  We show that a single polynomial entanglement measure is enough to verify
equivalence between generic $n$-qubit states under Stochastic Local Operations
with Classical Communication (SLOCC). SLOCC operations may be represented
geometrically by M\"obius transformations on the roots of the entanglement
measure on the Bloch sphere. Moreover, we show how the roots of the 3-tangle
measure classify 4-qubit generic states, and propose a method to obtain the
normal form of a 4-qubit state which bypasses the possibly infinite iterative
procedure.
