Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A conjecture of Watkins for quadratic twists


Authors: Jose A. Esparza-Lozano and Hector Pasten
Journal: Proc. Amer. Math. Soc. 149 (2021), 2381-2385
MSC (2020): Primary 11G05; Secondary 11F11, 11G18
DOI: https://doi.org/10.1090/proc/15376
Published electronically: March 25, 2021
MathSciNet review: 4246791
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Watkins conjectured that for an elliptic curve $E$ over $\mathbb {Q}$ of Mordell-Weil rank $r$, the modular degree of $E$ is divisible by $2^r$. If $E$ has non-trivial rational $2$-torsion, we prove the conjecture for all the quadratic twists of $E$ by squarefree integers with sufficiently many prime factors.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 11G05, 11F11, 11G18

Retrieve articles in all journals with MSC (2020): 11G05, 11F11, 11G18


Additional Information

Jose A. Esparza-Lozano
Affiliation: African Institute for Mathematical Sciences, Rue KG590 ST, Kigali, Rwanda
Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan
ORCID: 0000-0001-6555-2189
Email: josealanesparza@gmail.com

Hector Pasten
Affiliation: Pontificia Universidad Católica de Chile, Facultad de Matemáticas, 4860 Av. Vicuña Mackenna, Macul, RM, Chile
MR Author ID: 891758
Email: hector.pasten@mat.uc.cl

Keywords: Elliptic curve, rank, modularity
Received by editor(s): March 25, 2020
Received by editor(s) in revised form: October 13, 2020
Published electronically: March 25, 2021
Additional Notes: The first author was supported by a Carroll L. Wilson Award and the MIT International Science and Technology Initiatives (MISTI) during an academic visit to Pontificia Universidad Católica de Chile.
The second author was supported by FONDECYT Regular grant 1190442.
Communicated by: Matthew Papanikolas
Article copyright: © Copyright 2021 American Mathematical Society