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The Justin--Huzita--Hatori Axiom 6 of origami related to so-called neusisconstruction assures the solution of real cubic equations shown by Beloch in1936. We investigate a certain real cubic curve $F(x,y)=0$, say, Beloch's curvethat appears in the algorithm and prove that its shape is determined by thesignature of the Hessian $\mathcal{H}_F=-4(4p+q^2)$ at its uniquely existingsingular point $P(p,q)$. This viewpoint would shed new light on therelationship between Axioms 5 and 6.

On Beloch's curve that appears when solving real cubic with origami