Is supplement J required for EB1a?

[jaskhurana]

I got my I-140 approved under EB1a category. Do I need to submit a supplement J with my I-485? Since EB1a is self-petition, I don't really see the need for that but I just want to be sure. 

Also, if in the future, I change employers (same field of expertise), can I submit a supplement  J at that time while I-485 is under process? 

Thanks in advance!