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 $12$.
- Review status: reviewed
- Last edited by John Jones on 2018-06-19 15:39:06
- 2018-06-19 15:39:06 by John Jones (Reviewed)