  We present complete calculations of the electromagnetic form factors of the
$\Omega^-$ in the spacelike region and in the timelike region. The four elastic
form factors: electric charge ($G_{E0}$), magnetic dipole ($G_{M1}$), electric
quadrupole ($G_{E2}$) and magnetic octupole ($G_{M3}$), are estimated within
the covariant spectator quark model, in terms of the square momentum transfer
$q^2$. The free parameters of the $\Omega^-$ wave function, including a
$S$-wave state and two independent $D$-wave states radial wave functions and
the admixture coefficients are fixed by the comparison with the lattice QCD
data in the spacelike region ($Q^2=-q^2 \le 0$) and with the recent $e^+ e^-
\to \Omega^- \bar \Omega^+$ data from CLEO in the timelike region ($q^2 > 0$).
The estimates in the timelike region for square momentum transfer $q^2 \ge 4
M_\Omega^2$ are based on large-$q^2$ asymptotic relations ($M_\Omega$ is the
$\Omega^-$ mass). We examine also the impact of the large-$Q^2$ correlations
between different form factors and analyze the possible solutions. The electric
quadrupole and the magnetic octupole moments of the $\Omega^-$, and the $e^+
e^- \to \Omega^- \bar \Omega^+$ integrated cross sections for very large $q^2$
are estimated based on the model results.
