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Two-dimensional Maxwell-dilaton quantum gravity on AdS 2 with radius ℓ and a constant electric field E is studied. In conformal gauge, this is equivalent to a CFT on a strip. In order to maintain consistent boundary conditions, the usual conformal diffeomorphisms must be accompanied by a certain U(1) gauge transformation. The resulting conformal transformations are generated by a twisted stress tensor, which has a central charge c = 3kE 2 ℓ 4 /4 where k is the level of the U(1) current. This is an AdS 2 analog of the Brown-Henneaux formula c = 3ℓ/2G for the central charge of quantum gravity on AdS 3 .