The serial number is on the bottom of the machine - you have to turn it over - about under the needle bar.
What a wonderful find! I do get jealous for a second when I see a shiny black one, but my tan one sews perfectly so it doesn't last long. BTW, they really aren't a heavy duty machine even though mine came with four layers of leather under the needle. I have a back up, also tan, but a long bed. I haven't sewn with that one yet. The second one came with a full attachment box.