Abstract: The main result of this note is as follows:
Let M=(_C ^A _D ^B)∈SL(2,Z) be hyperbolic. Then the Atiyah's invariant
η(M)=-sign (trac (M))|m (M) Ψ₀ (M), whore m(M) is the index of M in the stable subgroup for
α=(A-D+√(A+D)²-4)/2C of the PSL (2, Z), and
Ψ₀(M)=(1)/3Ψ(α).