This book provides a thorough introduction to the theory of elliptic curves from a computational point of view.Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. Since elliptic curves are a special case of diophantine equations, methods from diophantine geometry enter the picture here. Applications to cryptography are also considered in the text.Concrete examples, algorithms and computations, often based on results obtained by the second author's research group at the University of Saarbrucken, are used throughout. Each chapter concludes with a wide selection of exercises.The book is addressed to graduate students and researchers in both fields, mathematics and computer science.
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