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A Comparison of Direct and Indirect Methods for Computing Selmer Groups of an Elliptic Curve

Djabri, Z.; Smart, Nigel, P.


Keyword(s): elliptic curves; selmer groups

Abstract: In this paper we examine differences between the two standard methods for computing the 2-Selmer group of an elliptic curve. In particular we focus on practical differences in the timings of the two methods. In addition we discuss how to proceed if one fails to determine the rank of the curve from the 2-Selmer group. Finally we mention briefly ongoing research into generalizing such methods to the case of computing the 3-Selmer group.

12 Pages

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