 Elliptic K3 surface from a quartic containing a line

A smooth quartic surface $X\subseteq {\mathbb{P}}^3$ containing a line $L$ is a K3 surface. The pencil of planes through $L$ cuts out $L$ plus a residual plane cubic; the divisor class $H-L$ has square zero and its basepoint-free pencil defines an elliptic fibration $X\to {\mathbb{P}}^1$.