We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to ...

The purpose of this paper is to give a down-to-earth proof of the well–known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.

Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)tors and the torsion subgroup E(K)tors, where K is a quadratic number field.