[red_trumpet]

I'd guess the term "elliptic" has more to do with elliptic operators[1] than with ellipses. Of course, ultimately elliptic operators are named after ellipses, but the association is not as direct as you might imagine[2].

[1] https://en.wikipedia.org/wiki/Elliptic_operator

[2] https://mathoverflow.net/a/359723/111897