Study of the $K3$ surfaces $X_t$ with $\NS(X_t)$ isomorphic to the lattice with Gram matrix
$$\begin{pmatrix}2t & 0 & 0\\
0 & -2 & 0\\
0 & 0 & -2
\end{pmatrix}$$
For $1\leq t \leq 50$, we had to determine
- Automorphism groups $\aut(X_t)$
- Upper bound on the number of orbits of $\cu$-curves on $X_t$
under the action of $\aut(X_t)$.