Shimura curve computations

  • Noam D. Elkies
Conference paper

DOI: 10.1007/BFb0054850

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1423)
Cite this paper as:
Elkies N.D. (1998) Shimura curve computations. In: Buhler J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

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

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