  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 Calabi-Yau 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 Neron-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.
