  We present optical photometry of XTE J2123-058 during its quiescent state
taken in 1999 and 2000. The dominant feature of our R-band light curve is the
ellipsoidal modulation of the secondary star, however, in order to fit this
satisfactorily we require additional components which comprise an X-ray heated
Roche-lobe filling secondary star, and an accretion disk bulge, i.e. where the
gas stream impacts the accretion disk. The observed dip near phase 0.8 is
interpreted as the eclipse of inner parts of the accretion disk by the bulge.
This scenario is highly plausible given the high binary inclination. Our fits
allow us to constrain the size of the quiescent accretion disk to lie in the
range 0.26-0.56R_L1 (68% confidence). Using the distance of 9.6 kpc and the
X-ray flux inferred from the heated hemisphere of the companion, we obtain an
unabsorbed X-ray luminosity of 1.2x10^33 erg/s for XTE J2123-058 in quiescence.
  From the observed quiescent optical/IR colors we find that the power-law
index (-1.4) for the spectral distribution of the accretion disk compares well
with other quiescent X-ray transients. We also re-analyse the optical light
curves of the soft X-ray transient XTE J2123-058 taken during its outburst and
decay in 1998. We use a robust method to fit the data using a refined X-ray
binary model. The model computes the light arising from a Roche-lobe filling
star and flared accretion disk irradiated by X-rays, and calculates the effects
of shadowing and mutual star/disk eclipses. We obtain relatively accurate
values for the binary inclination and mass ratio, which when combined with
spectroscopic results obtained in paper II gives a neutron star mass in the
range 1.04-1.56Mo (68% confidence).
