  We study the effects of magnetic fields and rotation on the core collapse of
a star of an initial mass of M = 20 solar masses using axisymmetric simulations
coupling special relativistic magnetohydrodynamics, an approximately
relativistic gravitational potential, and spectral neutrino transport. We
compare models of the same core with different, artificially added profiles of
rotation and magnetic field. A model with weak field and slow rotation does not
produce an explosion, while stronger fields and fast rotation open the
possibility of explosions. Whereas the neutrino luminosities of the exploding
models are the same as or even less than those of the non-exploding model,
magnetic fields locally in equipartition with the gas pressure provide a strong
contribution to the shock revival and the acceleration of bipolar outflows.
Among the amplification processes generating such strong fields, we find the
magneto-rotational instability. However, our limited grid resolution allows us
to find it only in limited regions of the model with the strongest pre-collapse
field ($10^{11}$ G) and fastest rotation.
