  We derive a spin-orbital model for insulating LaMnO_3 which fulfills the
SU(2) symmetry of S=2 spins at Mn^{3+} ions. It includes the complete e_g and
t_{2g} superexchange which follows from a realistic Mn^{2+} multiplet structure
in cubic site symmetry, and the Jahn-Teller induced orbital interactions. We
show that the magnetic ordering observed in LaMnO_3 is stabilized by a purely
electronic mechanism due to the e_g-superexchange alone, and provide for the
first time a quantitative explanation of the observed transition temperature
and the anisotropic exchange interactions.
