My serial # rejected on Apple help site. Airport Express
airport extreme flat with rounded corners
serial number rejected by apple help.
confounded
The last generation (5th) of the "flat" Extreme base stations was discontinued in 2013. That would mean that it would not qualify for AppleCare even if you bought it with another AppleCare-qualifying product (Mac desktop or laptop).
What question or issue do you have with your base station that you need assistance with?