Using 805 pb^-1 of e+e- annihilation data taken with the CLEO-c detector at psi(3770), sqrt{s}=3770 MeV, we report the first measurements of the electromagnetic form factors of the Lambda0, Sigma0, Sigma+, Xi0, Xi-, and Omega- hyperons for the large timelike momentum transfer of |Q^2|=14.2 GeV^2. The form factors for the different hyperons are found to vary by nearly a factor two. It is found that |G_M(Lambda0)|=1.66(24) x |G_M(Sigma0)|. The Lambda0 and Sigma0 hyperons have the same uds quark content, but differ in their isospin, and therefore the spin of the $ud$ quark pair. It is suggested that the spatial correlation implied by the singlet spin--isospin configuration in the Lambda0 is an example of strong diquark correlations in the Lambda0, as anticipated by Jaffe and Wilczek. Improved measurements of the branching fractions of psi(2S) -> p pbar and hyperon--antihyperon pairs are also reported.