Siksek, S. and 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. (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)
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).
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||T.J. Sango|
|Date Deposited:||13 May 2009 06:13|
|Last Modified:||25 Jun 2014 08:38|
|Resource URI:||https://kar.kent.ac.uk/id/eprint/17950 (The current URI for this page, for reference purposes)|