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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.

MSC:

14Q05 Computational aspects of algebraic curves
14H52 Elliptic curves
11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
11G05 Elliptic curves over global fields
11Y16 Number-theoretic algorithms; complexity
11Y35 Analytic computations
68W30 Symbolic computation and algebraic computation
14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
11-02 Research exposition (monographs, survey articles) pertaining to number theory

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