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Galois theory, discriminants and torsion subgroup of elliptic curves |
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| Authors: | Irene Garcí a-Selfa |
| Affiliation: | a Departamento de Matemáticas, Universidad de Huelva. Facultad de Ciencias Experimentales. Campus de “El Carmen”, Avenida de las Fuerzas Armadas, s/n. 21071 Huelva, Spain b Departamento de Matemáticas, Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM. 28049 Madrid, Spain c Departamento de Álgebra, Universidad de Sevilla. P.O. 1160. 41080 Sevilla, Spain |
| Abstract: | 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. |
| Keywords: | Primary, 11G05 Secondary, 11R16 |
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