  We present and analyse light curves of four transits of the Southern
hemisphere extrasolar planetary system WASP-4, obtained with a telescope
defocussed so the radius of each point spread function was 17 arcsec (44
pixels). This approach minimises both random and systematic errors, allowing us
to achieve scatters of between 0.60 and 0.88 mmag per observation over complete
transit events. The light curves are augmented by published observations and
analysed using the JKTEBOP code. The results of this process are combined with
theoretical stellar model predictions to derive the physical properties of the
WASP-4 system. We find that the mass and radius of the planet are M_b = 1.289
{+0.090 -0.090} {+0.039 -0.000} MJup and R_b = 1.371 {+0.032 -0.035} {+0.021
-0.000} RJup, respectively (statistical and systematic uncertainties). These
quantities give a surface gravity and density of g_b = 17.03 +0.97 -0.54 m/s2
and rho_b = 0.500 {+0.032 -0.021} {+0.000 -0.008} rhoJup, and fit the trends
for short-period extrasolar planets to have relatively high masses and surface
gravities. WASP-4 is now one of the best-quantified transiting extrasolar
planetary systems, and significant further progress requires improvements to
our understanding of the physical properties of low-mass stars.
