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On the φ-Selmer groups of the elliptic curves y2 = x3 − Dx
Published online by Cambridge University Press: 09 September 2016
Abstract
We 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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 1 , July 2017 , pp. 71 - 93
- Copyright
- Copyright © Cambridge Philosophical Society 2016
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