We present time-resolved spectroscopy and photometry of the cataclysmic
variable (CV) SDSSJ133941.11+484727.5 (SDSS1339) which has been discovered in
the Sloan Digital Sky Survey Data Release 4. The orbital period determined from
radial velocity studies is 82.524(24)min, close to the observed period minimum.
The optical spectrum of SDSS1339 is dominated to 90% by emission from the white
dwarf. The spectrum can be successfully reproduced by a three-component model
(white dwarf, disc, secondary) with Twd=12500K for a fixed log g=8.0, d=170pc,
and a spectral type of the secondary later than M8. The mass transfer rate
corresponding to the optical luminosity of the accretion disc is very
low,~1.7x10^-13Msun/yr. Optical photometry reveals a coherent variability at
641s with an amplitude of 0.025mag, which we interpret as non-radial pulsations
of the white dwarf. In addition, a long-period photometric variation with a
period of either 320min or 344min and an amplitude of 0.025mag is detected,
which bears no apparent relation with the orbital period of the system. Similar
long-period photometric signals have been found in the CVs
SDSSJ123813.73-033933.0, SDSSJ204817.85-061044.8, GW Lib and FS Aur, but so far
no working model for this behaviour is available.Comment: MNRAS, in press, 8 pages, 10 figures, some figures downgraded to meet
the file size constraint of arxiv.or