The U.S.S. Copernicus (NCC-58637) is an Oberth-class starship. Never seen onscreen, it is referenced on a computer screen that Data was using to investigate the parasite conspiracy in the Federation around 2364. The U.S.S. Copernicus was in the Sigma Antares region and requested fuel allocations, but Vice Admiral Maxwell Headroom of Starfleet Mission Operations Division denied the request.
Beta canon sources have the U.S.S. Copernicus studying solar winds and magnetic phenomena in the Alpha Quadrant. Tom Paris served aboard the Copernicus.
Used in both patrol and scientific endeavours, the Copernicus’s mission profile is Multirole Explorer.
As it has a wide open history, the Copernicus can be dropped into any campaign easily. In my current campaign, for example, it is in the Beta Quadrant as part of the Twentieth Fleet, and is primarily used as a courier ship. That may change, however.
U.S.S. Copernicus (PDF)