%0 PDF
%T The Distribution of 2-Selmer Ranks of Quadratic Twists of Elliptic Curves with Partial Two-Torsion.
%A Lemke Oliver, Robert J.; Klagsbrun, Zev.
%D 2017-07-07T07:52:52.729-04:00
%8 2017-07-07
%I Tufts University. Tisch Library.
%R http://localhost/files/h989rf451
%X This paper presents a new result concerning the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve over an arbitrary number field K with a single point of order two that does not have a cyclic 4-isogeny defined over its two-division field. We prove that at least half of all the quadratic twists of such an elliptic curve have arbitrarily large 2-Selmer rank, showing that the distribution of 2-Selmer ranks in the quadratic twist family of such an elliptic curve di ers from the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve having either no rational two-torsion or full rational two-torsion.
%[ 2018-10-09
%9 Text
%~ Tufts Digital Library
%W Institution