We consider $$AdS_2$$ A d S 2 solutions of M-theory which are obtained by twisted compactifications of M2-branes on a complex curve. They are of a generalized class, in the sense that the non-abelian part of the connection for the holomorphic bundle over the supersymmetric cycle is nontrivial. They are solutions of $$U(1)^4$$ U ( 1 ) 4 gauged supergravity in $$D=4$$ D = 4 , with magnetic flux over the curve, and then uplifted to $$D=11$$ D = 11 . We discuss the behavior of conformal fixed points as a function of the non-abelian connection. We also describe how they fit into the general description of wrapped M2-brane $$AdS_2$$ A d S 2 solutions and their higher-order generalizations, by showing that they satisfy the master equation for the eight-dimensional Kähler base space.