  Methods are reviewed for computing the instanton expansion of the
prepotential for N=2 Seiberg-Witten (SW) theory with non-hyperelliptic curves.
These results, if compared with the instanton expansion obtained from the
microscopic Lagrangian, will provide detailed tests of M-theory. We observe
group-theoretic regularities of the one-instanton prepotential which allow us
to "reverse engineer" a SW curve for SU(N) gauge theory with two
hypermultiplets in the antisymmetric representation and $N_f\leq 3$
hypermultiplets in the fundamental representations, a result not yet available
by other methods. Consistency with M-theory requires a curve of infinite order,
which we identify as a decompactified version of elliptic models of the type
described by Donagi and Witten, Uranga, and others. This leads us to a brief
discussion of some elliptic models that relate to our work.
