I am currently in the process of researching different forms of elliptic curves defined over prime fields. In many curve standards, such as NIST, Brainpool, etc, there exist a list of curve equations for Weierstrass, Montgomery, and (twisted) Edwards curves.
However, I wish to also investigate various other curve forms, such as Hessian, Doche-Icart-Kohel, Jacobi intersections, Jacobi quartics, etc, but unfortunately I have been unable to find any such standards covering the selection of these curves. I'd like to know if any such papers / websites exist that detail some curve equations for each form. A list of curve equations with different parameters for these forms would be ideal.