Picard's Sovereign-class ship, launched in 2372, which fought the Borg in First Contact and Shinzon in Nemesis.
The USS Enterprise-E was a Sovereign-class starship launched in 2372, after the loss of the Enterprise-D. The Sovereign class was faster and better armed than its predecessor, and Captain Picard took command with most of his former senior officers.
In Star Trek: First Contact, Starfleet kept Picard away from the Borg attack on Earth in 2373 because of his history as Locutus, but he joined the battle anyway and helped destroy the cube. The Enterprise then followed a Borg sphere back to 2063, where the crew protected Zefram Cochrane's first warp flight and fought off drones who had boarded the ship.
In Star Trek: Insurrection, Picard defied orders to stop a plan by the Son'a and a Starfleet admiral to remove the Ba'ku from their planet. In Star Trek: Nemesis, the ship fought Shinzon's warship Scimitar in the Bassen Rift and was badly damaged, and Data gave his life to destroy the Scimitar and save the crew.