  The largest error in the theoretical determination of the muon anomalous
magnetic moment is due to the low-energy hadronic vacuum polarization, which
cannot be calculated by perturbative QCD and requires nonperturbative
techniques. Recently, an accurate determination of the low-energy two-pion
contribution to muon $g-2$ has been obtained by a parametrization-free analytic
continuation of the pion vector form factor from other kinematical regions. In
this work we compare the results of the analytic continuation with direct
determinations at low momenta from experiment and lattice QCD. We also explore
the sensitivity of the method to the timelike data on the modulus of the form
factor used as input, by extending the input region to energies up to 0.76 GeV.
