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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Publicado: 2017
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v146_n2_p541_Kazalicki
http://hdl.handle.net/20.500.12110/paper_00029939_v146_n2_p541_Kazalicki
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00029939_v146_n2_p541_Kazalicki
record_format dspace
spelling paper:paper_00029939_v146_n2_p541_Kazalicki2023-06-08T14:23:36Z 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 rational elliptic curves of prime conductor and positive discriminant. © 2017 American Mathematical Society. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v146_n2_p541_Kazalicki 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.
title On a special case of Watkins’ conjecture
spellingShingle 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
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v146_n2_p541_Kazalicki
http://hdl.handle.net/20.500.12110/paper_00029939_v146_n2_p541_Kazalicki
_version_ 1768543778405089280

Ejemplares similares