It’s a 4 3/4 Barrel with eagle grips. Numbers match on cylinder, frame and trigger guard. How did barrel get shortened?
It's unusual that your SAA has a 4 3/4" barrel while the Colt Archive Letter says that the barrel length is "Not Listed". Because your barrel has the two-line Colt address you can be sure that this barrel was made in that length and was never shortened but it may not be the original barrel on your gun. Your gun's barrel should have the last four digits of the serial number stamped on the bottom. You may have to remove the ejector rod assembly to see it but the number would confirm whether or not the barrel has been replaced.