  We prove recursive formulas for $\tau_d$, the number of degree $d$ elliptic
curves with fixed j-invariant in P^n. We use analysis to relate the classical
invariant $\tau_d$ to the genus one perturbed invariant $RT_{1,d}$ defined
recently by Ruan and Tian (the later invariant can be computed inductively). By
considering a sequence of perturbations converging to zero, we then apply
Taubes' Obstruction Bundle method to compute the difference between the two
invariants.
