Edwards curves

Extended Jacobi-quartic coordinates

Hessian curves

Inverted Edwards coordinates

Jacobi intersections

Jacobi quartics

Jacobian coordinates

Projective coordinates

Tripling-oriented Doche/Icart/Kohel curves

Weierstrass curves

This is joint work by Daniel J. Bernstein and Tanja Lange, building on work by many authors.

New paper on the EFD: "Analysis and optimization of elliptic-curve single-scalar multiplication", to appear in the proceedings of Fq8.

See also the zoo pictures.

**Sneak preview:** A
new version of EFD
is in preparation,
with more coordinate systems,
more formulas,
fully automated formula verification,
and fully automated operation counts.