The basics of the theory of elliptic curves should be known to
everybody, be he (or she) a mathematician or a computer scientist.
Especially everybody concerned with cryptography should know the
elements of this theory. The purpose of the present textbook is to
give an elementary introduction to elliptic curves. Since this
branch of number theory is particularly accessible to
computer-assisted calculations, the authors make use of it by
approaching the theory under a computational point of view.
Specifically, the computer-algebra package SIMATH can be applied on
several occasions. However, the book can be read also by those not
interested in any computations. Of course, the theory of elliptic
curves is very comprehensive and becomes correspondingly
sophisticated. That is why the authors made a choice of the topics
treated. Topics covered include the determination of torsion
groups, computations regarding the Mordell-Weil group, height
calculations, S-integral points. The contents is kept as elementary
as possible. In this way it becomes obvious in which respect the
book differs from the numerous textbooks on elliptic curves
nowadays available.
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