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For a quadratic field $\mathcal{K}$ without rationally defined CM, we provethat there exists of a prime $p_{\mathcal{K}}$ depending only on $\mathcal{K}$such that if $d$ is a positive integer whose minimal prime divisor is greaterthan $p_{\mathcal{K}}$, then for any extension $L/\mathcal{K}$ of degree d andany elliptic curve $E/\mathcal{K}$, we have$E\left(L\right)_{\operatorname{tors}} =E\left(\mathcal{K}\right)_{\operatorname{tors}}$. By not assuming the GRH, thisis a generalization of the results by Genao, and Gon\'alez-Jim\'enez andNajman.

Growth of Torsion Groups of Elliptic Curves Over Number Fields without Rationally Defined CM