The aim of this book is to give an elementary introduction to the arithmetic of elliptic curves over number fields from a computational point of view, i.e. the text is equipped with the corresponding algorithms. In the book, the most important topics of elliptic curves are discussed, including the determination of torsion groups, computations concerning the Mordell-Weil group (in particular concerning the rank and a basis of that group), height calculations and the determination of integral and S-integral points. The computer algebra system SIMATH, developed by the second author, focuses just on elliptic curves and all elementary algorithms used in the book are implemented in SIMATH.

Reviewer:

pso