On the[...]-Selmer groups of the elliptic curves y 2 = x 3 - Dx

On the[...]-Selmer groups of the elliptic curves y 2 = x 3 - Dx

We study the variation of the[...]-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 num...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2017-07, Vol.163 (1), p.71
Hauptverfasser: KANE, DANIEL M, THORNE, JACK A
Format: Artikel
Sprache:eng
Schlagworte:
Integers
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We study the variation of the[...]-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[...]is fixed.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004116000724