An elliptic curve \(E\) defined over a number field \(K\) is said to have **bad reduction** at a prime \(\mathfrak{p}\) of \(K\) if the reduction of \(E\) modulo \(\mathfrak{p}\) is singular.
There are three types of bad reduction:

A curve has bad reduction at \(\mathfrak{p}\) if and only if \(\mathfrak{p}\) divides its discriminant.

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- Last edited by David Roe on 2020-03-27 17:50:36

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- 2020-03-27 17:50:36 by David Roe (Reviewed)
- 2018-06-17 21:36:45 by John Jones (Reviewed)

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