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.

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- Last edited by John Jones on 2018-06-19 18:55:02

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- 2018-06-19 18:55:02 by John Jones (Reviewed)