I have a compression fracture of the T11 when can I run? It has been 3 weeeks I can bike, hike, aqua run the eliptical trainer no pain

Wait. If it has only been 3 weeks since your injury, i would suggest waiting at least another 6 weeks before considering running. You may not be in pain but that does not mean that you are healed. It generally takes 10-12 weeks for a spinal fracture to heal. Wait until your dr. Clears you. Good luck.
Let me help you. I assume you are young our or middle age person, it take 3 month for the fracture to heel, you do not want to load this fracture more than you suppose too , so the bone maintain its height, so you avoid problems in the future. What you mention except the aqua run carry possible additional hazarded, like falling and additional injury. Better play it safe. Good luck thank, keep the good work.