  Let $M$ be a $2$-cusped hyperbolic $3$-manifold. By the work of Thurston, the
product of the derivatives of the holonomies of core geodesics of each Dehn
filling of $M$ is an invariant of it. In this paper, we classify Dehn fillings
of $M$ with sufficiently large coefficients using this invariant. Further, for
any given two Dehn fillings of $M$ (with sufficiently larger coefficients), if
their aforementioned invariants are the same, it is shown their complex volumes
are the same as well.
