  The electromagnetic form factors of the $\Lambda$ hyperon in the time-like
region are determined precisely through a dispersion-theoretical analysis of
the world data for the cross section of the annihilation process $e^+e^-\to
\bar{\Lambda}{\Lambda}$. The spectral function is represented by a
superposition of narrow and broad vector meson poles. We test different
scenarios for the spectral function and obtain a good description of the world
data in the time-like region. The uncertainties in the extracted form factors
are estimated by means of the bootstrap sampling method. The analytical
continuation of the form factors to the space-like region introduces large
errors due to the lack of data. When the electric $\Lambda$ radius from chiral
perturbation theory is taken as a constraint, the magnetic radius is predicted
as $r_M = 0.681 \pm 0.002$ fm. We also extract various vector meson to baryon
coupling constants.
