter VII: Elliptic Curves over Local Fields
Chapter VIII: Elliptic Curves over Global Fields
Chapter IX: Integral Points on Elliptic Curves
Chapter X: Computing the Mordell–Weil Group
Chapter XI: Algorithmic Aspects of Elliptic Curves

In this chapter we present basic facts about algebraic curves, curve algebraic algebraic curve projective variety curve i.e., projective varieties of dimension one, that will be needed for our study of elliptic curves. Actually, since elliptic curves are curves of genus one, one of our tasks will be to define the genus of a curve. As in Chapter I, we give references for those proofs that are not included.