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International Algorithmic Number Theory Symposium

ANTS 1998: Algorithmic Number Theory pp 1–47Cite as

Shimura curve computations

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Part of the book series: Lecture Notes in Computer Science ((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.

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Authors and Affiliations

  1. Harvard University, USA

    Noam D. Elkies

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  1. Noam D. Elkies
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/BFb0054850

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  • DOI: https://doi.org/10.1007/BFb0054850

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

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