Algorithms for Modular Elliptic Curves
by J. E. Cremona
Publisher: Cambridge University Press 1992
ISBN/ASIN: 0521418135
ISBN-13: 9780521418133
Number of pages: 351
Description:
Elliptic curves are of central importance in computational number theory with numerous applications in such areas as cryptography primality testing and factorization. This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves complete with computer implementation. In the first part the author describes in detail the construction of modular elliptic curves giving an explicit algorithm for their computation. Then a collection of algorithms for the arithmetic of elliptic curves is presented, some of these have not appeared in book form before. Finally an extensive set of tables is provided giving the results of the author's implementations of the algorithms.
Download or read it online for free here:
Download link
(multiple PDF files)
Similar books
Modular Forms, Hecke Operators, and Modular Abelian Varietiesby Kenneth A. Ribet, William A. Stein - University of Washington
Contents: The Main objects; Modular representations and algebraic curves; Modular Forms of Level 1; Analytic theory of modular curves; Modular Symbols; Modular Forms of Higher Level; Newforms and Euler Products; Hecke operators as correspondences...
(10125 views)
Harmonic Analysis, the Trace Formula, and Shimura Varietiesby J. Arthur, D. Ellwood, R. Kottwitz - American Mathematical Society
The goal of this volume is to provide an entry point into the challenging field of the modern theory of automorphic forms. It is directed on the one hand at graduate students and professional mathematicians who would like to work in the area.
(12966 views)
Geometry of Numbers with Applications to Number Theoryby Pete L. Clark - University of Georgia
The goal is to find and explore open questions in both geometry of numbers -- e.g. Lattice Point Enumerators, the Ehrhart-Polynomial, Minkowski's Convex Body Theorems, Minkowski-Hlawka Theorem, ... -- and its applications to number theory.
(10324 views)
The Smarandache Functionby C. Dumitrescu, V. Seleacu - Erhus University Press
The function in the title is originated from the Romanian mathematician Florentin Smarandache, who has significant contributions in mathematics and literature. This text introduces the Smarandache function and discusses its generalisations.
(12809 views)