Viper 4077 (4077NC) is a Viper Mark II flown by Lt. Kara "Starbuck" Thrace by during the Skirmish Over the Red Moon.
4077, with the aid of Brendan "Hot Dog" Costanza (Viper 1104), destroys all but one Raider when a Cylon patrol happens upon Thrace and her trainees during an exercise in proximity of the unnamed red moon. As 1104 succumbs to its damage, 4077 takes on the last surviving Raider, with both craft disabled and ensnared in the red moon's gravity as a result (TRS: "Act of Contrition").
As 4077 breaks up during entry, Thrace ejects and makes it to the moon's surface (TRS: "You Can't Go Home Again").
Notes
Scenes around the orbit of the red moon, just prior to Thrace's Viper being rammed, erroneously show the tail number as 7242NC. This is a re-use of existing CGI texture and is an error, as 7242 has numerous successive appearances after the Skirmish Over the Red Moon