Tougher groups (1/4)
nflist(G,’t) returns a regular extension of K of Q(t) with group G, i.e. such that
Gal(K/Q(t)) ≃ G and K ∩ Q = Q, given by a polynomial P ∈ Z[x, t]. By Hilbert
irreducibility, almost all specializations of t ∈ Q will give polynomials with group G over Q.
Discriminants of fields produced in this way are large (and the minimal discriminant is usually
unknown for these groups).
This is implemented for all nTk, n 6 11 with 5 exceptions (9T14, 9T15, 11T2, 11T3, 11T4) and
a few more groups in degree up to 15 (115 out of 477). The easy groups An and Sn are also
available in all degrees.
This database was provided by Jürgen Klüners and Gunter Malle and requires the nflistdata
package in degree n > 8.
PARI/GP day 2021 (02/06/2021) – p. 11/14