Suppose that $A subset C$ is an annulus whose two boundary components $Gamma, gamma$ are Jordan curves.

Suppose furthermore that $f$ maps a neighborhood for $Gamma$ biholomorphically to a neighborhood of $gamma$,

and that $f(Gamma)=gamma$. Then $T=overline{A} / f$ is a torus, with a distinguished closed curve.

We propose a fast method for numerically computing the complex modulus of $T$ and a related number $lambda$

which we call the virtual multiplier.