Stable Models of Elliptic Curves, Ring Class Fields, and Complex Multiplication

摘要

We introduce a new model for elliptic curves over rings of odd characteristic, and study its properties and its utility in numerical computations. They turn to be particularly interesting for elliptic curves with complex multiplication, for which they provide very simple stable equations. The invariants associated to these models allow an easy construction of ring class fields of certain imaginary quadratic orders, with interesting theoretical consequences and practical utility in numerical computations.