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Shimura curve computations

  • Noam D. Elkies
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1423)

Abstract

We give some methods for computing equations for certain Shimura curves, natural maps between them, and special points on them. We then illustrate these methods by working out several examples in varying degrees of detail. For instance, we compute coordinates for all the rational CM points on the curves X *(1) associated with the quaternion algebras over Q ramified at {2,3}, {2,5}, {2,7}, and {3,5}. We conclude with a list of open questions that may point the way to further computational investigation of these curves.

Keywords

Elliptic Curve Elliptic Curf Congruence Subgroup Quaternion Algebra Fractional Linear Transformation 
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 1998

Authors and Affiliations

  • Noam D. Elkies
    • 1
  1. 1.Harvard UniversityUSA

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