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Algorithms for Modular Elliptic Curves

Algorithms for Modular Elliptic Curves
Full Canadian Binding

2nd Edition

Out of Print

  • Date Published: May 1997
  • availability: Unavailable - out of print
  • format: Paperback
  • isbn: 9780521598200

Out of Print

Unavailable - out of print
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About the Authors
  • Elliptic curves are of central and growing importance in computational number theory, with numerous applications in such areas as cryptography, primality testing and factorisation. This book, now in its second edition, 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. Secondly 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 non-torsion 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 implementation 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. All researchers and graduate students of number theory will find this book useful, particularly those interested in the computational side of the subject. That aspect will make it appeal also to computer scientists and coding theorists.

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    Product details

    • Edition: 2nd Edition
    • Date Published: May 1997
    • format: Paperback
    • isbn: 9780521598200
    • length: 384 pages
    • dimensions: 220 x 298 x 27 mm
    • weight: 1.145kg
    • contains: 727 tables
    • availability: Unavailable - out of print
  • Table of Contents

    1. Introduction
    2. Modular symbol algorithms
    Appendix to chapter 2. Examples
    3. Elliptic curve algorithms
    4. The tables

  • Author

    J. E. Cremona, University of Exeter

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