Abstract
Given a non-CM elliptic curve E over Q of discriminant ∆E , define the “torsion conductor” mE to be the smallest positive integer so that the Galois representation on the torsion of E has image π−1(Gal(Q(E[mE ])/Q)), where π denotes the natural projection GL2(Ẑ) → GL2(Z/mEZ). We show that, uniformly for semi-stable non-CM elliptic curves E over Q, one has
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