  The zeros of classical Eisenstein series satisfy many intriguing properties.
Work of F. Rankin and Swinnerton-Dyer pinpoints their location to a certain arc
of the fundamental domain, and recent work by Nozaki explores their interlacing
property. In this paper we extend these distribution properties to a particular
family of Eisenstein series on Gamma(2) because of its elegant connection to a
classical Jacobi elliptic function cn(u) which satisfies a differential
equation. As part of this study we recursively define a sequence of polynomials
from the differential equation mentioned above that allow us to calculate zeros
of these Eisenstein series. We end with a result linking the zeros of these
Eisenstein series to an L-series.
