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Number fields were drawn from the following sources.

Complete lists of global number fields were computed using two techniques, Hunter searches (see Section 9.3 of [MR:1728313, 10.1007/978-1-4419-8489-0]) and class field theory (see Chapter 5 and Section 9.2 of [MR:1728313, 10.1007/978-1-4419-8489-0]). Hunter searches are named for named for John Hunter [MR:0091309], whose technique was refined significantly by M. Pohst [MR:0644904]. In some cases, the Hunter searches are "targeted" in that they focused on specific prime ramification [MR:1986816, 10.1090/S0025-5718-03-01510-2].

Class groups of imaginary quadratic fields with $|D|<2^{40}$ were computed by A. Mosunov and M. J. Jacobson, Jr. [MR:3471116, 10.1090/mcom3050].

Data on whether or not a field is monogenic, its index, and its inessential primes were computed using pair-gp and are based on Gaál [MR:1896601], Gras [MR:0846964], Śliwa [MR:0678997], Nart [MR:0779058], Mushtaq et. al. [MR:3844199], and a classical theorem of Dedekind.

Knowl status:
  • Review status: reviewed
  • Last edited by Andrew Sutherland on 2023-01-19 15:56:02
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