Learn more

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.

Additional acknowledgments

With the exception of the computation of class group data for quadratic imaginary fields, the computation of data for the number field section of the LMFDB was carried out by John Jones.

Initial page design was by Henri Cohen and John Cremona, with subsequent changes by John Jones.