A mystery phone [Telecom]

Not specifically, but it's a standard-format part number. Other manufacturers use it too; you can find examples in the KGP Logistics catalog. Let's parse it

510 = A standard desk set with two lines, using a "turnbutton pushbutton key" on the front left. See details. See for a reference of basic model numbers. The latter claims that a 510 is one line with a special function key and a 515 is two lines, but the 1963 BSP on porticus shows a two-line (or one-line, depending on which one) 510.

00 = color code. 00 is black. 44 is ash. 09 is ivory, 13 is beige.

45 is brown.

BA = non-modular. QBA is quarter-modular (fixed modular plug on wall cord); FBA full modular. I never did know what the "BA" stands for otherwise. Base? Current phones use VBA.

30 = feature code. 20 is ordinary, 27 has a message waiting light, 44 has A-lead control, 57 has data port and message light. I don't know about 30 though; it's not in the current catalog.

M= Metro dial. The numbers have letters on them (the standard ones).

(y'all know my real email.)