  We identify SDSSJ121010.1+334722.9 as an eclipsing post-common-envelope
binary, with an orbital period of P ~ 3 hrs, 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 GALEX near-ultraviolet flux, yields a
white dwarf temperature of 6000 +/- 200 K and a metallicity value of log(Z/H)=
-2.0 +/- 0.3. The sodium absorption doublet is used to measure the radial
velocity of the secondary star, K2 ~ 252 km/s and iron absorption lines in the
blue part of the spectrum provide the radial velocity of the white dwarf, K1 ~
95 km/s, yielding a mass ratio of q ~ 0.38. Light curve model fitting, using
the Markov Chain Monte Carlo (MCMC) method, gives the inclination angle as i =
(79.05 - 79.36) +/- 0.15 degrees, and the stellar masses as M1 = 0.415 +/-
0.010 solar-masses and M2 = 0.158 +/- 0.006 solar-masses. 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 R1 = (0.0157 - 0.0161) +/- 0.0003 solar-radii and the volume-averaged radius
of the tidally distorted secondary is R2 = (0.197 - 0.203) +/- 0.003
solar-radii. The white dwarf in J1210+3347 is a very strong He-core candidate.

Solar and Stellar Astrophysics