  We study the stringy genus one partition function of $N=2$ SCFT's. It is
shown how to compute this using an anomaly in decoupling of BRST trivial states
from the partition function. A particular limit of this partition function
yields the partition function of topological theory coupled to topological
gravity. As an application we compute the number of holomorphic elliptic curves
over certain Calabi-Yau manifolds including the quintic threefold. This may be
viewed as the first application of mirror symmetry at the string quantum level.
