CM elliptic curves over Q have natural density zero among all elliptic curves ordered by naive height, and the j=0 family accounts for 100% of the CM curves asymptotically.
Introduction to Analytic Number Theory
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The density and distribution of CM elliptic curves over $\mathbb{Q}$
CM elliptic curves over Q have natural density zero among all elliptic curves ordered by naive height, and the j=0 family accounts for 100% of the CM curves asymptotically.