Galois Theory, discriminants and torsion subgroups of elliptic curves

Details Galois Theory, discriminants and torsion subgroups of elliptic curves Galois Theory, discriminants and torsion subgroups of elliptic curves

2008-11-10

arxiv.org/abs/0811.1463v3

Journal of Pure and Applied Algebra 214, 1340-1346 (2010)

Mathematics

Number Theory

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

Scientific paper

10.1016/j.jpaa.2009.11.001

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.

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