Phoenix
The Phoenix was an Earth spaceship used in the 21st century. She was the first manned space craft to achieve the speed of light with warp drive. She is remembered as the ship that instigated the first contact with Vulcans.
Dr. Zefram Cochrane, the inventor of warp drive, built this warp ship inside a missile complex in Bozeman, Montana. The ship was initially an United States Air Force nuclear missile with titanium casing. It took Lily Sloane six months to scrounge enough titanium to build the four-meter cockpit of the Phoenix. Dr. Cochrane was the pilot, Lily Sloane was initially intended to be one of the co-pilots. William Riker and Geordi La Forge (both of the USS Enterprise-E, from 2373), however served as the crew.
On April 4th 2063, less than 48 hours away from launch, the Borg from the 24th century attempted to destroy the Phoenix. They managed to cause significant damage to various sections of the fuselage and the primary intercooler system. The damaged throttle assembly was leaking dangerous levels of theta radiation. There were temperature variations in the fuel manifold. The intermix chamber needed to be reconstructed. There was also a damaged warp plasma conduit that needed to be replaced. All damages were repaired in time for the launch.
On April 5th, around 11 am, the warp flight is launched. First-stage shutdown and separation is performed in orbit. Nacelles are extended, the warp core and plasma injectors are brought on-line and the nacelles are charged. It takes several seconds to accelerate to the speed where the warp barrier is broken. Light speed is then obtained by the craft. The second stage also has chemical engines. (Star Trek: First Contact; VOY: "Year of Hell")
On the computer display inside the Phoenix the warp drive is called the "space warp generator". The first flight of the Phoenix attracted the attention of a passing Vulcan ship, the T'Plana-Hath. The Vulcans decided to make first contact. First Contact Day is celebrated annually to commemorate this First Contact between Humans and Vulcans. (VOY: "Homestead")
A model of the Phoenix was kept in Travis Mayweather's old quarters aboard the ECS Horizon. (ENT: "Horizon")
Admiral Maxwell Forrest kept a similar model in his office on Earth. (ENT: "The Expanse", "Home")
A photograph of the Phoenix was on display in the 602 Club on Earth. A similar picture graced a wall of Admiral Forrest's office on Earth in 2154. (ENT: "First Flight", "Home")
By the 24th century, the Phoenix was an exhibit in the Smithsonian Institution. Jean-Luc Picard saw the exhibit many times as a boy, but was never allowed to touch it. The blueprints of the Phoenix are available on Federation starships. (Star Trek: First Contact)