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

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

Authors:
Knowl status:
• Review status: reviewed
• Last edited by John Jones on 2018-06-18 18:34:01
Referred to by:
History: