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An elliptic curve $E$ defined over a number field $K$ of class number $h(K)$ greater than $1$ may not have a global minimal model. In this case there still exist semi-global minimal models for $E$ which are local minimal models at all except one prime. At this prime, the discriminant valuation exceeds that of the minimal discriminant ideal by $12$.

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• Review status: reviewed
• Last edited by John Jones on 2018-06-19 15:39:06
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