Non-cyclic torsion of elliptic curves over imaginary quadratic fields of class number 1

Let $K$ be a non-cyclotomic imaginary quadratic field with class number 1 and $E/K$ an elliptic curve with $E(K)[2]\simeq \mathbb{Z}/2\mathbb{Z}\oplus \mathbb{Z}/2\mathbb{Z}.$ In this paper, we determine the torsion groups that can arise as $E{(L)}_{\text{tor}}$ where $L$ is any quadratic extension of $K.$