  We present the gravitational wave (GW) analysis of an extensive series of 3D
MHD core-collapse simulations. Our 25 models are launched from a 15 solar mass
progenitor, a spherically symmetric effective general relativistic potential,
the Lattimer-Swesty or the Shen equation of state (EoS), and a neutrino
parametrisation scheme which is accurate until about 5ms postbounce. For 3
representative models, we also include long-term neutrino physics by means of a
leakage scheme. Non- or only slowly rotating models show GW emission due to
prompt and proto-neutron star convection, allowing the distinction between the
two different nuclear EoS. For moderately or fast rotation rates models, we
find, in agreement with recent results, only a type I GW signature at core
bounce. Models which are set up with an initial central angular velocity of >~
2pi rad/s emit GWs due to the low T/|W| dynamical instability during the
postbounce phase. Weak B-fields do not notably influence the dynamical
evolution of the core and thus the GW emission. However, for strong initial
poloidal B-fields (~1e12 G),flux-freezing and field winding leads to conditions
where P_{mag}/P_{mat} ~ 1, causing the onset of a jet-like supernova explosion
and hence the emission of a type IV GW signal. In contradiction to axisymmetric
simulations, we find evidence that nonaxisymmetric fluid modes can counteract
or even suppress jet formation for models with strong initial toroidal
B-fields. We point out that the inclusion of the deleptonisation during the
postbounce phase is an indispensable issue for the quantitative prediction of
GWs from core-collapse supernovae, as it can alter the GW amplitude up to a
factor of 10 compared to a pure hydrodynamical treatment.
