Abstract
We characterize the possible reductions modulo $p$ of the $j$-invariants of supersingular elliptic curves which admit complex multiplication by a (potentially non-maximal) order $\mathcal O$ where the curve itself is defined over $\mathbb{Z}_p$. In particular, we show that the collection of possible $j$-invariants as well as some aspects of the distribution depends on which primes divide the discriminant and conductor of the order $\mathcal O$.
Citation
Andrew Fiori. "On the $j$-invariants of CM-elliptic curves defined over $\mathbb{Z}_p$." Funct. Approx. Comment. Math. 56 (2) 271 - 286, June 2017. https://doi.org/10.7169/facm/1617
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