Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero

DOI10.1090/S0025-5718-04-01644-8zbMath1084.11033OpenAlexW2016723714WikidataQ123150976 ScholiaQ123150976MaRDI QIDQ4821058

Amod Agashe, William A. Stein

Publication date: 7 October 2004

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-04-01644-8

zbMATH Keywords

torsionabelian varietiesmodular formsnewformsTate-Shafarevich groupvisibilityBirch and Swinnerton-Dyer conjecture

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Abelian varieties of dimension (> 1) (11G10) Jacobians, Prym varieties (14H40) Holomorphic modular forms of integral weight (11F11) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Arithmetic ground fields for abelian varieties (14K15)

Related Items

Invariant theory for the elliptic normal quintic. I: Twists of \(X(5)\), Selmer groups as flat cohomology groups, Exhibiting SHA[2 on hyperelliptic Jacobians], Torsion and Tamagawa numbers, Determination of the modular Jacobian varieties \(J_1(M,MN)\) with the Mordell-Weil rank zero, Visualizing elements of order in the Tate–Shafarevich group of an elliptic curve, Rational torsion in elliptic curves and the cuspidal subgroup, Periods of quadratic twists of elliptic curves, SQUARENESS IN THE SPECIAL L-VALUE AND SPECIAL L-VALUES OF TWISTS, Computational verification of the Birch and Swinnerton-Dyer conjecture for individual elliptic curves, A $p$-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties, The special \(L\)-value of the winding quotient of square-free level, On a conjecture of Agashe, Visibility and the Birch and Swinnerton-Dyer conjecture for analytic rank zero, Explicit Chabauty-Kim for the split Cartan modular curve of level 13, A divisibility related to the Birch and Swinnerton-Dyer conjecture, Visibility of Shafarevich-Tate groups of abelian varieties.

Uses Software

• Magma
• ecdata

Cites Work

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