Pulley (100, 100') equipped with a longitudinal axis, said pulley comprising an outer side and an inner side axially opposite the outer side, as well as: - a rim comprising: a zone intended to receive a belt connecting the rim to a first power transmission element, an inner periphery equipped with a plurality of lugs (13,14, 15, 16), at least two lugs (13, 14), diametrically opposite, being arranged on the outer side of the pulley (100, 100') and at least two other lugs (15, 16), also diametrically opposite, being arranged on the inner side of the pulley (100, 100'); - a hub intended to be secured to a second power transmission element; one of the power transmission elements being driving and the other being driven or vice versa; - at least two rings (40, 400, 40'), each ring (40, 400, 40') comprising at least four abutments (41, 42, 43, 44; 41', 42', 43', 44') diametrically opposite two-by-two (42, 44; 41, 43; 42', 44'; 41', 43') capable of engaging with the lugs (13, 14, 15, 16) of the rim and/or the lugs (32, 33, 32', 33') of the indexers (30, 30') so as to be able to be driven in rotation about said longitudinal axis; - an elastically deformable element of which a first end is mounted in contact with the first ring (40, 400) and of which a second end is mounted in contact with the second ring; characterized in that the pulley (100, 100') further comprises: - at least two indexers (30, 30') mounted fixed with respect to the hub, the first indexer being arranged on the outer side of the pulley and equipped on its outer periphery with at least two lugs (32, 33) diametrically opposite and the second indexer being arranged on the inner side of the pulley (100, 100') and equipped on its outer periphery with at least two lugs (32', 33') diametrically opposite; - one of the rings (40, 400; 40') being mounted between the inner periphery of the rim and the outer periphery of the first indexer and the other of the rings being mounted between the inner periphery of the rim and the outer periphery of the second indexer, said at least four abutments (41, 42, 43, 44; 41', 42', 43', 44') being thus adapted to cooperate with the lugs (32, 33, 32', 33') of the indexers (30, 30') so as to be able to be driven in rotation about said longitudinal axis. - a rim comprising: a zone intended to receive a belt connecting the rim to a first power transmission element, an inner periphery equipped with a plurality of lugs (13,14, 15, 16), at least two lugs (13, 14), diametrically opposite, being arranged on the outer side of the pulley (100, 100') and at least two other lugs (15, 16), also diametrically opposite, being arranged on the inner side of the pulley (100, 100'); a zone intended to receive a belt connecting the rim to a first power transmission element, an inner periphery equipped with a plurality of lugs (13,14, 15, 16), at least two lugs (13, 14), diametrically opposite, being arranged on the outer side of the pulley (100, 100') and at least two other lugs (15, 16), also diametrically opposite, being arranged on the inner side of the pulley (100, 100'); - a hub intended to be secured to a second power transmission element; one of the power transmission elements being driving and the other being driven or vice versa; - at least two rings (40, 400, 40'), each ring (40, 400, 40') comprising at least four abutments (41, 42, 43, 44; 41', 42', 43', 44') diametrically opposite two-by-two (42, 44; 41, 43; 42', 44'; 41', 43') capable of engaging with the lugs (13, 14, 15, 16) of the rim and/or the lugs (32, 33, 32', 33') of the indexers (30, 30') so as to be able to be driven in rotation about said longitudinal axis; - an elastically deformable element of which a first end is mounted in contact with the first ring (40, 400) and of which a second end is mounted in contact with the second ring; - at least two indexers (30, 30') mounted fixed with respect to the hub, the first indexer being arranged on the outer side of the pulley and equipped on its outer periphery with at least two lugs (32, 33) diametrically opposite and the second indexer being arranged on the inner side of the pulley (100, 100') and equipped on its outer periphery with at least two lugs (32', 33') diametrically opposite; - one of the rings (40, 400; 40') being mounted between the inner periphery of the rim and the outer periphery of the first indexer and the other of the rings being mounted between the inner periphery of the rim and the outer periphery of the second indexer, said at least four abutments (41, 42, 43, 44; 41', 42', 43', 44') being thus adapted to cooperate with the lugs (32, 33, 32', 33') of the indexers (30, 30') so as to be able to be driven in rotation about said longitudinal axis.