Siksek, S., Smart, Nigel P. (1997) On the complexity of computing the 2-Selmer group of an elliptic curve. Glasgow Mathematical Journal, 39 . pp. 251-257. ISSN 0017-0895. (doi:10.1017/s0017089500032183) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:17950)
| The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |
| Official URL: https://doi.org/10.1017/s0017089500032183 |
Abstract
In this paper we give an algorithm for computing the 2-Selmer group of an elliptic curve Y-2 = X-3 + AX + B which has complexity O(L-D(0.5, c(1))), 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(root D).
| Item Type: | Article |
|---|---|
| DOI/Identification number: | 10.1017/s0017089500032183 |
| Subjects: | Q Science > QA Mathematics (inc Computing science) |
| Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
| Depositing User: | T.J. Sango |
| Date Deposited: | 13 May 2009 06:13 UTC |
| Last Modified: | 09 Mar 2023 11:31 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/17950 (The current URI for this page, for reference purposes) |
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