$\mathbb{Q}$-bases of the N\'eron-Severi groups of certain elliptic surfaces

P. Stiller computed the Picard numbers of several families of elliptic surfaces, the rank of the N'eron-Severi groups of these surfaces. However he did not give the generators of these groups. In this paper we give $\mathbb Q$-bases of these groups explicitly. If these surfaces are rational, then we also show that they are $\mathbb{Z}$-bases.