other than, you know, how to play them...

i recently received a Conn C tuba as payment for repairing a guy's ugly E♭ sousaphone (it was held together with duct tape - pictures here - http://flic.kr/s/aHsjysBKGP" target="_blank ). when i gave him the E♭ sousaphone back, in playable condition, he gave me this wonderful Conn C tuba, which i have been playing the hell out of...
problem is, i don't know what it is...
it has the name Conn engraved (well, "stamped", really) on the bell, and the serial number (762417) indicates that it was made some time between 1958 and 1959, but the model number is nowhere to be found.
i think it's either a 56J or a 5J, but i don't know.
it can be seen here - http://flic.kr/p/bJGmxn" target="_blank - along side my Elkhorn E♭ tuba. more pictures are available, if needed.
do any of you other tuba nuts know how to tell the difference? i'd be obliged if anyone could tell me...

thanks!