Propriétés arithmétiques d'une famille de surfaces K3

We study a family of K3 surfaces which have a big automorphism group. We begin with generalisations of Silverman's results: construction of canonical heights, density of rational points in one orbit,... We continue the study in estimating the density of rational points on the orbiting rational curves; this estimate is compatible with Batyrev–Manin conjecture. Moreover we settle, under more geometric hypothesis, the number of rational points of such surfaces of bounded height.