We show that if E / Q is an elliptic curve without complex multiplication and for which there is a prime q such that the image of ρ ¯ E , q is contained in the normaliser of a split Cartan subgroup of GL 2 (F q) , then ρ ¯ E , p surjects onto GL 2 (F p) for every prime p > 37 . This result complements a previous result by the author. We also prove analogue results for certain families of Q -curves, building on results of Ellenberg (Am J Math 126(4):763–787, 2004) and Le Fourn (Math Ann 365(1–2):173–214, 2016).