On the φ-Selmer groups of the elliptic curves y 2 = x 3 - Dx
Accepted version
Peer-reviewed
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Authors
Kane, DM
Thorne, JA
Abstract
jats:titleAbstract</jats:title>jats:pWe study the variation of the φ-Selmer groups of the elliptic curvesjats:italicy</jats:italic>jats:sup2</jats:sup>=jats:italicx</jats:italic>jats:sup3</jats:sup>−jats:italicDx</jats:italic>under quartic twists by square-free integers. We obtain a complete description of the distribution of the size of this group when the integerjats:italicD</jats:italic>is constrained to lie in a family for which the relative Tamagawa number of the isogeny φ is fixed.</jats:p>
Description
Keywords
4903 Numerical and Computational Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Mathematical Proceedings of the Cambridge Philosophical Society
Conference Name
Journal ISSN
0305-0041
1469-8064
1469-8064
Volume Title
163
Publisher
Cambridge University Press (CUP)
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Sponsorship
National Science Foundation; Clay Mathematics Institute