Maximal and minimal curves of the form $y^3=x^{(q^2+1)/2}+x$

Guilherme Dias, Saeed Tafazolian

Let $p\ge 5$ be a prime with $p\equiv -1(\mathrm{mod}3)$, let $q=p^r$, and consider \[ \cC:\qquad y^3=x^{(q^2+1)/2}+x \] over $\F_{q^6}$. We prove the exact formula \[ \#\cC(\F_{q^6})=q^6+…