On a special case of Watkins’ conjecture
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- by Matija Kazalicki and Daniel Kohen PDF
- Proc. Amer. Math. Soc. 146 (2018), 541-545 Request permission
Corrigendum: Proc. Amer. Math. Soc. 147 (2019), 4563-4563.
Abstract:
Watkins’ conjecture asserts that for a rational elliptic curve $E$ the degree of the modular parametrization is divisible by $2^r$, where $r$ is the rank of $E$. In this paper, we prove that if the modular degree is odd, then $E$ has rank zero. Moreover, we prove that the conjecture holds for all rank two rational elliptic curves of prime conductor and positive discriminant.References
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Additional Information
- Matija Kazalicki
- Affiliation: Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
- MR Author ID: 837906
- Email: matija.kazalicki@math.hr
- Daniel Kohen
- Affiliation: Departamento de Matemática, Universidad de Buenos Aires and IMAS-CONICET, Ciudad Universitaria, Buenos Aires Argentina
- MR Author ID: 1157618
- Email: dkohen@dm.uba.ar
- Received by editor(s): January 20, 2017
- Received by editor(s) in revised form: March 31, 2017
- Published electronically: September 6, 2017
- Additional Notes: The first author’s work was supported by the QuantiXLie Center of Excellence
The second author’s work was supported by a doctoral fellowship of the Consejo Nacional de Inevsitagciones Científicas y Técnicas - Communicated by: Kathrin Bringmann
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 541-545
- MSC (2010): Primary 11G05; Secondary 11G20
- DOI: https://doi.org/10.1090/proc/13759
- MathSciNet review: 3731689