Abstract Let $$\ell $$ ℓ be an odd prime and d a positive integer. We determine when there exists a degree-d number field K and an elliptic curve E / K with $$j(E)\in \mathbb {Q}\setminus \{0,1728\}$$ j ( E ) ∈ Q \ { 0 , 1728 } for which $$E(K)_\mathrm {tors}$$ E ( K ) tors contains a point of order $$\ell $$ ℓ , conditionally on a conjecture of Sutherland. We likewise determine when there exists such a pair (K, E) for which the image of the associated mod- $$\ell $$ ℓ Galois representation is contained in a Cartan subgroup or its normalizer. We do the same under the stronger assumption that E is defined over $$\mathbb {Q}$$ Q .