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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.

Knowl status:
  • Review status: reviewed
  • Last edited by David Roe on 2020-03-27 17:50:36
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