There are genus one curves over \mathbb{Q} of every odd index

DOI10.1515/crll.2002.047zbMath1002.11050OpenAlexW2058214040MaRDI QIDQ4529765

William A. Stein

Publication date: 6 May 2002

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crll.2002.047

zbMATH Keywords

elliptic curveGalois representationmodular curveKolyvagin's Euler system of Heegner points

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Arithmetic ground fields for curves (14H25)

Related Items

Period and index of genus one curves over global fields ⋮ There are genus one curves of every index over every infinite, finitely generated field ⋮ The period-index obstruction for elliptic curves ⋮ Computational verification of the Birch and Swinnerton-Dyer conjecture for individual elliptic curves

Uses Software

• ecdata

Cites Work

• Eisenstein series on the metaplectic group and nonvanishing theorems for automorphic L-functions and their derivatives
• Non-vanishing of \(L\)-functions and applications
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