An imaginary quadratic field is a quadratic field 
with 
.
Special cases are summarized in the following table.
 | field members |
 | Gaussian integer |
 | Eisenstein integer |
For the class number, Kimura (2026) reports exactly 16453493 imaginary quadratic fields with class number at most 2000. The largest absolute fundamental discriminant in the reported list is 1062350083. The argument combines formally checked analytic bounds with a sieve and table computations that are not formally verified. The full classification has not been independently verified here. Kimura (2026) reports substantial AI assistance in the mathematics, formalization, and computations.
