  We investigate the impact of rotation and magnetic fields on the dynamics and
gravitational wave emission in 2D core-collapse supernova simulations with
neutrino transport. We simulate 17 different models of $15\,M_\odot$ and
$39\,M_\odot$ progenitor stars with various initial rotation profiles and
initial magnetic fields strengths up to $10^{12}\, \mathrm{G}$, assuming a
dipolar field geometry in the progenitor. Strong magnetic fields generally
prove conducive to shock revival, though this trend is not without exceptions.
The impact of rotation on the post-bounce dynamics is more variegated, in line
with previous studies. A significant impact on the time-frequency structure of
the gravitational wave signal is found only for rapid rotation or strong
initial fields. For rapid rotation, the angular momentum gradient at the
proto-neutron star surface can appreciably affect the frequency of the dominant
mode, so that known analytic relations for the high-frequency emission band no
longer hold. In case of two magnetorotational explosion models, the deviation
from these analytic relations is even more pronounced. One of the
magnetorotational explosions has been evolved to more than half a second after
the onset of the explosion and shows a subsidence of high-frequency emission at
late times. Its most conspicuous gravitational wave signature is a
high-amplitude tail signal. We also estimate the maximum detection distances
for our waveforms. The magnetorotational models do not stick out for higher
detectability during the post-bounce and explosion phase.
