On a special case of Watkins’ conjecture

Autores
Kazalicki, Matija; Kohen, Daniel
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Kazalicki, Matija. University of Sagreb; Croacia
Fil: Kohen, Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Materia
Modular
Degree
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/55470
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/55470
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling On a special case of Watkins’ conjectureKazalicki, MatijaKohen, DanielModularDegreehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Watkins’ 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.Fil: Kazalicki, Matija. University of Sagreb; CroaciaFil: Kohen, Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaAmerican Mathematical Society2017-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55470Kazalicki, Matija; Kohen, Daniel; On a special case of Watkins’ conjecture; American Mathematical Society; Proceedings of the American Mathematical Society; 146; 2; 4-2017; 541-5450002-9939CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2018-146-02/S0002-9939-2017-13759-9/info:eu-repo/semantics/altIdentifier/doi/10.1090/proc/13759info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:38:38Zoai:ri.conicet.gov.ar:11336/55470instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:38:38.508CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On a special case of Watkins’ conjecture
title On a special case of Watkins’ conjecture
spellingShingle On a special case of Watkins’ conjecture
Kazalicki, Matija
Modular
Degree
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
dc.creator.none.fl_str_mv Kazalicki, Matija
Kohen, Daniel
author Kazalicki, Matija
author_facet Kazalicki, Matija
Kohen, Daniel
author_role author
author2 Kohen, Daniel
author2_role author
dc.subject.none.fl_str_mv Modular
Degree
topic Modular
Degree
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Kazalicki, Matija. University of Sagreb; Croacia
Fil: Kohen, Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
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.
publishDate 2017
dc.date.none.fl_str_mv 2017-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/55470
Kazalicki, Matija; Kohen, Daniel; On a special case of Watkins’ conjecture; American Mathematical Society; Proceedings of the American Mathematical Society; 146; 2; 4-2017; 541-545
0002-9939
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55470
identifier_str_mv Kazalicki, Matija; Kohen, Daniel; On a special case of Watkins’ conjecture; American Mathematical Society; Proceedings of the American Mathematical Society; 146; 2; 4-2017; 541-545
0002-9939
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2018-146-02/S0002-9939-2017-13759-9/
info:eu-repo/semantics/altIdentifier/doi/10.1090/proc/13759
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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