  Many interesting questions about F-theory models, including several
concerning the F-theory swampland, involve massless matter charged under U(1)
gauge symmetries. It is therefore important to better understand the geometric
properties of F-theory models realizing various U(1) charges. We propose that,
for F-theory models described by elliptic fibrations in Weierstrass form, the
U(1) charge of light matter is encoded in the orders of vanishing of the
section components corresponding to the U(1) gauge symmetry. We give specific
equations relating the U(1) charges to the orders of vanishing that seem to
hold for both U(1)-charged singlets and for matter additionally charged under a
simply-laced nonabelian gauge algebra. Our formulas correctly describe
properties of F-theory models in the prior literature, and we give an argument
that they should describe the orders of vanishing for arbitrarily high U(1)
charges. They also resemble formulas for the $p$-adic valuations of elliptic
divisibility sequences developed by Stange [arXiv:1108.3051]. These proposals
could serve as a U(1) analogue of the Katz-Vafa method, allowing one to
determine U(1) charges without resolution. Additionally, they predict geometric
information about F-theory models with general U(1) charges, which may be
useful for exploring the F-theory landscape and swampland.
