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An elliptic curve $E$ defined over a number field $K$ is said to have multiplicative reduction at a prime $\mathfrak p$ of $K$ if the reduction of $E$ modulo $\mathfrak p$ has a nodal singularity.

The case of multiplicative reduction is further subdivided into split multiplicative reduction and nonsplit multiplicative reduction.

Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-06-19 18:55:02
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