New and old results will be presented on the Envelope, $E(A)$, which is a bounded region in the complex plane that contains the eigenvalues of a complex matrix $A$. $E(A)$ is the intersection of an infinite number of regions defined by elliptic curves. As such, $E(A)$ resembles and is contained in the numerical range of $A$, which is the intersection of an infinite number of half-planes. The Envelope, however, can be much smaller than the numerical range, while not being much harder to compute.