D4 inflectionary curve genus conjecture

Let $n=2\ell$, assume that $\operatorname{char}(F)$ is zero or sufficiently positive, and let $\mathcal{C}_m$ be the $m$-th inflectionary curve from $y^n=x^5+x^3+sx$. D4 genus conjecture. The geometric genus of $\mathcal{C}_m$ is $0$ for $m=3$ and $\left\lceil\frac{m^2}{2}-m+1\right\rceil$ for every $m\geq4$. Together with the predicted singularity and Newton polygon data, this gives the expected genus in every degree; the supplied text does not prove the formula.