If you have a student edition that was previously installed on a computer and you still have the Product Code, go to this page: https://www.studentteacherlicensing.com/lost.cfm
You can put in the product code and it will give you the serial number.
I eventually got this link from Adobe, but only after asking 5 times in 10 different ways, waiting on hold for 3 hours (live people were of no assistance and did not know enough to provide this link). Exasperating and it definitely gives you the idea that Adobe would prefer that you not figure it out.
Good luck!