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.

arXiv commentNew version, some typos fixed and the proof of the lemma in the Appendix has been expanded

Cited by in corpus (3)

• Torsion of rational elliptic curves over quadratic fields
• On the squareness of the discriminant of elliptic curves with an isogeny
• On the ubiquity of trivial torsion on elliptic curves