data:
- - class_group: []
    class_number: 1
    cm: false
    coeffs:
    - 1
    - 12
    - 58
    - 144
    - 182
    - 80
    - -28
    - -16
    - 11
    - -4
    - -8
    - 0
    - 1
    conductor: 0
    degree: 12
    dirichlet_group: []
    disc_abs: 677021181018112
    disc_rad: 14
    disc_sign: -1
    frobs:
    - - 2
      - - 0
    - - 3
      - - - 12
          - 1
    - - 5
      - - - 12
          - 1
    - - 7
      - - 0
    - - 11
      - - - 6
          - 2
    - - 13
      - - - 4
          - 3
    - - 17
      - - - 6
          - 1
        - - 3
          - 2
    - - 19
      - - - 12
          - 1
    - - 23
      - - - 6
          - 2
    - - 29
      - - - 2
          - 6
    - - 31
      - - - 6
          - 1
        - - 3
          - 2
    - - 37
      - - - 6
          - 2
    - - 41
      - - - 2
          - 3
        - - 1
          - 6
    - - 43
      - - - 2
          - 6
    - - 47
      - - - 6
          - 1
        - - 3
          - 2
    - - 53
      - - - 6
          - 2
    - - 59
      - - - 12
          - 1
    gal_is_abelian: false
    gal_is_cyclic: false
    gal_is_solvable: true
    galois_disc_exponents:
    - 48
    - 20
    galois_label: 12T14
    galt: 14
    grd: 20.244560739185545
    id: 18370807
    index: 1
    inessentialp: []
    is_galois: false
    is_minimal_sibling: false
    iso_number: 2
    label: 12.6.677021181018112.2
    local_algs:
    - 2.12.24.318
    - 7.3.2.2
    - 7.3.2.2
    - 7.6.5.5
    minimal_sibling:
    - 8
    - 0
    - -12
    - 0
    - 4
    - 0
    - 1
    - 0
    - 2
    - 0
    - -3
    - 0
    - 1
    monogenic: 0
    num_ram: 2
    r2: 3
    ramps:
    - 2
    - 7
    rd: 17.2140682826
    regulator:
      __RealLiteral__: 0
      data: '931.906866489'
      prec: 44
    res:
      gal:
      - 1,0,-8,0,35,0,-118,0,293,0,-532,0,351,0,518,0,125,0,-6,0,7,0,6,0,1
      sib:
      - 8,0,-12,0,4,0,1,0,2,0,-3,0,1
    subfield_mults:
    - 1
    - 1
    - 1
    - 1
    subfields:
    - -2.0.1
    - 1.-2.-1.1
    - -2.-4.-2.0.1
    - -8.0.24.0.-10.0.1
    torsion_gen: \( -1 \)
    torsion_order: 2
    units:
    - \( \frac{176}{49} a^{11} + \frac{4}{49} a^{10} - \frac{1448}{49} a^{9} - \frac{97}{7}
      a^{8} + \frac{2160}{49} a^{7} - \frac{422}{7} a^{6} - \frac{740}{7} a^{5} +
      \frac{14871}{49} a^{4} + \frac{32184}{49} a^{3} + \frac{23082}{49} a^{2} + \frac{1104}{7}
      a + \frac{1027}{49} \)
    - \( \frac{176}{49} a^{11} + \frac{4}{49} a^{10} - \frac{1448}{49} a^{9} - \frac{97}{7}
      a^{8} + \frac{2160}{49} a^{7} - \frac{422}{7} a^{6} - \frac{740}{7} a^{5} +
      \frac{14871}{49} a^{4} + \frac{32184}{49} a^{3} + \frac{23082}{49} a^{2} + \frac{1104}{7}
      a + \frac{978}{49} \)
    - \( a \)
    - \( \frac{333}{49} a^{11} - \frac{82}{49} a^{10} - \frac{2684}{49} a^{9} - \frac{87}{7}
      a^{8} + \frac{4048}{49} a^{7} - \frac{934}{7} a^{6} - 161 a^{5} + \frac{29531}{49}
      a^{4} + \frac{53066}{49} a^{3} + \frac{31869}{49} a^{2} + \frac{1255}{7} a +
      \frac{951}{49} \)
    - \( \frac{414}{49} a^{11} - \frac{87}{49} a^{10} - \frac{3296}{49} a^{9} - \frac{138}{7}
      a^{8} + \frac{4785}{49} a^{7} - \frac{1089}{7} a^{6} - \frac{1434}{7} a^{5}
      + \frac{35304}{49} a^{4} + \frac{68010}{49} a^{3} + \frac{45069}{49} a^{2} +
      \frac{2013}{7} a + \frac{1783}{49} \)
    - \( a^{11} - a^{10} - 7 a^{9} + 3 a^{8} + 8 a^{7} - 24 a^{6} - 4 a^{5} + 84 a^{4}
      + 98 a^{3} + 46 a^{2} + 12 a \)
    - \( \frac{15}{7} a^{11} - \frac{9}{7} a^{10} - \frac{118}{7} a^{9} + 2 a^{8}
      + \frac{181}{7} a^{7} - \frac{358}{7} a^{6} - \frac{235}{7} a^{5} + \frac{1422}{7}
      a^{4} + 271 a^{3} + \frac{727}{7} a^{2} + \frac{82}{7} a - \frac{4}{7} \)
    - \( \frac{101}{7} a^{11} - \frac{34}{7} a^{10} - \frac{795}{7} a^{9} - 20 a^{8}
      + \frac{1152}{7} a^{7} - \frac{1991}{7} a^{6} - \frac{2161}{7} a^{5} + \frac{8774}{7}
      a^{4} + 2209 a^{3} + \frac{9426}{7} a^{2} + \frac{2717}{7} a + \frac{296}{7}
      \)
    used_grh: false
    zk:
    - '1'
    - a
    - a^2
    - a^3
    - a^4
    - a^5
    - a^6
    - a^7
    - a^8
    - 1/7*a^9 - 2/7*a^8 - 3/7*a^7 + 1/7*a^6 - 3/7*a^5 + 2/7*a^4 + 1/7*a^3 + 3/7*a
      - 1/7
    - 1/7*a^10 + 2/7*a^7 - 1/7*a^6 + 3/7*a^5 - 2/7*a^4 + 2/7*a^3 + 3/7*a^2 - 2/7*a
      - 2/7
    - 1/49*a^11 - 3/49*a^10 + 1/49*a^9 - 1/7*a^8 - 17/49*a^7 - 2/7*a^6 + 2/7*a^5 -
      11/49*a^4 + 19/49*a^3 - 11/49*a^2 - 1/7*a - 16/49
label_cols:
- label
labels:
- 12.6.677021181018112.2
tables:
- nf_fields
timestamp: '2024-05-18T12:33:52.072510'