We investigate quantum lens spaces, , introduced by Brzeziński and Szymański as graph -algebras. We give a new description of as graph -algebras amending an error in the original paper by Brzeziński and Szymański. Furthermore, for , we give a number-theoretic invariant, when all but one weight are coprime to the order of the acting group r. This builds upon the work of Eilers, Restorff, Ruiz, and Sørensen.