Cortalian's timeship was the Type 75 Homeworld timeship who was bonded to the disgraced High Councillor, Cortalianesquertal vel-Lineacrux.
When Cortalian was exiled from the Homeworld, she was allowed to take her ship with her, which she held to be the one and only kindness her former people had awarded her while "kicking her out". Cortalian and her timeship appeared to share a close bond; it hummed at her approach and she was seen to pat its exterior affectionately.
She used her timeship to set up the First Auction in Heaven on the planet Kratoam, where it adopted the form of an aluminium tree, intentionally clashing with the lack of artificiality on the unpopulated planet. During the Auction, Cortalian sold the sarcophagus of Apep to a Faction Paradox splinter group in exchange for a future version of her own timeship key, which she was fated to lose in the future, where it had preemptively been found by the Faction.
After Intrepid killed Cortalian, Kifah picked up both the past and future version of the key, which allowed Intrepid, Kifah and Gustav to escape the malfunctioning planet by stealing the ship (although Intrepid was not sure how to fly a timeship, having dropped out of the Academy before learning that particular set of skills). (PROSE: Going Once, Going Twice)