A turbomachine includes a low-pressure shaft that drives a fan shaft in rotation by a coupling assembly including a first shaft on which are formed plural first axial grooves, a second shaft on which are formed plural second axial grooves, and a coupling device including rolling elements and an annular cage positioned between the first shaft and the second shaft. The rolling elements are positioned between one of the first axial grooves and one of the second axial grooves to couple in rotation the first and the second shaft. Each first and second groove has a first and a second substantially planar surface inclined with respect to one another and extending along the axis.