data:
- - class_group:
    - 3
    class_number: 3
    cm: true
    coeffs:
    - 49
    - -42
    - 43
    - -8
    - 7
    - -1
    - 1
    conductor: 57
    degree: 6
    dirichlet_group:
    - 1
    - 20
    - 49
    - 7
    - 26
    - 11
    disc_abs: 3518667
    disc_rad: 57
    disc_sign: -1
    frobs:
    - - 2
      - - - 6
          - 1
    - - 3
      - - 0
    - - 5
      - - - 6
          - 1
    - - 7
      - - - 1
          - 6
    - - 11
      - - - 2
          - 3
    - - 13
      - - - 3
          - 2
    - - 17
      - - - 6
          - 1
    - - 19
      - - 0
    - - 23
      - - - 6
          - 1
    - - 29
      - - - 6
          - 1
    - - 31
      - - - 1
          - 6
    - - 37
      - - - 1
          - 6
    - - 41
      - - - 6
          - 1
    - - 43
      - - - 3
          - 2
    - - 47
      - - - 6
          - 1
    - - 53
      - - - 6
          - 1
    - - 59
      - - - 6
          - 1
    gal_is_abelian: true
    gal_is_cyclic: true
    gal_is_solvable: true
    galois_disc_exponents:
    - 3
    - 4
    galois_label: 6T1
    galt: 1
    grd: 12.332838034173273
    id: 5871804
    index: 1
    inessentialp: []
    is_galois: true
    is_minimal_sibling: true
    iso_number: 1
    label: 6.0.3518667.1
    local_algs:
    - 3.6.3.2
    - 19.3.2.2
    - 19.3.2.2
    monogenic: 0
    num_ram: 2
    r2: 3
    ramps:
    - 3
    - 19
    rd: 12.3328380342
    regulator:
      __RealLiteral__: 0
      data: '7.80862678603'
      prec: 44
    res:
      sex:
      - 7,-6,-1,1
      - 1,-1,1
      - 0,1
    subfield_mults:
    - 1
    - 1
    subfields:
    - 1.-1.1
    - 7.-6.-1.1
    torsion_gen: \( \frac{6}{259} a^{5} - \frac{5}{259} a^{4} + \frac{5}{37} a^{3}
      + \frac{1}{259} a^{2} + \frac{215}{259} a + \frac{7}{37} \)
    torsion_order: 6
    units:
    - \( \frac{30}{259} a^{5} - \frac{25}{259} a^{4} + \frac{25}{37} a^{3} - \frac{254}{259}
      a^{2} + \frac{1075}{259} a - \frac{150}{37} \)
    - \( \frac{5}{259} a^{5} - \frac{5}{37} a^{4} - \frac{2}{37} a^{3} - \frac{215}{259}
      a^{2} + \frac{30}{37} a - \frac{99}{37} \)
    used_grh: false
    zk:
    - '1'
    - a
    - a^2
    - a^3
    - 1/7*a^4 - 1/7*a
    - 1/259*a^5 - 1/37*a^4 + 7/37*a^3 - 43/259*a^2 + 6/37*a - 5/37
label_cols:
- label
labels:
- 6.0.3518667.1
tables:
- nf_fields
timestamp: '2024-04-25T14:47:22.895368'