Some observations about isogenies between \(K3\) surfaces

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 Apéry-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.