Determine whether prime isolation and genus-zero discriminants reflect one fact

Determine whether the fact that the census isolates exactly the primes 3, 5, and 11 is mathematically equivalent to the fact that the Shimura curves X^{2p} have genus zero exactly for p = 3, 5, and 11, or establish an implication in either direction.

Background

The finite census isolates a prime p when p is the entire odd part of an anisotropic discriminant group, yielding quaternion discriminant 2p. It isolates precisely 3, 5, and 11. Independently, the genus formula for Shimura curves gives genus zero for X^{2p} for exactly the same three primes.

The paper emphasizes that the two conditions arise from unrelated computations and provides no prime where they disagree, leaving their apparent coincidence unresolved.