By Joseph H. Silverman

The idea of elliptic curves is exclusive via its lengthy background and by way of the variety of the tools which have been utilized in its examine. This booklet treats the mathematics strategy in its sleek formula, by using easy algebraic quantity concept and algebraic geometry. Following a quick dialogue of the mandatory algebro-geometric effects, the publication proceeds with an exposition of the geometry and the formal staff of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and international fields. ultimate chapters care for essential and rational issues, together with Siegels theorem and specific computations for the curve Y = X + DX, whereas 3 appendices finish the entire: Elliptic Curves in features 2 and three, crew Cohomology, and an summary of extra complicated issues.

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