show · ec.good_supersingular_reduction all knowls · up · search:

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

Authors:
Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-06-18 18:32:58
Referred to by:
History: (expand/hide all)