An elliptic curve \(E\) defined over a number field \(K\) is said to have **supersingular reduction** at a prime \(\mathfrak{p}\) of \(K\) if the reduction \(E_{\mathfrak{p}}\) of \(E\) modulo \(\mathfrak{p}\) is smooth, and \(E_{\mathfrak{p}}\) is supersingular.

An elliptic curve \(E_{\mathfrak{p}}\) defined over a finite field of characteristic \(p\) is **supersingular** if \(E_{\mathfrak{p}}(\overline{\F_p})\) has no \(p\)-torsion.

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- Review status: reviewed
- Last edited by John Cremona on 2022-02-04 09:04:20

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- 2022-02-04 09:04:20 by John Cremona (Reviewed)
- 2018-06-18 18:32:58 by John Jones (Reviewed)

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