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In this note we study the constraints on F-theory GUTs with extra $U(1)$'s inthe context of elliptic fibrations with rational sections. We consider thesimplest case of one abelian factor (Mordell-Weil rank one) and investigate theconditions that are induced on the coefficients of its Tate form. Convertingthe equation representing the generic hypersurface $P_{112}$ to this Tate'sform we find that the presence of a U(1), already in this local description, isconsistent with the exceptional ${\cal E}_6$ and ${\cal E}_7$ non-abeliansingularities. We briefly comment on a viable ${\cal E}_6\times U(1)$ effectiveF-theory model.

F-GUTs with Mordell-Weil U(1)'s