Algorithms for modular elliptic curves. (English) Zbl 0758.14042

Cambridge: Cambridge University Press. 343 p. (1992).
Elliptic curves become more and more important in computational number theory. They are used in cryptography, primality testing, factorisation etc.
The book under review contains many algorithms and remarks to their implementation concerning elliptic curves. It starts with an algorithm for the computation of modular elliptic curves using modular symbols. One can find algorithms to compute torsion and non-torsion points, to compute heights, to find isogenies and periods, to compute the rank etc.
At the end of the book one can find a lot of tables with the results of these algorithms.
Reviewer: G.Pfister (Berlin)


14Q05 Computational aspects of algebraic curves
14H52 Elliptic curves
68W30 Symbolic computation and algebraic computation
14G35 Modular and Shimura varieties
14-04 Software, source code, etc. for problems pertaining to algebraic geometry
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
68-02 Research exposition (monographs, survey articles) pertaining to computer science