Minimal generators and Göttingen covariants for powers of binary forms

Assume that $r$ divides $d$. Let $X=X_{e,d}$ be the variety of binary $d$-ics that are perfect $\frac{d}{e}$-th powers of binary $e$-ics, and let $I_X$ be its defining ideal. Let $\mathfrak g$ denote the ideal generated by the Göttingen covariants. Minimal-generation and Göttingen-ideal conjectures. The ideal $I_X$ is always minimally generated in degree $r+1$, and

$$\mathfrak g=I_X.$$

These are experimental conjectures extending the examples discussed in the paper. They assert both the degree of minimal generation and that the Göttingen covariants generate the entire ideal; neither assertion is resolved in the supplied text.