The word elliptic appears quite often in mathematics; I will list a few occurrences below. For some of these, it is clear to me how they are related; for instance, elliptic functions (named after ellipses, see here) are the functions on elliptic curves over $\mathbb C$. For others, I do not know if there is a relationship at all.
- Elliptic integrals
- Elliptic functions
- Elliptic curves
- Elliptic genera (in the sense of Hirzebruch)
- Elliptic (as opposed to parabolic or hyperbolic) isometries of the hyperbolic plane
- Elliptic partial differential operators, elliptic PDEs
- Elliptic cohomology
I am interested in the etymology of this word, in particular, the origins of the different usages listed above. More precisely, I was wondering whether there is, in a way, a single "strain" for all uses of elliptic in mathematics, going all the way back to ellipses in Euclidean geometry.