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 (SDSS) 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 per cent by emission from the white dwarf (WD). The spectrum can be successfully reproduced by a three-component model (white dwarf, disc, secondary) with TWD=12500K for a fixed logg= 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, ~= 1.7 × 10-13Msolaryr-1. 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 320 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, GWLib and FSAur, but so far no working model for this behaviour is available.