  We study E-eigenvalues of a symmetric tensor $f$ of degree $d$ on a
finite-dimensional Euclidean vector space $V$, and their relation with the
E-characteristic polynomial of $f$. We show that the leading coefficient of the
E-characteristic polynomial of $f$, when it has maximum degree, is the
$(d-2)$-th power (respectively the $((d-2)/2)$-th power) when $d$ is odd
(respectively when $d$ is even) of the $\widetilde{Q}$-discriminant, where
$\widetilde{Q}$ is the $d$-th Veronese embedding of the isotropic quadric
$Q\subseteq\mathbb{P}(V)$. This fact, together with a known formula for the
constant term of the E-characteristic polynomial of $f$, leads to a closed
formula for the product of the E-eigenvalues of $f$, which generalizes the fact
that the determinant of a symmetric matrix is equal to the product of its
eigenvalues.
