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The recently evaluated two-pion contribution to the muon g-2 and the phase ofthe pion electromagnetic form factor in the elastic region, known from \pi\piscattering by Fermi-Watson theorem, are exploited by analytic techniques forfinding correlations between the coefficients of the Taylor expansion at t=0and the values of the form factor at several points in the spacelike region. Wedo not use specific parametrizations and the results are fully independent ofthe unknown phase in the inelastic region. Using for instance, from recentdeterminations, <r^2_\pi> = (0.435 \pm 0.005) fm^2 and F(-1.6GeV^2)=0.243^{+0.022}_{-0.014}, we obtain the allowed ranges 3.75GeV^{-4}\lesssim c \lesssim 3.98 GeV^{-4} and 9.91 GeV^{-6}\lesssim d \lesssim10.46 GeV^{-6} for the curvature and the next Taylor coefficient, with a strongcorrelation between them. We also predict a large region in the complex planewhere the form factor can not have zeros.

Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region