  Even if there are too many elliptic fibrations to investigate and describe on
the singular $K3$ surface $Y_{10}$ of discriminant 72 and belonging to the
Ap\'ery-Fermi pencil $(Y_k)$, we find on it many interesting properties. For
example some of its elliptic fibrations with 3-torsion section induce by
3-isogeny either an elliptic fibration of $Y_2$, the unique $K3$ surface of
discriminant 8, or an elliptic fibration of other $K3$ surfaces of discriminant
72.
