  Gravitational waveform predictions from 3D simulations of explosions of
non-rotating massive stars with no magnetic fields have been extensively
studied. However, the impact of magnetic fields and rotation on the
core-collapse supernova gravitational-wave signal is not well understood beyond
the core-bounce phase. Therefore, we perform four magnetohydrodynamical
simulations of the explosion of a $15\,M_{\odot}$ star with the SFHx and SFHo
equations of state. All of the models start with a weak magnetic field strength
of $10^{8}$\,G, and two of the models are rapidly rotating. We discuss the
impact of the rotation and magnetic fields on the gravitational-wave signals.
We find that the weak pre-collapse fields do not have a significant impact on
the gravitational-wave signal amplitude. With rapid rotation, the f/g-mode
trajectory can change in shape, and the dominant emission band becomes broader.
We include the low-frequency memory component of the gravitational-wave signal
from both matter motions and neutrino emission anisotropy. We show that
including the gravitational waves from anisotropic neutrino emission increases
the supernova detection distances for the Einstein Telescope, and would also be
detectable out to Mpc distances by a moon-based gravitational-wave detector.
