Post-common envelope binaries from SDSS - XV. Accurate stellar parameters for a cool 0.4 M-circle dot white dwarf and a 0.16 M-circle dot M dwarf in a 3 h eclipsing binary

We identify SDSS J121010.1+334722.9 as an eclipsing post-common-envelope binary, with an orbital period of P-orb = 2.988h, containing a very cool, low-mass, DAZ white dwarf and a low-mass main-sequence star of spectral type M5. A model atmosphere analysis of the metal absorption lines detected in the blue part of the optical spectrum, along with the Galaxy Evolution Explorer near-ultraviolet flux, yields a white dwarf temperature of T-eff,T-WD = 6000 +/- 200 K and a metallicity value of log [Z/H] = -2.0 +/- 0.3. The Na I lambda lambda 8183.27, 8194.81 absorption doublet is used to measure the radial velocity of the secondary star, K-sec = 251.7 +/- 2.0 km s(-1), and Fe I absorption lines in the blue part of the spectrum provide the radial velocity of the white dwarf, K-WD = 95.3 +/- 2.1 km s(-1), yielding a mass ratio of q = 0.379 +/- 0.009. Light-curve model fitting, using the Markov chain Monte Carlo method, gives the inclination angle as i = (79.degrees 05-79.degrees 36) +/- 0.degrees 15, and the stellar masses as M-WD = 0.415 +/- 0.010 M-circle dot and M-sec = 0.158 +/- 0.006 M-circle dot. Systematic uncertainties in the absolute calibration of the photometric data influence the determination of the stellar radii. The radius of the white dwarf is found to be R-WD = (0.0157-0.0161) +/- 0.0003 R-circle dot and the volume-averaged radius of the tidally distorted secondary is R-sec,R- (vol.aver.) = (0.197-0.203) +/- 0.003 R-circle dot. The white dwarf in SDSS J121010.1+334722.9 is a very strong He-core candidate.