By a *supersingular Abelian scheme*, I mean an Abelian scheme which is fibrewise a supersingular Abelian variety, i.e. isogenous to a product of supersingular elliptic curves (F. Oort, *Subvarieties of moduli spaces*. Invent. Math. **24** (1974), 95–119).

Let $\mathscr{A}$ be a supersingular Abelian scheme over an *integral* variety over $\mathbf{F}_p$. Is it true that $\mathscr{A}$ is isogenous to a product of relative elliptic curves over $X$? I am looking for a reference. Equations (0.4.1), (0.4.2) in [Li-Oort, *Moduli of Supersingular Abelian Varieties*, LNM 1680] seem to imply this.