Black Zero

The Black Zero spaceship was a craft used by General Zod to escape Krypton's destruction. Originally a prison ship for Kryptonians, Zod took it over and used it as transport to the planet Earth with Faora in search of Kal-El.

During the war on Krypton
After General Zod and his followers tried to stage a coup d'etat on the Council of Five and take over the running of the planet Krypton, they were eventually captured. Given that this was the worst crime committed on Krypton in many thousands of years, the Council decided to reuse an old ship; Black Zero to put Zod and his followers away and send them to the Phantom Zone.

When Krypton is destroyed due to its unstable core, the Phantom Zone Projector is affected by the explosion which releases the Black Zero ship. As Krypton is destroyed, Zod and his followers retrofit the ship as their new flagship and decide to go to Earth.