What is a supersingular elliptic curve over arbitrary rings

I read in Katz Mazur's book on moduli spaces of elliptic curves that an elliptic curve over an $$\mathbb{F}_p$$-algebra $$R$$ is called ordinary if its geometric points are all ordinary. Now the question is, when such an elliptic curve is supersingular? I mean, if I consider an elliptic curve $$E$$ over $$R$$, which is in fact a family of elliptic curves, may I say that it is supersingular if all the elliptic curves over the geometric points of R are supersingular?