Taylor's conjecture on the class-invariant homomorphism for CM elliptic curves

Let $A/L$ be an elliptic curve with everywhere good reduction and admitting complex multiplication by the ring of integers of a quadratic imaginary number field $K$. For $\lambda\in\mathcal{O}_K$ coprime to the number of roots of unity in $K$, let $\Psi_L$ be the class-invariant homomorphism associated with the isogeny induced by $\lambda$.

Taylor's conjecture.

$$A(L)_{\operatorname{tors}}\subseteq\ker(\Psi_L).$$

The conjecture predicts that the class-invariant homomorphism is trivial on the torsion subgroup of the Mordell–Weil group in this CM, everywhere-good-reduction setting. The supplied text gives no resolution status.