2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136023This paper investigates the strength of the trace field as a commensurability invariant of hyperbolic 3-manifolds. We construct an infinite family of two-component hyperbolic link complements which are pairwise incommensurable and have the same trace field, and infinitely many 1-cusped finite volume hyperbolic 3-manifolds with the same property. We also show that the two-component link complements above have integral traces, but each has a mutant with a nonintegral trace.29 pages, 9 figures; added emails and affiliations for authorsGeometric Topology57M50text