Superconformal Fixed Points with E_n Global Symmetry

We obtain the elliptic curve and the Seiberg-Witten differential for an $N=2$ superconformal field theory which has an $E_8$ global symmetry at the strong coupling point $\tau=e^{\pi i/3}$. The differential has 120 poles corresponding to half the charged states in the fundamental representation of $E_8$, with the other half living on the other sheet. Using this theory, we flow down to $E_7$, $E_6$ and $D_4$. A new feature is a $\lambda_{SW}$ for these theories based on their adjoint representations. We argue that these theories have different physics than those with $\lambda_{SW}$ built from the fundamental representations.