Let $E: y^2=x^3+ax+b$ be a nonsingular short Weierstrass cubic over $\mathbb R$, and define the polynomial map $f: \mathbb{R} \to \mathbb{R}$ by $f(x)=x^3+ax+b$. Then the real affine locus is the union of the graphs
over the set $\{x\in\mathbb R:f(x)\ge 0\}$. If $f$ has one real root $r$, this set is the ray $[r,\infty)$. If $f$ has three distinct real roots $r_1<r_2<r_3$, this set is