I could not help to notice the relative poor shape the dial of your Longines is in.
The process of printing looks like a hand-made job and 'Conquest ' is spelled rather with Q than with G. Most Conquest models between '55 and '60 had yellow- or rose-gold indices, few had white-gold.
Slightly lower-end-of-the-market but identical models were named 'All Guard ' or simply 'Automatic ' that had steel indices and a black (or dark blue) sweeping second. Their 19AS movements were equipped with 17 jewels, against 19 jewels for the Conquest models.
Your winding crown is 100% original; don't loose it because they are very scarce!
ciao, Ben.