Longines flagship 1957

Hi I have this longines only the dial the michanism as ghe photos. I think is a 1957 flagship in accordance with the serial number. I need information about this if you know beacause i want to find the case to fix it and I do not know which is the right one. The size diameter and the type of authenticity. I searching online for “30l flagship” and i dont finding that exact dial variation. I measure the dial michanism as a photo and is about 34.5 mm. I need the right case reference of the matching watch.

You can try sending the serial number (10444112) to Longines for an Extract from the archives. This may give you the reference # https://www.longines.com/en-us/certificate-of-authenticity