A conjecture of Watkins for quadratic twists

DOI10.1090/proc/15376zbMath1468.11125arXiv2102.04185OpenAlexW3099797675WikidataQ113822995 ScholiaQ113822995MaRDI QIDQ4985374

Jose A. Esparza-Lozano, Hector Pasten

Publication date: 23 April 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.04185

zbMATH Keywords

elliptic curverankmodularity

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Holomorphic modular forms of integral weight (11F11) Arithmetic aspects of modular and Shimura varieties (11G18)

Related Items (1)

Watkins’s conjecture for elliptic curves with non-split multiplicative reduction

Uses Software

• LMFDB

Cites Work

• Computing modular degrees using \(L\)-functions
• Modular abelian varieties of odd modular degree
• The Manin constant. (With an appendix by J. Cremona)
• On a conjecture of Watkins
• Elliptic curves of odd modular degree
• Finiteness theorems for abelian varieties over number fields.
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• The Manin constant in the semistable case
• The Arithmetic of Elliptic Curves
• Modular Parametrizations of Elliptic Curves
• On a special case of Watkins’ conjecture
• Corrigendum to “On a special case of Watkins’ conjecture”
• Periods of quadratic twists of elliptic curves
• Computing the Modular Degree of an Elliptic Curve
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