The **local data** of an elliptic curve \(E\) defined over a number field \(K\) at a prime \(\mathfrak{p}\) of \(K\) consists of

- the Tamagawa number \(c_{\mathfrak{p}}\)
- the Kodaira symbol
- the reduction type
- the local root number
- the conductor valuation \(\text{ord}_{\mathfrak{p}}(\mathfrak{N})\)
- the discriminant_valuation \(\text{ord}_{\mathfrak{p}}(\mathfrak{D})\)
- the j-invariant denominator valuation \(\text{ord}_{\mathfrak{p}}(j)_{-}\)

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**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2018-06-19 01:00:26

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- 2018-06-19 01:00:26 by John Jones (Reviewed)