When $K$ has class number $1$ all elliptic curves over $K$ have global minimal models. In general, there is an obstruction to the existence of a global minimal model for each elliptic curve $E$ defined over $K$, which is an ideal class of $K$. In case this class is nontrivial for $E$, there is a semi-global minimal model for $E$, which is minimal at all primes except one, the ideal class of that one prime being the obstruction class.
- Review status: reviewed
- Last edited by John Jones on 2018-06-18 18:29:07
- 2018-06-18 18:29:07 by John Jones (Reviewed)