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

If $E$ has good reduction at every prime of $K$ then $E$ is said to have **everywhere good reduction**.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Cremona on 2020-12-03 10:27:55

**Referred to by:**

**History:**(expand/hide all)

- 2020-12-03 10:27:55 by John Cremona (Reviewed)
- 2018-06-18 18:31:08 by John Jones (Reviewed)

**Differences**(show/hide)