  We investigate quantum lens spaces, $C(L_q^{2n+1}(r;\underline{m}))$,
introduced by Brzezi\'nski-Szyma\'nski as graph $C^*$-algebras. For $n\leq 3$,
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 S\{o}rensen.
