  We prove that the family $\mathcal{I}_{F_0}$ of elliptic curves over number
fields that are geometrically isogenous to an elliptic curve with
$F_0$-rational $j$-invariant is typically bounded in torsion. Under an
additional uniformity assumption, we also prove that the family
$\mathcal{I}_{d_0}$ of elliptic curves over number fields that are
geometrically isogenous to an elliptic curve with degree $d_0$ $j$-invariant is
typically bounded in torsion.
