  In this article we consider the three parameter family of elliptic curves
$E_t: y^2-4(x-t_1)^3+t_2(x-t_1)+t_3=0, t\in\C^3$ and study the modular
holomorphic foliation $\F_{\omega}$ in $\C^3$ whose leaves are constant locus
of the integration of a 1-form $\omega$ over topological cycles of $E_t$. Using
the Gauss-Manin connection of the family $E_t$, we show that $\F_{\omega}$ is
an algebraic foliation. In the case $\omega=\frac{xdx}{y}$, we prove that a
transcendent leaf of $\F_{\omega}$ contains at most one point with algebraic
coordinates and the leaves of $\F_{\omega}$ corresponding to the zeros of
integrals, never cross such a point. Using the generalized period map
associated to the family $E_t$, we find a uniformization of $\F_{\omega}$ in
$T$, where $T\subset \C^3$ is the locus of parameters $t$ for which $E_t$ is
smooth. We find also a real first integral of $\F_\omega$ restricted to $T$ and
show that $\F_{\omega}$ is given by the Ramanujan relations between the
Eisenstein series.
