Bielliptic modular curves X0* (N)

Let N ≥ 1 be a integer such that the modular curve X0* (N) has genus ≥ 2. We prove that X0* (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X0* (N) is bielliptic over the base field for all these values of N, except X0*(160) that is not bielliptic over Q but it does over...

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Autores: Bars Cortina, Francesc|||0000-0003-4779-3995, González Rovira, Josep
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:240651
Acceso en línea:https://ddd.uab.cat/record/240651
https://dx.doi.org/urn:doi:10.1016/j.jalgebra.2020.02.028
Access Level:acceso abierto
Palabra clave:Arithmetic geometry
Hyperelliptic curves
Bielliptic curves
Quadratic points
Elliptic curves
Modular curves
Involutions
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spelling Bielliptic modular curves X0* (N)Bars Cortina, Francesc|||0000-0003-4779-3995González Rovira, JosepArithmetic geometryHyperelliptic curvesBielliptic curvesQuadratic pointsElliptic curvesModular curvesInvolutionsLet N ≥ 1 be a integer such that the modular curve X0* (N) has genus ≥ 2. We prove that X0* (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X0* (N) is bielliptic over the base field for all these values of N, except X0*(160) that is not bielliptic over Q but it does over Q(√-1). Moreover, we prove that the set of all quadratic points over Q for the modular curve X0* (N) is infinite exactly for 100 values of N. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501SMURhttp://purl.org/coar/version/c_71e4c1898caa6e32info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/240651https://dx.doi.org/urn:doi:10.1016/j.jalgebra.2020.02.028reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-75980-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MDM-2014-0445Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2015-66180-Ropen accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2406512026-06-06T12:50:31Z
dc.title.none.fl_str_mv Bielliptic modular curves X0* (N)
title Bielliptic modular curves X0* (N)
spellingShingle Bielliptic modular curves X0* (N)
Bars Cortina, Francesc|||0000-0003-4779-3995
Arithmetic geometry
Hyperelliptic curves
Bielliptic curves
Quadratic points
Elliptic curves
Modular curves
Involutions
title_short Bielliptic modular curves X0* (N)
title_full Bielliptic modular curves X0* (N)
title_fullStr Bielliptic modular curves X0* (N)
title_full_unstemmed Bielliptic modular curves X0* (N)
title_sort Bielliptic modular curves X0* (N)
dc.creator.none.fl_str_mv Bars Cortina, Francesc|||0000-0003-4779-3995
González Rovira, Josep
author Bars Cortina, Francesc|||0000-0003-4779-3995
author_facet Bars Cortina, Francesc|||0000-0003-4779-3995
González Rovira, Josep
author_role author
author2 González Rovira, Josep
author2_role author
dc.subject.none.fl_str_mv Arithmetic geometry
Hyperelliptic curves
Bielliptic curves
Quadratic points
Elliptic curves
Modular curves
Involutions
topic Arithmetic geometry
Hyperelliptic curves
Bielliptic curves
Quadratic points
Elliptic curves
Modular curves
Involutions
description Let N ≥ 1 be a integer such that the modular curve X0* (N) has genus ≥ 2. We prove that X0* (N) is bielliptic exactly for 69 values of N. In particular, we obtain that X0* (N) is bielliptic over the base field for all these values of N, except X0*(160) that is not bielliptic over Q but it does over Q(√-1). Moreover, we prove that the set of all quadratic points over Q for the modular curve X0* (N) is infinite exactly for 100 values of N.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
SMUR
http://purl.org/coar/version/c_71e4c1898caa6e32
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/240651
https://dx.doi.org/urn:doi:10.1016/j.jalgebra.2020.02.028
url https://ddd.uab.cat/record/240651
https://dx.doi.org/urn:doi:10.1016/j.jalgebra.2020.02.028
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-75980-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MDM-2014-0445
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2015-66180-R
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
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
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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