  We use a Fourier transform spectrometer based on a difference frequency
generation optical frequency comb to measure high-resolution, low-pressure,
room-temperature spectra of methane in the 1250 - 1380 cm$^{-1}$ range. From
these spectra, we retrieve line positions and intensities of 678 lines of two
isotopologues: 157 lines from the $^{12}$CH${_4}$ ${\nu}$${_4}$ fundamental
band, 131 lines from the $^{13}$CH${_4}$ ${\nu}$${_4}$ fundamental band, as
well as 390 lines from two $^{12}$CH${_4}$ hot bands, ${\nu}$${_2}$ +
${\nu}$${_4}$ - ${\nu}$${_2}$ and 2${\nu}$${_4}$ - ${\nu}$${_4}$. For another
165 lines from the $^{12}$CH${_4}$ ${\nu}$${_4}$ fundamental band we retrieve
line positions only. The uncertainties of the line positions range from 0.19 to
2.3 MHz, and their median value is reduced by a factor of 18 and 59 compared to
the previously available data for the $^{12}$CH${_4}$ fundamental and hot
bands, respectively, obtained from conventional FTIR absorption measurements.
The new line positions are included in the global models of the spectrum of
both methane isotopologues, and the fit residuals are reduced by a factor of 8
compared to previous absorption data, and 20 compared to emission data. The
experimental line intensities have relative uncertainties in the range of 1.5 -
7.7%, similar to those in the previously available data; 235 new
$^{12}$CH${_4}$ line intensities are included in the global model.
