  Active region (AR) 12673 produced many M-class and several X-class flares,
one of which being an X9.3 flare, which is recorded as the largest solar flare
in solar cycle 24. We studied the evolution of the three-dimensional
flare-productive magnetic field within AR 12673, using a time series of
nonlinear force-free field extrapolations of every 12 hours from September 4th
00:00 UT to 6th 00:00 UT. Our analysis found that three magnetic flux ropes
(MFRs) are formed by September 4th, one of which produced the X9.3 flare on
September 6th. One MFR has positive magnetic twist which is a different sign
from other two MFRs. Since the temporal evolution of the magnetic flux of the
MFR accumulating the positive twist is consistent with the profile of the GOES
X-ray flux well observed from September 4th to 6th, we suggest that the
formation of the MFR having the positive twist is closely related to the
occurrence of the M-class flares including an M5.5 flare. We further found a
magnetic null in the magnetic field surrounding the MFRs, in particular, above
the MFR having positive twist before the M5.5 flare which is the largest
M-flare observed during this period. By comparing with the AIA 1600 angstrom
images, we found that the footpoints of the overlying field lines are anchored
to the area where the brightening was initially observed. Therefore, we suggest
that reconnection induced by the torus instability of the positively twisted
MFR at the null possibly drived the M5.5 flare.
