What is the name of Zefram Cochrane's first warp ship?

Zefram Cochrane’s first warp ship was the Phoenix.

In Star Trek lore, Cochrane built the Phoenix in post–World War III Montana by converting an old Titan II nuclear missile. The improvised vessel carried his experimental warp drive, making it humanity’s first warp-capable spacecraft. Its historic flight took place on April 5, 2063.

The Phoenix’s warp flight was detected by the Vulcan survey ship T’Plana-Hath. The Vulcans then landed and made peaceful contact with Cochrane and the human survivors at the launch site. This event became the symbolic beginning of humanity’s entry into the wider interstellar community and is commemorated as First Contact Day.

The Phoenix is sometimes confused with the USS Enterprise, NX-01, or the Daedalus-class ships. Those are later vessels: the NX-01 belongs to the early United Federation era, while the Daedalus class represents a subsequent generation of starships. Cochrane himself also appears in the earlier Original Series episode “Metamorphosis,” but the detailed account of the Phoenix and its flight was established in the film Star Trek: First Contact.