Reductions of an elliptic curve and their Tate-Shafarevich groups

DOI10.1007/S00208-004-0517-2zbMath1062.11039OpenAlexW1976181015WikidataQ102399035 ScholiaQ102399035MaRDI QIDQ1889454

Alina Carmen Cojocaru, William Duke

Publication date: 2 December 2004

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-004-0517-2

zbMATH Keywords

Tate-Shafarevich groupelliptic curves over function fieldsBSD conjecture

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

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The absolute discriminant of the endomorphism ring of most reductions of a non-CM elliptic curve is close to maximal ⋮ Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height ⋮ Small discriminants of complex multiplication fields of elliptic curves over finite fields ⋮ Primes, elliptic curves and cyclic groups ⋮ An observation on the cyclicity of the group of the \(\mathbb F_p\)-rational points of Abelian surfaces ⋮ Degree bounds for projective division fields associated to elliptic modules with a trivial endomorphism ring ⋮ Obstructions to reciprocity laws related to division fields of Drinfeld modules

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