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For a fixed number field and an elliptic curve defined and semi-stable overthis number field, we consider the set of prime numbers p such that the Galoisrepresentation attached to the p-torsion points of the elliptic curve isreducible. When the number field satisfies a certain necessary condition, wegive an explicit bound, depending only on the number field and not on thesemi-stable elliptic curve, for these primes. This generalizes previous resultsof Kraus.

Crit\`ere d'irr\'eductibilit\'e pour les courbes elliptiques semi-stables sur un corps de nombres