  Processes with precisely known cross sections, like neutrino electron elastic
scattering ($\nu e^{-} \!\rightarrow \nu e^{-}$) and inverse muon decay
($\nu_\mu e^{-} \!\rightarrow \mu^{-} \nu_e$) have been used by MINERvA to
constrain the uncertainty on the NuMI neutrino beam flux. This work presents a
new measurement of neutrino elastic scattering with electrons using the medium
energy \numubar enhanced NuMI beam. A sample of 578 events after background
subtraction is used in combination with the previous measurement on the \numu
beam and the inverse muon decay measurement to reduce the uncertainty on the
\numu flux in the \numu-enhanced beam from 7.6\% to 3.3\% and the \numubar flux
in the \numubar-enhanced beam from 7.8\% to 4.7\%.
