Galois theory, discriminants and torsion subgroup of elliptic curves
Copyright policy )Galois theory, discriminants and torsion subgroup 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.
New version, some typos fixed and the proof of the lemma in the Appendix has been expanded
Algebra and Number Theory, Mathematics - Number Theory, 11R32, 11G05, Matemáticas, Galois theory, Torsion subgroup, Galois Representations, P-Adic L-Function, Elliptic Curve, FOS: Mathematics, Elliptic curves, Number Theory (math.NT), Cubic equations
Algebra and Number Theory, Mathematics - Number Theory, 11R32, 11G05, Matemáticas, Galois theory, Torsion subgroup, Galois Representations, P-Adic L-Function, Elliptic Curve, FOS: Mathematics, Elliptic curves, Number Theory (math.NT), Cubic equations
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