We present a detailed analysis of the extremely low luminosity white d
warf ESO 439-26. The measured trigonometric parallax of pi = 0 ''.0237
+/- 0 ''.0030, together with the observed V magnitude of 20.52, yield
s an absolute visual magnitude of M(V) = 17.4 +/- 0.3. ESO 439-26 thus
lies more than 1 mag faintward of the observed cutoff of the white-dw
arf luminosity function in the Galactic disk and could therefore be th
e coolest and hence oldest white dwarf ever detected. However, we show
from a detailed analysis of the optical energy distribution that the
intrinsic low luminosity of ESO 439-26 is the result of its small radi
us, or large mass. Our best solution is reached with T-eff = 4560 +/-
100 K, log g = 9.04 +/- 0.14, and a pure-helium atmospheric compositio
n. Evolutionary models are used to derive a mass of M = 1.21 +/- 0.07
M(.) and a cooling age of 6.4 +/- 0.3 Gyr, a value that is smaller tha
n the current estimates of the age of the Galactic disk.