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Disparity in Selmer ranks of quadratic twists of elliptic curves

✍ Scribed by Klagsbrun, Zev; Mazur, Barry; Rubin, Karl


Book ID
120091232
Publisher
John Hopkins University Press
Year
2013
Tongue
English
Weight
577 KB
Volume
178
Category
Article
ISSN
0003-486X

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Mordell–Weil Ranks of Quadratic Twists o
✍ Gwynneth Coogan; Jorge JimenΓ©z-Urroz πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 146 KB

Motivated by a conjecture of Mazur, Kuwata and Wang proved that for elliptic curves E 1 and E 2 whose j-invariants are not simultaneously 0 or 1728, there exist infinitely many square-free integers d for which the rank of the Mordell-Weil group of the d-quadratic twists of E 1 and E 2 satisfy: rkΓ°E