We define two invariants for (semiprime right Goldie) algebras, one for algebras graded by arbitrary abelian groups, which is unchanged under twists by 2cocycles on the grading group, and one for Z-graded or Z ≥0 -filtered algebras. The first invariant distinguishes quantum algebras which are "truly multiparameter" apart from ones that are "essentially uniparameter", meaning cocycle twists of uniparameter algebras. We prove that both invariants are stable under adjunction of polynomial variables. Methods for computing these invariants for large families of algebras are given, including quantum nilpotent algebras and algebras admitting one quantum cluster, and applications to non-isomorphism theorems are obtained.2010 Mathematics Subject Classification. Primary 16K40; Secondary 16S85, 16T20, 17B37, 13F60. Key words and phrases. Locally finite graded and filtered algebras, 2-cocycle twists of algebras, Alev-Dumas invariants, stable invariants, maximal tori of automorphism groups.