Hessian form of an elliptic curve

In geometry, the Hessian curve is a plane curve similar to folium of Descartes. It is named after the German mathematician Otto Hesse. This curve was suggested for application in elliptic curve cryptography, because arithmetic in this curve representation is faster and needs less memory than arithmetic in standard Weierstrass form.

Let ${\displaystyle K}$ be a field and consider an elliptic curve ${\displaystyle E}$ in the following special case of Weierstrass form over ${\displaystyle K}$:

...
Wikipedia