  Let K be a fixed number field and G its absolute Galois group. We give a
bound C(K), depending only on the degree, the class number and the discriminant
of K, such that for any elliptic curve E defined over K and any prime number p
strictly larger than C(K), the image of the representation of G attached to the
p-torsion points of E contains a subgroup of homotheties of index smaller than
12.
