Galois Theory, discriminants and torsion subgroups of elliptic curves
We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the squareness of the discriminant of the elliptic curve.
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41955 |
| Acceso en línea: | http://hdl.handle.net/11441/41955 https://doi.org/10.1016/j.jpaa.2009.11.001 |
| Access Level: | acceso abierto |
| Palabra clave: | Elliptic curves Cubic equations Torsion subgroup Galois theory |
| Sumario: | We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the squareness of the discriminant of the elliptic curve. |
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