Let $\phi:S\rightarrow \mathbb{P}^1$ be an elliptic fibration of a compact complex surface. Assume that there is a multiple section $s$ of $\phi$. Is it true that $H^0(\mathbb{P}^1,R^2f_*\mathbb{R})$ is generated by the class of section $s$ and $H^2(\mathbb{P}^1,f_*\mathbb{R})$ is generated by the fiber class of $\phi$? I would appreciate it if someone could introduce a good reference to me.