A question about gorgons

Two questions, I guess. The first one I can google. Is gorgons capitalized? I don't think it should be (any more than giants or centaurs would be).

But the second question I did google with no luck. In various myth and analysis of gorgons, have the serpents ever been equated to phallic symbols? In other words, why snakes? Everything I see online has to do with the horrible visage turning people to stone. Are the snakes simply a scary part of that?

Thanks and happy Halloween!