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We solve the classification problem for integrable lattices of the form$u_{,t}=f(u_{-2},\dots,u_2)$ under the additional assumption of invariance withrespect to the group of linear-fractional transformations. The obtained listcontains 5 equations, including 3 new. Difference Miura type substitutions arefound which relate these equations with known polynomial lattices. We alsopresent some classification results for the generic lattices.

Integrable M\"obius invariant evolutionary lattices of second order