Critère d'irréductibilité pour les courbes elliptiques semi-stables sur un corps de nombres ; Irreducibility criterion for semistable elliptic curves over a number field

For a fixed number field and an elliptic curve defined and semistable 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 semistable elliptic curve, for these primes. This generalizes previous results of Kraus.