Galois Theory, discriminants and torsion subgroups of elliptic curves
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2008
- arXiv:
- arXiv:0811.1463
- Bibcode:
- 2008arXiv0811.1463G
- Keywords:
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- Mathematics - Number Theory;
- 11R32;
- 11G05
- E-Print:
- New version, some typos fixed and the proof of the lemma in the Appendix has been expanded