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On the phi-Selmer groups of the elliptic curves y(2) = x(3) - Dx

  • Author(s): Kane, Daniel M
  • Thorne, Jack A
  • et al.
Abstract

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.

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