On the Complex and Real Hessian Polynomials

Table 2

Complex cubic curves which are not complex Hessian curves.

𝑥𝑦^2+𝑒𝑦=𝑎𝑥^3+𝑏𝑥^2+𝑐𝑥+𝑑,𝑎∈ℂ^∗,𝑏,𝑐,𝑑,𝑒∈ℂ	𝑥𝑦=𝑎𝑥^3+𝑏𝑥^2+𝑐𝑥+𝑑,𝑎∈ℂ^∗,𝑏,𝑐,𝑑∈ℂ
𝑦=𝑎𝑥^3+𝑏𝑥^2+𝑐𝑥+𝑑,𝑎∈ℂ^∗,𝑏,𝑐,𝑑∈ℂ	𝑥^3+𝑏𝑥^2+𝑐𝑥+𝑑=0,𝑏,𝑐,𝑑∈ℂ