Bean's discriminant-area maximality conjecture for binary forms

Let $F$ be a binary form of degree $n$ with complex coefficients and nonzero discriminant $D_F$. Let $M_n$ be the maximal value of $|D_F|^{1/(n(n-1))}A_F$ over all such forms. For a real invertible matrix $M\in\operatorname{GL}_2(\mathbb R)$, write $F_M(x,y)=F(ax+by,cx+dy)$ when M=\left(\begin{smallmatrix}a&b\c&d\end{smallmatrix}\right), and say that two forms are equivalent under $\operatorname{GL}_2(\mathbb R)$ if one is obtained from the other in this way.

Bean's conjecture. The maximum is attained precisely when $F$, up to multiplication by a complex number, is equivalent under $\operatorname{GL}_2(\mathbb R)$ to $F_{n,n}$. In particular,

$$M_n=D_{F_{n,n}}^{1/(n(n-1))}A_{F_{n,n}}.$$

This conjecture is cited by the source as a conjecture of Bean and is described as naturally complementing the preceding lower-bound conjecture. No resolution is given in the supplied text.