On The $j$-Invariants of CM-Elliptic Curves Defined Over ${\mathbb{Z}}_p$

Abstract

We characterize the possible reductions of $j$-invariants of elliptic curves which admit complex multiplication by an order $\mathcal{O}$ where the curve itself is defined over ${\mathbb{Z}}_p$. In particular, we show that the distribution of these $j$-invariants depends on which primes divide the discriminant and conductor of the order.

14 pages

References in corpus (2)

• An arithmetic intersection formula for denominators of Igusa class polynomials
• Twists of Shimura Curves