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The Kodaira symbol of an elliptic curve $$E$$ defined over a number field encodes the reduction type of $$E$$ at a prime $$\mathfrak{p}$$ of $$K$$. It describes the combinatorics of the special fiber of the Néron model of the elliptic curve. The Néron model is obtained from the local minimal model for $$E$$ at $$\mathfrak{p}$$ using Tate's algorithm. For an exact definition and properties, consult a text on elliptic curves.

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• Review status: reviewed
• Last edited by John Jones on 2018-06-19 00:53:01
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