Let \(E\) be an elliptic curve defined over a number field \(F\) with \(j\)-invariant \(j(E)\) belonging to a subfield \(F_0\) of \(F\). Put \(d=[F:\mathbb{Q}]\) and \(d_0=[F_0:\mathbb{Q}]\) (so that \(d_0|d\)) and let \(E(F)_{\mathrm{tor}}\) be the set of all torsion points of \(E\) defined over \(F\). It is well known that \(E(F)_{\mathrm{tor}}\) is finite and a few uniform bounds in terms of polynomials in \(d\) for \(\# E(F)_{\mathrm{tor}}\) (as \(E\) varies through all non-CM elliptic curves defined over \(F\)) have been conjectured (and sometimes proved) in recent years. The authors generalize a bound of K. Arai [J. Théor. Nombres Bordx. 20, No. 1, 23–43 (2008; Zbl 1211.11066)] on the image of the Galois representation of torsion points (using group theoretic arguments on \(p\)-adic analytic groups) and use a recent result of A. Lozano-Robledo [Res. Number Theory 4, Paper No. 6, 39 p. (2018; Zbl 1439.11137)] on ramification of fields generated by torsion points, to prove a bound of type \[ \# E(F)_{\mathrm{tor}} \leqslant C(\varepsilon, F_0)d^{\frac{5}{2}+\varepsilon} \] for all \(\varepsilon >0\), for all non CM elliptic curves defined over \(F\) and for some classes of fields \(F_0\), i.e. \(F_0\) imaginary quadratic of class number larger than 1, or (under GRH) \(F_0\) any field not containing the Hilbert class field of an imaginary quadratic field, or for fields \(F_0\) for which there exists a prime \(\ell_0(d_0)\) such that for any prime \(\ell>\ell_0(d_0)\) the modular curve \(X_0(\ell)\) has no noncuspidal non CM point of degree \(d_0\).