This is a holy grail instrument right here. A rare horn from 1935, late in the time period where Conn was developing their legendary "Naked Lady" saxophones (so named for the bell engraving). This one has virtually all of the features of these later horns, and a few 'transitional' features which make it very rare, such as the double socket neck tenon combined with the over-slung octave key (called the "New York" neck). In other words, some of the horns from this transitional era were treated like prototypes, with designers trying out ideas on commercially available horns, which may or may not have been adopted in the final design. Another interesting thing about this instrument is that the serial number has an additional "A" stamped at the end of it, which is not typical. No information has survived to indicate what this might mean but I have heard 2 plausible theories. One of which says the "A" was used to designate prototype instruments with a specific set of features, and the other says that the "A" was stamped on particularly great playing saxophones at the factory, to designate them for use by endorsed Conn artists (no pun intended).
Condition-wise, this one is wearing about 60% of its original lacquer, and the body is straight with only minor dents and dings. It has a very old set of original Conn Reso-Pads installed, and still plays quite well on these. A world class jazz alto - these were widely considered the absolute best in their day, and will out-tone and out-volume virtually any horn made since as well. Make an appointment to come by and check it out.