Compressor (4, 6) for an axial turbomachine, such as an aircraft turbojet engine, the compressor (4, 6) comprising: - a rotor (112; 212; 312); - at least two rows of stator vanes; the rotor (112; 212; 312) comprising: - a drum (140; 240; 340), substantially axisymmetric in shape and made of composite material, the drum (140; 240; 340) having a radially outer surface (141; 241; 341); - at least one annular row of rotor blades (124; 224; 324), each rotor blade (124; 224; 324) including a vane (125; 225; 325) having a pressure surface (125.1) and a suction surface (125.2), the annular row comprising a first rotor blade (124; 224; 324) and a second rotor blade (124; 224; 324) directly circumferentially adjacent to the first rotor blade (124; 224; 324); wherein the rotor comprises at least one shell (150; 250; 350) for fastening the rotor blades (124; 224; 324) to the drum (140; 240; 340), the one or more shells (150; 250; 350) being attached to the external surface (141; 241; 341) of the drum (140; 240; 340) and forming a connecting surface between the pressure surface (125.1) of the first rotor blade (124; 224; 324) and the suction surface (125.2) of the second rotor blade (124; 224; 324), the one or more shells comprising, and being attached directly to the drum by means of an upstream flange (154; 254; 354) and of a downstream flange (158; 258; 358); wherein the flanges (154; 254; 354; 158; 258; 358) have an L-shaped cross-section comprising respectively a branch (154. 1; 254.1; 354.1; 158.1; 258.1; 358.1) conforming to the drum (140; 240; 340) and attached directly thereto; and a branch (154.2; 254.2; 354.2; 158.2; 258.2; 358.2) connected to a central portion (156; 256; 356) of the one or more shells which is radially raised with respect to the drum (140; 240; 340), the compressor (4, 6) being such that the at least one annular row of rotor blades (124; 224; 324) is arranged axially between the at least two annular rows of stator vanes, wherein each row of stator vanes is supported by an inner ferrule axially overlapping the drum (140; 240; 340), the inner ferrule and the shell (150; 250; 350) overlapping radially. - a rotor (112; 212; 312); - at least two rows of stator vanes; the rotor (112; 212; 312) comprising: - a drum (140; 240; 340), substantially axisymmetric in shape and made of composite material, the drum (140; 240; 340) having a radially outer surface (141; 241; 341); - at least one annular row of rotor blades (124; 224; 324), each rotor blade (124; 224; 324) including a vane (125; 225; 325) having a pressure surface (125.1) and a suction surface (125.2), the annular row comprising a first rotor blade (124; 224; 324) and a second rotor blade (124; 224; 324) directly circumferentially adjacent to the first rotor blade (124; 224; 324); - a drum (140; 240; 340), substantially axisymmetric in shape and made of composite material, the drum (140; 240; 340) having a radially outer surface (141; 241; 341); - at least one annular row of rotor blades (124; 224; 324), each rotor blade (124; 224; 324) including a vane (125; 225; 325) having a pressure surface (125.1) and a suction surface (125.2), the annular row comprising a first rotor blade (124; 224; 324) and a second rotor blade (124; 224; 324) directly circumferentially adjacent to the first rotor blade (124; 224; 324); wherein the rotor comprises at least one shell (150; 250; 350) for fastening the rotor blades (124; 224; 324) to the drum (140; 240; 340), the one or more shells (150; 250; 350) being attached to the external surface (141; 241; 341) of the drum (140; 240; 340) and forming a connecting surface between the pressure surface (125.1) of the first rotor blade (124; 224; 324) and the suction surface (125.2) of the second rotor blade (124; 224; 324), the one or more shells comprising, and being attached directly to the drum by means of an upstream flange (154; 254; 354) and of a downstream flange (158; 258; 358); wherein the flanges (154; 254; 354; 158; 258; 358) have an L-shaped cross-section comprising respectively a branch (154. 1; 254.1; 354.1; 158.1; 258.1; 358.1) conforming to the drum (140; 240; 340) and attached directly thereto; and a branch (154.2; 254.2; 354.2; 158.2; 258.2; 358.2) connected to a central portion (156; 256; 356) of the one or more shells which is radially raised with respect to the drum (140; 240; 340), the compressor (4, 6) being such that the at least one annular row of rotor blades (124; 224; 324) is arranged axially between the at least two annular rows of stator vanes, wherein each row of stator vanes is supported by an inner ferrule axially overlapping the drum (140; 240; 340), the inner ferrule and the shell (150; 250; 350) overlapping radially.