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Ranks of Elliptic Curves Over Function Fields

Published online by Cambridge University Press:  01 February 2010

Alan G. B. Lauder
Alan G. B. Lauder
Affiliation:
Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB, United Kingdom, lauder@maths.ox.ac.uk

Abstract

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We present experimental evidence to support the widely held belief that one half of all elliptic curves have infinitely many rational points. The method used to gather this evidence is a refinement of an algorithm due to the author which is based upon rigid and crystalline cohomology.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 11 , 2008 , pp. 172 - 212
Copyright
Copyright © London Mathematical Society 2008

References

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Supplementary material: File

JCM 11 Lauder Appendix 1

Lauder Appendix 1

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Supplementary material: File

JCM 11 Lauder Appendix 2

Lauder Appendix 2

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JCM 11 Lauder Appendix 3

Lauder Appendix 3

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JCM 11 Lauder Appendix 4

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JCM 11 Lauder Appendix 5

Lauder Appendix 5

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JCM 11 Lauder Appendix 6

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