Spectral Curves for Almost-Complex Tori in $S^6$

To each non-isotropic almost-complex immersion of a 2-torus into $S^6$ we associate an algebraic curve, called the spectral curve, and a linear flow in the intersection of two Prym varieties on this spectral curve. We show that generically the spectral curve is smooth and compute the dimension of the moduli space of such curves and of the torus in which the eigenline bundles lie.