Cyclicity conjecture for elliptic curves

Let $E/\mathbb{Q}$ be a non-CM elliptic curve. For each positive integer $k$, let $E[k]$ be the $k$-torsion subgroup and let $\mathbb{Q}(E[k])$ be the field obtained by adjoining the coordinates of all points in $E[k]$. Define

$$\pi_E^{\mathrm{cyc}}(x)=\#\{p\leq x:E_p(\mathbb{F}_p)\text{ is cyclic}\}.$$

Here $E_p/\mathbb{F}_p$ denotes the reduction of $E$ at a prime of good reduction, and $\mu$ is the Möbius function. Cyclicity conjecture.

$$\pi_E^{\mathrm{cyc}}(x)\sim \left(\sum_{k\geq 1}\frac{\mu(k)}{[\mathbb{Q}(E[k]):\mathbb{Q}]}\right)\operatorname{li}(x).$$

This predicts the density of primes for which the group of points on the reduced elliptic curve is cyclic. The source gives no resolution status, so the conjecture is recorded as open.