Congruent Number Theta Coefficients to 1012

  • William B. Hart
  • Gonzalo Tornaría
  • Mark Watkins
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)


We report on a computation of congruent numbers, which subject to the Birch and Swinnerton-Dyer conjecture is an accurate list up to 1012. The computation involves multiplying long theta series as per Tunnell (1983). The method, which we describe in some detail, uses a multimodular disk based technique for multiplying polynomials out-of-core which minimises expensive disk access by keeping data truncated.


Modular Form Elliptic Curf Arithmetic Progression Polynomial Multiplication Theta Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • William B. Hart
    • 1
  • Gonzalo Tornaría
    • 2
  • Mark Watkins
    • 3
  1. 1.Mathematics InstituteWarwick UniversityCoventryUnited Kingdom
  2. 2.Centro de MatemáticaUniversidad de la RepúblicaMontevideoUruguay
  3. 3.Department of Mathematics and StatisticsUniversity of SydneyAustralia

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