Good ordinary reduction (reviewed)

An elliptic curve \(E\) defined over a number field \(K\) is said to have ordinary 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 ordinary.

An elliptic curve \(E_{\mathfrak{p}}\) defined over a finite field of characteristic \(p\) is ordinary if \(E_{\mathfrak{p}}(\overline{\F_p})\) has nontrivial \(p\)-torsion.