(covers information from several alternate timelines)
Made of marble, the statue had a height of about twenty meters. It portrayed Cochrane gazing up at the sky, with one hand "reaching toward the future," as described by Geordi La Forge. (Star Trek: First Contact, ENT: "Carbon Creek")
When the crew of the USS Enterprise-E traveled back in time to the events of First Contact in 2063, La Forge told Cochrane about the statue, mimicking its posture while in Cochrane's company. When Cochrane was caught trying to flee from the hero-worshiping Starfleet officers shortly thereafter, he anxiously declared that he didn't want to be a statue. Commander William T. Riker was surprised that La Forge had even told him. (Star Trek: First Contact)
Captain Jonathan Archer kept a small, statuette version of the original aboard Enterprise NX-01 on a shelf in his quarters starting with the ship's launch in 2151. (ENT: "Broken Bow", "Fortunate Son", et al.)
In 2154 of an alternate timeline wherein Captain Archer contracted anterograde amnesia due to infection by interspatial parasites, Archer used the statuette to defend himself against a Xindi-Reptilian who had boarded Enterprise and was intruding in his quarters. Although the figurine broke as Archer fought the Xindi warrior, he used its main part to stab the intruder, killing the Xindi. The statuette was not only reassembled thereafter and placed back on Archer's desk but was also included in a makeshift settlement on Ceti Alpha V by 2165 of that timeline, at which point it could be found on a shelving unit in a bedroom where Archer slept. (ENT: "Twilight")
The statuette of Zefram Cochrane that frequently appears on I AM ERROR was designed by illustrator Doug Drexler. ("Broken Bow" text commentary, ENT Season 1 DVD) However, he originally created it for the Star Trek Encyclopedia, before Enterprise even began airing; at this point, it showed the figurine as if it was the statue spoken about and impersonated in First Contact. (Star Trek Encyclopedia, 3rd ed., p. 81) Drexler recalled, "I went directly to the art supply on Laurel Canyon, picked up an armature, some roma plastilina, and got to work. By the end of the day, there it stood." The design was not only influenced by La Forge's description in First Contact, but also took inspiration from Jean-Luc Picard. "The final touch was to adapt Picard’s distinctive two finger 'engage!' point," Drexler explained, "as if our erstwhile captain was invoking this very statue each time he gave the order for the great starship to go to warp."
Prior to presenting the model as an option for using on the set for Captain Archer's quarters, Drexler waited until Set Decorator James Mees was desperately looking for additional set dressing for that room, very shortly before Executive Producer Rick Berman visited the set during preproduction. Upon first seeing the model, Berman was astonished and asked where it had come from. A little later, Mees played a practical joke on Drexler by claiming he had replied that he himself had sculpted the model.
In the final draft script for "Twilight", a note regarding the appearance of the Cochrane statuette in Archer's bedroom in 2165 of the alternate timeline featured in that episode stated, "We may notice that it’s been glued together after being broken in half." However, this is not apparent in the episode. Another difference between those two depictions of the statuette is that, although the final version of the episode showed it on a shelving unit in Archer's bedroom of 2165, the figurine was scripted to be on a desk.
At least eight identical "stunt" statue props were created for the production of "Twilight". Three statuette props were sold in both the 40 Years of Star Trek: The Collection and It's A Wrap! sale and auction.    These were copies, however; the original prop remained in Doug Drexler's possession.