Abstract
It is known that in the moduli space A1 of elliptic curves, there exist precisely 9 Q-rational points corresponding to the isomorphism class of elliptic curves with complex multiplication by the ring of algebraic integers of a principal imaginary quadratic number field. Here, we prove that in the moduli space A2 of principally polarized abelian surfaces, there exist precisely 19 Q-rational points corresponding to the isomorphism class of abelian surfaces whose endomorphism rings are isomorphic to the rings of algebraic integers of some imaginary cyclic quartic number fields.
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