  This paper provides a simple method to extract the zeros of some weight two
Eisenstein series of level $N$ where $N=2,3,5$ and $7$. The method is based on
the observation that these Eisenstein series are integral over the graded
algebra of modular forms on $SL(2,Z)$ and their zeros are `controlled' by those
of $E_4$ and $E_6$ in the fundamental domain of $\Gamma_0(N)$.
