An Algorithm for Determining Torsion Growth of Elliptic Curves

We present a fast algorithm that takes as input an elliptic curve defined over Q and an integer d and returns all the number fields K of degree d' dividing d such that E(K)tors contains E(F)tors as a proper subgroup, for all F⊈K. We ran this algorithm on all elliptic curves of conductor less th...

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Detalhes bibliográficos
Autores: González Jiménez, Enrique, Najman, Filip
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/710748
Acesso em linha:http://hdl.handle.net/10486/710748
https://dx.doi.org/10.1080/10586458.2020.1771638
Access Level:acceso abierto
Palavra-chave:Elliptic curves
torsion over number fields
Matemáticas
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spelling An Algorithm for Determining Torsion Growth of Elliptic CurvesGonzález Jiménez, EnriqueNajman, FilipElliptic curvestorsion over number fieldsMatemáticasWe present a fast algorithm that takes as input an elliptic curve defined over Q and an integer d and returns all the number fields K of degree d' dividing d such that E(K)tors contains E(F)tors as a proper subgroup, for all F⊈K. We ran this algorithm on all elliptic curves of conductor less than 400.000 (a total of 2.483.649 curves) and all d≤23 and collected various interesting data. In particular, we find a degree 6 sporadic point on X1(4,12), which is so far the lowest known degree a sporadic point on X1(m,n), for m≥2The firstauthorwaspartiallysupportedbythegrantMTM2015–68524–P.Thesecondauthorgratefullyacknowledgessupport from theQuantiXLieCenterofExcellence,aprojectco-financedbytheCroatianGovernmentandEuropeanUnionthroughthe EuropeanRegionalDevelopmentFund-theCompetitivenessandCohesionOperationalProgramme(GrantKK.01.1.1.01.0004)and bytheCroatianScienceFoundationundertheprojectno.IP-2018-01-1313WileyDepartamento de MatemáticasFacultad de Ciencias20202020-06-13research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/710748https://dx.doi.org/10.1080/10586458.2020.1771638reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7107482026-06-23T12:46:27Z
dc.title.none.fl_str_mv An Algorithm for Determining Torsion Growth of Elliptic Curves
title An Algorithm for Determining Torsion Growth of Elliptic Curves
spellingShingle An Algorithm for Determining Torsion Growth of Elliptic Curves
González Jiménez, Enrique
Elliptic curves
torsion over number fields
Matemáticas
title_short An Algorithm for Determining Torsion Growth of Elliptic Curves
title_full An Algorithm for Determining Torsion Growth of Elliptic Curves
title_fullStr An Algorithm for Determining Torsion Growth of Elliptic Curves
title_full_unstemmed An Algorithm for Determining Torsion Growth of Elliptic Curves
title_sort An Algorithm for Determining Torsion Growth of Elliptic Curves
dc.creator.none.fl_str_mv González Jiménez, Enrique
Najman, Filip
author González Jiménez, Enrique
author_facet González Jiménez, Enrique
Najman, Filip
author_role author
author2 Najman, Filip
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Elliptic curves
torsion over number fields
Matemáticas
topic Elliptic curves
torsion over number fields
Matemáticas
description We present a fast algorithm that takes as input an elliptic curve defined over Q and an integer d and returns all the number fields K of degree d' dividing d such that E(K)tors contains E(F)tors as a proper subgroup, for all F⊈K. We ran this algorithm on all elliptic curves of conductor less than 400.000 (a total of 2.483.649 curves) and all d≤23 and collected various interesting data. In particular, we find a degree 6 sporadic point on X1(4,12), which is so far the lowest known degree a sporadic point on X1(m,n), for m≥2
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-06-13
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/710748
https://dx.doi.org/10.1080/10586458.2020.1771638
url http://hdl.handle.net/10486/710748
https://dx.doi.org/10.1080/10586458.2020.1771638
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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