An inclined-axis axial piston machine includes a housing, a drive shaft and a cylinder barrel. The drive shaft is mounted in the housing so as to be rotatable with respect to a first axis of rotation and is integral with a flange. Each piston is coupled to the flange via a ball joint. A multiplicity of counting perforations are arranged in a periodically distributed and continuous manner over an outer circumferential surface of the flange. The housing accommodates a sensor arranged opposite the counting perforations such that rotation of the drive shaft causes a signal change at the sensor. Each counting perforation is formed integrally from the flange, in the form of a recess having a single continuous perimeter. A side wall of the recess, starting from the perimeter, extends uninterruptedly, without sharp bends or offsets, over the entire circumference of the perimeter.