Why is the Picard-Fuchs equation for elliptic curves of second order?

Question

Consider the elliptic curve defined by a polynomial $$ F(x,y,z) = t(x^3 + y^3 + z^3) - 3xyz $$ If we consider the period integral $$ \pi(t) = \int_{\gamma} \omega(t) $$ where $\gamma$ is a $1$-cycle defined at and around $F$ for a variation of $t$. We can associate a second-order differential equation $$ \frac{d^2 \pi(t)}{dt^2} + A(t)\frac{d\pi(t)}{dt} + B(t) = 0 $$ called the Picard-Fuchs equation. Why is this differential equation second order? Does this have something to do with the real dimension of the complex variety?