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A comparison of direct and indirect methods for computing Selmer groups of an elliptic curve

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Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

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Abstract

In this paper we examine differences between the two standard methods for computing the 2-Selmer group of an elliptic curve. In particular we focus on practical differences in the timings of the two methods. In addition we discuss how to proceed if one fails to determine the rank of the curve from the 2-Selmer group. Finally we mention briefly ongoing research into generalizing such methods to the case of computing the 3-Selmer group.

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Author information

Authors and Affiliations

  1. Institute of Maths and Statistics, University of Kent at Canterbury, CT2 7NF, Canterbury, Kent, UK

    Z. Djabri

  2. Hewlett-Packard Laboratories, Filton Road, BS12 6QZ, Stoke Gifford, Bristol, UK

    N. P. Smart

Authors
  1. Z. Djabri
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  2. N. P. Smart
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Djabri, Z., Smart, N.P. (1998). A comparison of direct and indirect methods for computing Selmer groups of an elliptic curve. 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/BFb0054888

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  • DOI: https://doi.org/10.1007/BFb0054888

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  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

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