On the φ-Selmer groups of the elliptic curves y2 = x3 − Dx. (9th September 2016) - KANE, DANIEL M.; THORNE, JACK A.
Abstract: We study the variation of the φ-Selmer groups of the elliptic curves y 2 = x 3 − Dx under quartic twists by square-free integers. We obtain a complete description of the distribution of the size of this group when the integer D is constrained to lie in a family for which the relative Tamagawa number of the isogeny φ is fixed.