On a special case of Watkins’ conjecture

Watkins’ conjecture asserts that for a rational elliptic curve E the degree of the modular parametrization is divisible by 2r, 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 rati...

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Autores principales: Kazalicki, M., Kohen, D.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00029939_v146_n2_p541_Kazalicki
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00029939_v146_n2_p541_Kazalicki2023-10-03T13:55:18Z On a special case of Watkins’ conjecture Kazalicki, M. Kohen, D. Watkins’ conjecture asserts that for a rational elliptic curve E the degree of the modular parametrization is divisible by 2r, 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. © 2017 American Mathematical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00029939_v146_n2_p541_Kazalicki
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description Watkins’ conjecture asserts that for a rational elliptic curve E the degree of the modular parametrization is divisible by 2r, 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. © 2017 American Mathematical Society.
format JOUR
author Kazalicki, M.
Kohen, D.
spellingShingle Kazalicki, M.
Kohen, D.
On a special case of Watkins’ conjecture
author_facet Kazalicki, M.
Kohen, D.
author_sort Kazalicki, M.
title On a special case of Watkins’ conjecture
title_short On a special case of Watkins’ conjecture
title_full On a special case of Watkins’ conjecture
title_fullStr On a special case of Watkins’ conjecture
title_full_unstemmed On a special case of Watkins’ conjecture
title_sort on a special case of watkins’ conjecture
url http://hdl.handle.net/20.500.12110/paper_00029939_v146_n2_p541_Kazalicki
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