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Computing the p-Selmer Group of an Elliptic Curve
Djabri, Z.; Schaefer, Edward F.; Smart, Nigel P.
Keyword(s): elliptic curves; Selmer group; Mordell-Weil rank
Abstract: Please Note. This abstract contains mathematical formulae which cannot be represented here. In this paper we explain how to bound the p-Selmer group of an elliptic curve over K, a number field. 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 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. Notes: Z. Djabri, Institute of Maths and Statistics, University of Kent at Canterbury, Canterbury, Kent, CT2 7NF, U.K. Edward F. Schaefer, Department of Mathematics, Santa Clara University, Santa Clara, CA 95053, U.S.A.
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