The number of known geometric equivalence classes of Weyl-Heisenberg SICs in dimension d equals the cardinality of the ideal class monoid of the real quadratic order of discriminant (d+1)(d-3) for d=4 to 90, with conjectures extending the equality and refining class-field predictions for the vector
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SIC-POVMs and orders of real quadratic fields
The number of known geometric equivalence classes of Weyl-Heisenberg SICs in dimension d equals the cardinality of the ideal class monoid of the real quadratic order of discriminant (d+1)(d-3) for d=4 to 90, with conjectures extending the equality and refining class-field predictions for the vector