Curve25519 and Curve448 will be added to the NIST SP 800 this year as new curve schemas for elliptical curve encryption.
Curve25519 is an elliptic curve Diffie–Hellman and uses the equation: y2 = x3 + 486662x2 + x . You can read more about the curve here.
I found this was a really interesting example of the theoretical stuff we have been reading about in actual use / public domain. I had no idea different curves had Wikipedia pages and public discussion.
Here is a reference for some of the things that use Curve 25519: https://ianix.com/pub/curve25519-deployment.html