NCC-1685

From Memory Alpha, the free Star Trek reference

NCC-1685 was the registry number of a Federation starship which underwent a layover at Starbase 11. The ship's number was seen on a chart indicating the repair status of several vessels. (TOS: "Court Martial")

[edit] Background

Unfortunately, we don't know what this ship was named since it was only identified by its hull number. This registry was assigned to the USS Eagle in Greg Jein's registry list, but a different number was assigned to that vessel in a graphic in Star Trek VI: The Undiscovered Country