Some Improvements to 4-Descent on an Elliptic Curve

  • Tom Fisher
Conference paper

DOI: 10.1007/978-3-540-79456-1_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5011)
Cite this paper as:
Fisher T. (2008) Some Improvements to 4-Descent on an Elliptic Curve. In: van der Poorten A.J., Stein A. (eds) Algorithmic Number Theory. ANTS 2008. Lecture Notes in Computer Science, vol 5011. Springer, Berlin, Heidelberg

Abstract

The theory of 4-descent on elliptic curves has been developed in the PhD theses of Siksek [18], Womack [21] and Stamminger [20]. Prompted by our use of 4-descent in the search for generators of large height on elliptic curves of rank at least 2, we explain how to cut down the number of class group and unit group calculations required, by using the group law on the 4-Selmer group.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Tom Fisher
    • 1
  1. 1.DPMMS, Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK

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