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Algorithms for Modular Elliptic Curves
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  • Title Algorithms for Modular Elliptic Curves
  • Author(s) J. E. Cremona
  • Publisher: Cambridge University Press (November 27, 1992); 2nd Edition (1997)
  • Hardcover/Paperback 351 pages
  • eBook PDF Files, DVI, PostScript, etc.
  • Language: English
  • ISBN-10: 0521418135
  • ISBN-13: 978-0521418133
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Book Description

This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves with remarks on computer implementation.

It is in three parts. First, the author describes in detail the construction of modular elliptic curves, giving an explicit algorithm for their computation using modular symbols. Second, a collection of algorithms for the arithmetic of elliptic curves is presented; some of these have not appeared in book form before. They include: finding torsion and nontorsion points, computing heights, finding isogenies and periods, and computing the rank. Finally, an extensive set of tables is provided giving the results of the author's implementations of the algorithms. These tables extend the widely used "Antwerp IV Tables" in two ways, the range of conductors (up to 1000) and the level of detail given for each curve. In particular the quantities relating to the Birch-Swinnerton-Dyer conjecture have been computed in each case and are included.

About the Authors
  • Victor Shoup is Associate Professor at The Courant Institute of Mathematical Sciences at New York University.

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