Determination of the modular Jacobian varieties \(J_1(M,MN)\) with the Mordell-Weil rank zero

DOI10.1007/s40993-023-00430-4OpenAlexW4327844780MaRDI QIDQ2696578

Koji Matsuda

Publication date: 14 April 2023

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.08215

zbMATH Keywords

elliptic curvesmodular curvestorsion groups

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52)

Uses Software

• Magma
• SageMath
• LMFDB

Cites Work

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• Bielliptic modular curves \(X_1(M,N)\)
• Finiteness theorems for abelian varieties over number fields.
• Twists of modular forms and endomorphisms of abelian varieties
• Galois properties of torsion points on abelian varieties
• Twists of newforms and pseudo-eigenvalues of \(W\)-operators
• Modular curves and the Eisenstein ideal
• The Magma algebra system. I: The user language
• Torsion points on elliptic curves and \(q\)-coefficients of modular forms
• Sporadic cubic torsion
• On the factors of the Jacobian variety of a modular function field
• Torsion points on elliptic curves defined over quadratic fields
• Les Schémas de Modules de Courbes Elliptiques
• Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero

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