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dc.contributor.author
Cremona, John
dc.contributor.author
Pacetti, Ariel Martín
dc.date.available
2020-12-02T20:07:43Z
dc.date.issued
2019-05
dc.identifier.citation
Cremona, John; Pacetti, Ariel Martín; On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1; London Mathematical Society; Proceedings of the London Mathematical Society; 118; 5; 5-2019; 1245-1276
dc.identifier.issn
0024-6115
dc.identifier.uri
http://hdl.handle.net/11336/119668
dc.description.abstract
The main result of this paper is to extend from Q to each of the nine imaginary quadratic fields of class number 1 a result of [Serre, Duke Math. J. 54 (1987) 179–230] and [Mestre–Oesterlé, J. reine. angew. Math 400 (1989) 173–184], namely that if E is an elliptic curve of prime conductor, then either E or a 2-, 3- or 5-isogenous curve has prime discriminant. For four of the nine fields, the theorem holds with no change, while for the remaining five fields the discriminant of a curve with prime conductor is (up to isogeny) either prime or the square of a prime. The proof is conditional in two ways: first that the curves are modular, so are associated to suitable Bianchi newforms; and second that a certain level-lowering conjecture holds for Bianchi newforms. We also classify all elliptic curves of prime power conductor and non-trivial torsion over each of the nine fields: in the case of 2-torsion, we find that such curves either have CM or with a small finite number of exceptions arise from a family analogous to the Setzer–Neumann family over Q.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
London Mathematical Society
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
11G05 (PRIMARY)
dc.subject
14H52 (SECONDARY)
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2020-11-19T21:20:09Z
dc.identifier.eissn
1460-244X
dc.journal.volume
118
dc.journal.number
5
dc.journal.pagination
1245-1276
dc.journal.pais
Reino Unido
dc.journal.ciudad
Londres
dc.description.fil
Fil: Cremona, John. University of Warwick; Reino Unido
dc.description.fil
Fil: Pacetti, Ariel Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
dc.journal.title
Proceedings of the London Mathematical Society
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1112/plms.12214
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms.12214
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