Wan–Xi's constant-equality conjecture for CM elliptic curves

Let $E/\mathbb{Q}$ be a CM elliptic curve, let $r\neq 0$ be a fixed integer, let $C_{E,r}$ be the Lang–Trotter constant, and let $\overline{\omega}_{E,r}$ be the explicit constant arising from the Hardy–Littlewood-based asymptotic for $\pi_{E,r}(x)$. Wan–Xi's conjecture. The two constants should be equal:

$$\overline{\omega}_{E,r}=C_{E,r}.$$

The conjecture asserts that the alternative constant obtained through primes represented by quadratic polynomials agrees with the original Lang–Trotter constant. The paper states that this equality is verified for $20$ CM elliptic curves, while the general claim is not stated as resolved.