On the phi-Selmer groups of the elliptic curves y(2) = x(3) - Dx
- Author(s): Kane, Daniel M;
- Thorne, Jack A
- et al.
Published Web Locationhttps://doi.org/10.1017/S0305004116000724
AbstractWe study the variation of the φ-Selmer groups of the elliptic curves y2 = x3 − 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.