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Elliptic curves with 2-torsion contained in the 3-torsion field

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
dc.contributor.authorBRAU AVILA, Julio
hal.structure.identifierDepartment of Mathematics, Statistics and Computer Science [Chicago] [UIC]
dc.contributor.authorJONES, Nathan
dc.date.accessioned2024-04-04T03:19:05Z
dc.date.available2024-04-04T03:19:05Z
dc.date.issued2016
dc.identifier.issn0002-9939
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194471
dc.description.abstractEnThere is a modular curve X'(6) of level 6 defined over Q whose Q-rational points correspond to j-invariants of elliptic curves E over Q for which Q(E[2]) is a subfield of Q(E[3]). In this note we characterize the j-invariants of elliptic curves with this property by exhibiting an explicit model of X'(6). Our motivation is two-fold: on the one hand, X'(6) belongs to the list of modular curves which parametrize non-Serre curves (and is not well-known), and on the other hand, X'(6)(Q) gives an infinite family of examples of elliptic curves with non-abelian "entanglement fields," which is relevant to the systematic study of correction factors of various conjectural constants for elliptic curves over Q.
dc.language.isoen
dc.publisherAmerican Mathematical Society
dc.title.enElliptic curves with 2-torsion contained in the 3-torsion field
dc.typeArticle de revue
dc.identifier.doi10.1090/proc/12786
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv1406.1262
bordeaux.journalProceedings of the American Mathematical Society
bordeaux.page925-936
bordeaux.volume144
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01111744
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01111744v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.date=2016&rft.volume=144&rft.issue=3&rft.spage=925-936&rft.epage=925-936&rft.eissn=0002-9939&rft.issn=0002-9939&rft.au=BRAU%20AVILA,%20Julio&JONES,%20Nathan&rft.genre=article


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