Reid–Walsh conjecture on knot complements in a commensurability class

Let $M$ be a hyperbolic knot complement in $\mathbb{S}^3$. Two finite-volume hyperbolic 3-manifolds are commensurable when they share a common finite-degree cover; the commensurability class of $M$ is the collection of manifolds commensurable with it. Reid–Walsh's conjecture. The commensurability class of $M$ contains at most three knot complements. The conjecture relates the search for hidden symmetries to the distribution of knot complements among commensurability classes. The source gives no resolution, so it remains open.