  Let $\ell$ be an odd prime and $K$ a field of characteristic different from
$\ell$. Let $\bar{K}$ be an algebraic closure of $K$. Assume that $K$ contains
a primitive $\ell$th root of unity. Let $n \ne \ell$ be another odd prime. Let
$f(x)$ and $h(x)$ be degree $n$ polynomials with coefficients in $K$ and
without repeated roots.
  Let us consider superelliptic curves $C_{f,\ell}: y^{\ell}=f(x)$ and
$C_{h,\ell}: y^{\ell}=h(x)$ of genus $(n-1)(\ell-1)/2$, and their jacobians
$J^{(f,\ell)}$ and $J^{(h,\ell)}$, which are $(n-1)(\ell-1)/2$-dimensional
abelian varieties over $\bar{K}$.
  Suppose that one of the polynomials is irreducible and the other reducible
over $K$. We prove that if $J^{(f,\ell)}$ and $J^{(h,\ell)}$ are isogenous over
$\bar{K}$ then both endomorphism algebras $\mathrm{End}^{0}(J^{(f,\ell)})$ and
$\mathrm{End}^{0}(J^{(h,\ell)})$ contain an invertible element of
multiplicative order $n$.
