Abstract: Two hyperbolic manifolds are commensurable if they share a common
finite sheeted cover. This notion partitions the set of hyperbolic 3-
manifolds into commensurability classes. An interesting question is to find
objects in a commensurability class that appear to be rare. Using the term
knot complement to denote S^3-K, Reid and Walsh have conjectured that there
are at most three hyperbolic knot complements in a given commensurablity
class. Boileau, Boyer, Cebanu, and Walsh showed the conjecture holds for
knot complements that do not admit hidden symmetries ie knot complements
that do not cover a rigid cusped orbifold. After providing some of the
necessary background, I will show that an interesting class of knot
complements does not admit hidden symmetries.