A dual-flow jet engine comprising a fixed structure, a central core, and a cowl comprising a fixed part and a mobile cowl mounted to be rotationally mobile on the fixed structure via hinges with swan neck fitting. The fixed part has a first edge and the mobile cowl has a second edge, in which, when the mobile cowl is in a closed position, the second edge extends against the first edge. For each hinge with swan neck fitting, the fixed part is hollowed at the first edge, so as to delimit a recess opposite the swan neck fitting and allow the passage of the swan neck fitting when the mobile cowl switches from the closed position to the open position. The recess for each hinge with swan neck fitting allows for a reduction of the dimensions of the swan neck during the movement of the mobile cowl.