Mordell-Weil lattice of Inose's Elliptic $K3$ surface arising from the product of 3-isogenous elliptic curves

Masato Kuwata, Kazuki Utsumi

From the product of two elliptic curves, Shioda and Inose constructed an elliptic $K3$ surface having two ${\mathrm{II}}^{\ast }$ fibers. Its Mordell-Weil lattice structure depends on the…