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On The $j$-Invariants of CM-Elliptic Curves Defined Over $\mathbb{Z}_p$
Published 15 Jun 2015 in math.NT | (1506.04646v2)
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.
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