Eupheme was discovered Mar. 4, 2003 by Scott S. Sheppard at the Mauna Kea Observatory in Hawaii, and originally designated S/2003 J3.
Eupheme is a member of the Ananke group, a family of Jovian satellites which have similar orbits and are therefore thought to have a common origin. The group probably began as an asteroid that was captured by Jupiter's gravity and then suffered a collision which broke off a number of pieces. The largest remaining chunk was named "Ananke," and the smaller pieces became the other 15 moons in the Ananke group.
All of the Ananke moons are retrograde, which means that they orbit Jupiter in the opposite direction from the planet's rotation. Their orbits are also eccentric (elliptical rather than circular) and rather highly inclined with respect to Jupiter's equatorial plane. All of these characteristics support the idea that the Ananke satellites began as a captured asteroid, rather than forming as part of the original Jupiter system. None of the Ananke members is massive enough to pull itself into a sphere, so they are probably all irregularly shaped.
Eupheme has a mean radius of about less than a mile or about one kilometer, (assuming an albedo of 0.04). At a mean distance of about 13 million miles (20.2 million kilometers) from Jupiter, it takes about 584 Earth days to complete one orbit.
In mythology, Eupheme is the spirit of praise and good omen, the granddaughter of Zeus, and the sister of Philophrosyne.