Trivial Selmer Groups and Even Partitions of a Graph
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چکیده
For a square-free number n = p1p2 . . . pk Feng and Xiong in [FX] give a way to construct a corresponding graph on k-vertices and then give necessary and sufficient conditions on these graphs for the integers n to determine when the elliptic curve En : y = x3−n2x has trivial 2-Selmer groups. These conditions involve understanding when a graph is even. In this note we give a substantial understanding when graphs are even. Our main results count the number of square-free n less than X such that the 2-Selmer groups are trivial (Sn = {1} and S′ n = {±1,±n}).
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تاریخ انتشار 2004