The degree-3 covering map conjecture for elliptic surfaces

Let $\pi_2$ be the elliptic fibration constructed from a point of ${\mathcal M}'_{K,1}$, let $\sigma_0$ be its zero section, and let $\phi$ be the map associated with the corresponding point of ${\mathcal M}'_3$. The restriction of $\pi_2$ to $\sigma_0$ is a degree-$3$ map to the base of $\pi_2$. Degree-3 covering map conjecture. The degree-$3$ map from $\sigma_0$ to the base of $\pi_2$ coincides with the map $\phi$ in the corresponding point of ${\mathcal M}'_3$. This conjecture is supported by computational experiments and identifies the section-induced covering with the map parametrized by ${\mathcal M}'_3$; the supplied text gives no resolution.