Djabri, Z. and Schaefer, E.F. and Smart, N.P. (2000) Computing the p-Selmer group of an elliptic curve. Transactions of the American Mathematical Society, 352 (12). pp. 5583-5597. ISSN 0002-9947.
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In this paper we explain how to bound the p-Selmer group of an elliptic curve over a number field K. Our method is an algorithm which is relatively simple to implement, although it requires data such as units and class groups from number fields of degree at most p(2) - 1. Our method is practical for p = 3, but for larger values of p it becomes impractical with current computing power. In the examples we have calculated, our method produces exactly the p-Selmer group of the curve, and so one can use the method to find the Mordell-Weil rank of the curve when the usual method of 2-descent fails.
|Uncontrolled keywords:||elliptic curves; Mordell-Weil rank; Selmer group|
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||P. Ogbuji|
|Date Deposited:||27 Mar 2009 14:41|
|Last Modified:||27 Mar 2009 14:41|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/16388 (The current URI for this page, for reference purposes)|
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