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NCC-4186 was a Federation Miranda-class starship operated by Starfleet during the 24th century

In 2373, NCC-4186 and the Second Fleet, joined with the USS Defiant and IKS Rotarran, following the evacuation of DS9, for a counterattack against the Dominion forces. (DS9: "Call to Arms")

USS Defiant, Excelsiors and Mirandas at SB375

NCC-4186 was on patrol near Starbase 375, while the USS Defiant was stationed there, early during the Dominion War in 2374. Other ships present during those periods included the IKS Rotarran, USS Defiant, and USS Centaur. (DS9: "Sons and Daughters", "Behind the Lines")

Later that year, NCC-4186, USS Trial, USS Late, and one other Miranda-class starship were near Deep Space 9, shortly after it had been retaken by the Federation Alliance. They were accompanied by three Klingon Birds-of-Prey, two Galaxy-class starships, a Vor'cha-class attack cruiser, and a Bajoran interceptor. (DS9: "You Are Cordially Invited")

Federation starbase patrolled by Federation starships

NCC-4186 was on patrol near the Federation starbase where Quark's cousin Gaila was imprisoned in 2374. (DS9: "The Magnificent Ferengi")

Later that year, NCC-4186 and USS Trial, along with the two Galaxy-class starships and the Bajoran interceptor, were again present at DS9. (DS9: "The Reckoning")

Prior to the first Battle of Chin'toka, NCC-4186, USS Trial, USS Late were joined by three D'deridex-class Warbirds, three Birds-of-Prey, two Galaxy-class starships, and a Bajoran interceptor. (DS9: "Tears of the Prophets")

In 2375, NCC-4186 solely patrolled around Deep Space 9. (DS9: "Afterimage") A short time later, NCC-4186, USS Trial, USS Late again resumed patrols around Deep Space 9. (DS9: "Treachery, Faith and the Great River" DS9: "Strange Bedfellows", "Tacking Into the Wind"))

NCC-4186 was built from an AMT/Ertl model kit of the USS Reliant. The registry was a result of the rearrangement of numbers decals from 1-8-6-4 to get 4-1-8-6. A similar method was used in naming and registering of the Trial.
Visual Effects Supervisor David Stipes has made use of additional model kits, labeled "NCC-1948" for the Trial and "NCC-9481" for the Late, again achieved by rearranging the model kit registry decal, for the closing fleet shots in "Call to Arms". [1]
The model's name appears to be labeled USS Alert.
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