Superhumps and spin-period variations in the intermediate polar RX J2133.7+5107

We report the results of long-term time series photometry on RX J2133.7+ 5107, an intermediate polar distinguished by its long orbital period (7.14 h) and rapid rotation (571 s) of its white dwarf. The light curves show the presence of a conspicuous modulation with a 6.72-h period, 6.1 +/- 0.1 per cent shorter than the orbital period, which we interpret as a (negative) superhump associated with the nodal precession of the accretion disc. This detection may prove a challenge to the idea that superhumps are limited to binaries of short orbital period. Our rotational timings over the 7 yr spanned by our observations show spin-up at a rate of 3.41(2) ms yr(-1) or, equivalently, on a time-scale | P/ P | = 0.17 x 10(6) yr. The latter is sensibly shorter than the time-scale of spin period variations reported for other intermediate polars, possibly due to a greater accretion rate.