50-500 usd
Be specific, what model?
What is the value of a 12 gauge Browning shotgun serial J68824?
You need to contact a professional who deals exclusivley with Brownings. What you describe, if done by Browning, was a custom order and it's value could be more than a small nation's GDP.
Without anymore information; 100-10000 USD
1000 USD
$350
Basically impossible to value a weapon with just the gauge and sn.
If you mean a Browning B-2000 12 gauge shotgun then the value would be 495 dollars for a shotgun in the condition you describe.
You will have to call Browning with the serial number to find out.
Not a valid Browning serial number.
Browning never made a Model 51 shotgun.
http://www.browning.com/products