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On the complexity of computing the 2-Selmer group of an elliptic curve

Published online by Cambridge University Press:  18 May 2009

S. Siksek  and
N. P. Smart
S. Siksek
Affiliation:
Institute of Mathematics and Statistics, University of Kent at Canterbury Canterbury, Kent CT2 7NF, England
N. P. Smart
Affiliation:
Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol Bs12 6Qz, England
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Abstract

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In this paper we give an algorithm for computing the 2-Selmer group of an elliptic curve

which has complexity O(LD(0·5),c1)), where D is the absolute discriminant of the curve. Our algorithm is unconditional but the complexity estimate assumes the GRH and a standard conjecture on the distribution of smooth reduced ideals. This improves on the corresponding algorithm of Birch and Swinnerton-Dyer, which has complexity of O(√D).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 3 , September 1997 , pp. 251 - 257
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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