  For a fixed number field and an elliptic curve defined and semi-stable over
this number field, we consider the set of prime numbers p such that the Galois
representation attached to the p-torsion points of the elliptic curve is
reducible. When the number field satisfies a certain necessary condition, we
give an explicit bound, depending only on the number field and not on the
semi-stable elliptic curve, for these primes. This generalizes previous results
of Kraus.
