Er, I don't think the modem was invented in late
50's.
Modems have been used to send data over phone lines (and over radio)
since at least 1940.
They may have been called "Terminal units", but they did the basic modem
things of mod/demodulating data onto an audio carrier.
Sure, but that has no relevance to the original question of when modems
were first used to send binary data (not text) from one computer to another
over a telephone line.