Hessian form of an elliptic curve

In geometry, a Hessian curve is a cubic plane curve similar to the folium of Descartes that belongs to the Hesse pencil. It is named after the German mathematician Otto Hesse. In projective coordinates, the projective equation of a Hessian curve is

For every nonsingular cubic plane curve there is a change of projective coordinates that transforms the equation of the curve into the above Hessian form.

Theses curves are used in elliptic curve cryptography, because arithmetic in this curve representation is faster and needs less memory than arithmetic in standard Weierstrass form.

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