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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?

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