Complete classification of the torsion structures of rational elliptic curves over quintic number fields
We classify the possible torsion structures of rational elliptic curves over quintic number fields. In addition, let E be an elliptic curve defined over Q and let G=E(Q)tors be the associated torsion subgroup. We study, for a given G, which possible groups G⊆H could appear such that H=E(K)tors, for...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/711098 |
| Acceso en línea: | http://hdl.handle.net/10486/711098 https://dx.doi.org/10.1016/j.jalgebra.2017.01.012 |
| Access Level: | acceso abierto |
| Palabra clave: | Rationals Elliptic Curves Quintic Number Fields Torsion Subgroup Matemáticas |
| Sumario: | We classify the possible torsion structures of rational elliptic curves over quintic number fields. In addition, let E be an elliptic curve defined over Q and let G=E(Q)tors be the associated torsion subgroup. We study, for a given G, which possible groups G⊆H could appear such that H=E(K)tors, for [K:Q]=5. In particular, we prove that at most there is one quintic number field K such that the torsion grows in the extension K/Q, i.e., E(Q)tors⊊E(K)tors |
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