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.

Detalhes bibliográficos
Autores: García Selfa, Irene, González Jiménez, Enrique, Tornero Sánchez, José María
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2010
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41955
Acesso em linha:http://hdl.handle.net/11441/41955
https://doi.org/10.1016/j.jpaa.2009.11.001
Access Level:acceso abierto
Palavra-chave:Elliptic curves
Cubic equations
Torsion subgroup
Galois theory
Descrição
Resumo: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.