The prefix of 8Z indicates that you have a Browning light weight model auto-5 shotgun that was made in the first year of production,which was 1958.The value cannot be determined without you providing the overall condition of your shotgun,its bore condition,and what type of barrel is on the shotgun(Plain,solid matte rib,or vent rib type).
See what they are selling for at Gunsamerica. http://www.gunsamerica.com/ That should give you a pretty good idea.
Go to Browning's website under Support then go to Date your firearm. Value of any used firearm depends upon condition and area of sale.
100-1000 USD or so
Is it a Browning? If so,is it a BPS,B80,A500,Double Auto,Auto5,Gold,A-Bolt,O/U or SxS? What gauge? Your question is sort of like asking, "I have a truck. What is it worth?".
50-500 usd
What is the value of a 12 gauge Browning shotgun serial J68824?
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.
Browning never made a Model 51 shotgun.
Not a valid Browning serial number.