The Elicona sector was a region of space near the Canopus Core territory of the United Federation of Planets in the Beta Quadrant. As of the 2370s, the area was unpopulated and unclaimed. The closest Starfleet facility was Starbase 117, and the sector was considered quite remote by the rest of the Federation.
On stardate 47515.4 in 2370, the USS Magellan was assigned to investigate the disappearance of the USS Alcubierre in the Elicona sector. (Star Trek Adventures: A Star Beyond the Stars)