USS Potemkin (NCC-1657)

The USS Potemkin (NCC-1657) was a Federation Constitution-class starship operated by Starfleet. 
In 2268, the Potemkin was part of a small task force that participated in war games to field test the experimental M-5 computer, which had been designed by Doctor Richard Daystrom. The M-5 was installed aboard the Potemkin's sister ship, the USS Enterprise. 
When the M-5 unit suffered a disastrous malfunction during simulated combat, it caused the Enterprise to attack the other Starfleet ships with full phasers rather than minimum-strength beams that were standard for such situations. At least five hundred people aboard the USS Lexington and the USS Excalibur were killed in the initial attack. The Potemkin and the USS Hood attempted to retreat, but were nonetheless hit numerous times by full phasers from the Enterprise. This resulted in an unspecified number of casualties. 
Following the crippling of the Excalibur, the Potemkin and the other two remaining ships were ordered to destroy the Enterprise to end the threat. Fortunately, the Enterprise was able to deactivate the M-5 computer before the three-ship battle force attacked.
In 2269, the Potemkin was scheduled to rendezvous with the Enterprise in the Beta Aurigae system. The two ships were assigned to conduct gravitational studies of that binary system. The Enterprise, however, was diverted by a distress call from Camus II, causing the mission with the Potemkin to be delayed. 
In 2270, the Potemkin was ordered to transfer a shipment of the life-saving medicine, strobolin, from Beta Canopus to the freighter USS Huron. The Huron was then to transfer the drug to the Enterprise so that it would be received within the three-day time frame needed to cure Spock's choriocytosis infection.
In the next twenty-three years, like her sister ship the Enterprise, the Potemkin was refitted.
In 2293, the Potemkin was conducting a scientific survey near Klingon territory during the time Operation Retrieve was proposed. The location of the Potemkin was labeled in the star chart for the "Operation: Retrieve" command briefing. This star chart was seen in the office of the Federation President on Earth. In the operation, the starship would have been the command ship for the operation and would make the attempt to rescue the hostages James Kirk and Leonard McCoy from Rura Penthe. This starship would have been flanked by both the USS Eagle and the USS Excelsior.