For a quadratic field $\mathcal{ K}$ without rationally defined CM, we prove that 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 greater than $p_{ \mathcal{ K}}$, then for any extension $L/\mathcal{ K}$ of degree d and any 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, this is a generalization of the results by Genao, and Gon\'alez-Jim\'enez and Najman.
Categories: math.NT