On the Selmer Group of Twists of Elliptic Curves with Q-Rational Torsion Points

DOI10.4153/CJM-1988-028-9zbMath0646.14024OpenAlexW2088116632MaRDI QIDQ3789684

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Publication date: 1989

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4153/cjm-1988-028-9

zbMATH Keywords

\(p\)-class group\(\mathbb Q\)-rational torsion pointSelmer group of twists of elliptic curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (9)

Elliptic curves of rank zero satisfying the \(p\)-part of the Birch and Swinnerton-Dyer conjecture ⋮ The effect of torsion on the distribution of \(\text Ш\) among quadratic twists of an elliptic curve ⋮ Elements of class groups and Shafarevich-Tate groups of elliptic curves ⋮ Canonical periods and congruence formulae ⋮ Construction of elliptic curves with large Iwasawa \(\lambda\)-invariants and large Tate-Shafarevich groups ⋮ L-series with nonzero central critical value ⋮ On Ranks of Twists of Elliptic Curves and Power-Free Values of Binary Forms ⋮ Selmer groups of twists of elliptic curves over \(K\) with \(K\)-rational torsion points ⋮ Elliptic curves satisfying the Birch and Swinnerton-Dyer conjecture mod 3

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