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Trying to determine what rear end is in my 56 Bel Air. Originally it was a 3 on the tree 6 cyl, subsequent owner changed to 350 crate engine with 700R4 transmission. Don't know if the rear end was changed. See attached photo. These are the only markings on the rear end. Can't find anything that matches in cross reference manual.
 

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The cast numbers you've shown will give you a little information about the differential case itself, but the rest of the puzzle is determined by a few stamped characters on the opposite side of the case. They will possibly be hard to spot and read:
Wall Concrete Cement Rock Metal

These will tell you where and when it was made, and the ratio (so long as it hasn't been changed along the way). There are a couple of places to decode those characters, but can't put my finger on it yet... Hopefully you'll be able to find them. It'll take some effort, degreaser, possibly a wire wheel...
JR
 

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JR is spot on....The only thing you can tell from that number (3707306) in your pic is that it is a 55/56 open rear end.
 

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1956 Corvette upgraded to 57 RPO 579D, including SB400, Rochester FI, Muncie, HD brakes/susp
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That casting number is for a 56 case. I'm surprised there is not a casting date next to the casting number. casting dates will start with a letter (A through L) for the month and then 3-4 numbers for the day/year.
As mentioned, there should/MAY be some stamped letters/numbers on the passenger side of the case.
NORMALLY, a 56 6cyl/3sp had a 3.70 rear gear ratio. I do not know what the OD ratio is for your 700R4, probably between .6 and .7, but with a 3.70 rear, your equivalent final ratio would be in the 2.2-2.7 range.
 
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