%0 Journal Article %T The distribution of 2-Selmer ranks of quadratic twists of elliptic curves with partial two-torsion %A Zev Klagsbrun %A Robert J. Lemke Oliver %J Mathematics %D 2013 %I arXiv %R 10.1112/S0025579315000121 %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 differs 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. %U http://arxiv.org/abs/1307.7030v1