Caract\`ere d'isog\'enie et crit\`eres d'irr\'eductibilit\'e

This article deals with the Galois representation attached to elliptic curves with an isogeny of prime degree over a number field. We first determine uniform criteria for the irreducibility of Galois representations attached to elliptic curves in some infinite families, characterised by their reduction type at some fixed places of the base field. Then, we give an explicit form for a bound that appear in a theorem of Momose. Finally, we use these results to precise a previous theorem of the author about the homotheties contained in the image of the Galois representation.