With a Smith gun in that serial number range, the simplest/surest way to determine frame ID is to check the serial number prefix stamped on the water table. If the prefix is an "R" stamp, the gun has a "Regular", or standard Smith frame; if the serial number prefix is "FW", the gun was built using Hunter's "Feather Weight", or smaller gun frame. If the serial number stamp prefix is "RE", or "FWE"; the gun was shipped with factory installed auto ejectors, but the ejector option code was the only optional feature code ever stamped on a Smith gun frame. Note also that these serial number prefix stamps do not apply to Smith gun made prior to about 1917-18 when no serial number prefix stamps were used. Also, Marlin era Smith guns produced from 1945-1950 can be identified by another serial number prefix stamp that will include the letter "S". All Marlin era guns will be stamped with the prefix "FWS" or "FWSE", as Marlin did not produce Smith guns using the "R" frame size. Finally, Marlin made Smith guns produced from 1967-1972 feature another serial number stamp as follows "FWM"; but auto ejectors were never offered on those Smith guns produced at the Marlin gun works.
Finally, the only other Smith gun prefix serial number stamp was for the experimental "C" frame; a hybrid frame that combined the FW sized frame with lock plates from an "R" frame. If this gun should be one of those; then one would pay whatever it took, as collectors are still searching for one of the illusvie six examples noted in Brophy's book (and you won't get lucky, as the serial number you posted is not one of those six).
And as to calling a Smith gun an "Elsie"; I can't do that, as that name reminds me of the Borden's Milk smiling cow logo. To me "Elsie" is a sissy name unbecoming the gold lightning bolts seen on a high grade Smith gun and which are illustrative of the sudden death a Smith gun wields upland game; I just refer to mind as "the Smith".