data:
- - class_group: []
    class_number: 1
    cm: false
    coeffs:
    - 2
    - -12
    - 23
    - -2
    - 1
    - 8
    - -3
    - -2
    - 1
    conductor: 0
    degree: 8
    dirichlet_group: []
    disc_abs: 481890304
    disc_rad: 14
    disc_sign: 1
    frobs:
    - - 2
      - - 0
    - - 3
      - - - 4
          - 2
    - - 5
      - - - 2
          - 4
    - - 7
      - - 0
    - - 11
      - - - 2
          - 4
    - - 13
      - - - 2
          - 4
    - - 17
      - - - 4
          - 2
    - - 19
      - - - 4
          - 2
    - - 23
      - - - 2
          - 4
    - - 29
      - - - 2
          - 4
    - - 31
      - - - 2
          - 4
    - - 37
      - - - 2
          - 4
    - - 41
      - - - 4
          - 2
    - - 43
      - - - 2
          - 4
    - - 47
      - - - 2
          - 4
    - - 53
      - - - 2
          - 4
    - - 59
      - - - 4
          - 2
    gal_is_abelian: false
    gal_is_cyclic: false
    gal_is_solvable: true
    galois_disc_exponents:
    - 12
    - 6
    galois_label: 8T4
    galt: 4
    grd: 12.172184414459759
    id: 12356631
    inessentialp:
    - 2
    is_galois: true
    is_minimal_sibling: false
    iso_number: 3
    label: 8.0.481890304.3
    local_algs:
    - 2.2.3.3
    - 2.2.3.3
    - 2.2.3.3
    - 2.2.3.3
    - 7.8.6.2
    minimal_sibling:
    - 2
    - 3
    - 3
    - -1
    - 1
    monogenic: -1
    num_ram: 2
    r2: 4
    ramps:
    - 2
    - 7
    rd: 12.1721844145
    regulator:
      __RealLiteral__: 0
      data: '77.3449401793'
      prec: 44
    res:
      sib:
      - -10,-4,5,-2,1
      - 2,3,3,-1,1
    subfield_mults:
    - 1
    - 1
    - 1
    - 1
    - 2
    - 2
    subfields:
    - 2.0.1
    - -14.0.1
    - 2.-1.1
    - 2.-8.9.-2.1
    - -10.-4.5.-2.1
    - 2.3.3.-1.1
    torsion_gen: \( -1 \)
    torsion_order: 2
    units:
    - \( \frac{1}{16} a^{6} - \frac{1}{8} a^{4} - \frac{1}{4} a^{3} - \frac{1}{16}
      a^{2} - \frac{1}{8} \)
    - \( \frac{1}{2} a^{7} - \frac{13}{16} a^{6} - \frac{7}{4} a^{5} + \frac{27}{8}
      a^{4} + \frac{3}{2} a^{3} - \frac{15}{16} a^{2} + \frac{21}{2} a - \frac{23}{8}
      \)
    - \( \frac{3}{16} a^{6} - \frac{1}{4} a^{5} - \frac{9}{8} a^{4} + \frac{3}{2}
      a^{3} + \frac{41}{16} a^{2} - \frac{3}{2} a + \frac{1}{8} \)
    used_grh: false
    zk:
    - '1'
    - a
    - a^2
    - a^3
    - 1/2*a^4 - 1/2*a^2
    - 1/4*a^5 - 1/4*a^4 - 1/4*a^3 + 1/4*a^2 - 1/2*a - 1/2
    - 1/16*a^6 - 1/8*a^4 - 1/4*a^3 - 1/16*a^2 - 1/8
    - 1/32*a^7 - 1/32*a^6 - 1/16*a^5 - 1/16*a^4 + 3/32*a^3 + 1/32*a^2 + 7/16*a - 7/16
label_cols:
- label
labels:
- 8.0.481890304.3
tables:
- nf_fields
timestamp: '2024-04-25T07:47:19.370209'