We prove that the Hessian transformation of a plane projective cubic corresponds to a 3-endomorphism of a model elliptic curve. By exploiting this result, we investigate a family of functional graphs -- called Hessian graphs -- defined by the Hessian transformation. We show that, over arbitrary fields of characteristics different from 2 and 3, the Hessian graphs inherit distinctive features from the arithmetic of the model curve. We then specialize our analysis to the finite-field case, proving several regularities of Hessian graphs.     «

We prove that the Hessian transformation of a plane projective cubic corresponds to a 3-endomorphism of a model elliptic curve. By exploiting this result, we investigate a family of functional graphs -- called Hessian graphs -- defined by the Hessian transformation. We show that, over arbitrary fields of characteristics different from 2 and 3, the Hessian graphs inherit distinctive features from the arithmetic of the model curve. We then specialize our analysis to the finite-field case, proving...    »