A bstract The Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X contains information about the abelian sector of the six-dimensional theory obtained by compactifying F-theory on X . After examining features of the abelian anomaly coefficient matrix and U(1) charge quantization conditions of general F-theory vacua, we study CalabiYau threefolds with Mordell-Weil rank-one as a first step towards understanding the features of the Mordell-Weil group of threefolds in more detail. In particular, we generate an interesting class of F-theory models with U(1) gauge symmetry that have matter with both charges 1 and 2. The anomaly equations — which relate the Néron-Tate height of a section to intersection numbers between the section and fibral rational curves of the manifold — serve as an important tool in our analysis.