Quartic Points on \(\mathcal {C}_2 (7)\)

We determine geometrically the algebraic points of degree 4 in \(\mathbb {Q}\) on the curve with affine equation \(y^7 = x (x - 1)^2\) . This curve has been studied by O. Sall and had given in Sall (C R Acad Sci Paris Ser I 336:117–120, 2003) a parametrization of cubic points in 2003. In this note we extend the work of O. Sall to points of degree 4 over \(\mathbb {Q}\) using a geometric method.