"The Asgard computer core is equipped with its own power source that will not infringe on your ship's ZPM."

The Asgard power core was the most advanced form of compact energy generation ever developed by the Asgard. Its first and only use was powering the computer core given to the Tau'ri shortly before the Asgard's mass extinction. Unfortunately, when activated the power core emits a unique subspace signal (possibly indicating it draws energy from subspace) which can be perceived and tracked by advanced sensor systems. Although the exact details of its operation are unknown, the power core was capable of powering a time dilation field around the Odyssey (in conjunction with a Zero Point Module) for roughly 50 years before giving out. (SG1: "Unending")