  We identified a new ultra-distant comet C/2019 E3 (ATLAS) exhibiting
preperihelion cometary activity at heliocentric distances $\gtrsim\!20$ au,
making it the fourth member of this population after C/2010 U3 (Boattini),
C/2014 UN$_{271}$ (Bernardinelli-Bernstein), and C/2017 K2 (PANSTARRS). From
serendipitous archival data, we conducted analyses of the comet, finding that
the activity was consistent with steady-state behaviour, suggestive of
sublimation of supervolatiles, that the cross-section of dust increased
gradually on the inbound leg of the orbit, varying with heliocentric distances
as $r_{\rm H}^{-1.5 \pm 0.4}$, and that the dust was produced at a rate of
$\gtrsim\!10^2$ kg s$^{-1}$ within the observed timespan. Our modelling of the
largely symmetric morphology of the comet suggests that the dust environment
was likely dominated by mm-scale dust grains ejected at speeds $\lesssim\!0.4$
m s$^{-1}$ from the sunlit hemisphere of the nucleus. Assuming a typical
geometric albedo of 0.05 and adopting several simplistic thermophysical models,
we estimated the nucleus to be at least $\sim\!3$ km across. We also measured
the colour of the comet to be consistent with other long-period comets, except
being slightly bluer in $g-r$. With our astrometric measurements, we determined
an improved orbit of the comet, based upon which we derived that the comet is
dynamically new and that its perihelion distance will further shrink due to the
Galactic tide. We conclude the paper by comparing the known characteristics of
the known ultra-distant comets.
