data:
- - class_group:
    - 2
    - 4
    class_number: 8
    cm: true
    coeffs:
    - 28561
    - 0
    - -4394
    - 0
    - 1859
    - 0
    - 260
    - 0
    - 114
    - 0
    - 18
    - 0
    - 1
    conductor: 0
    degree: 12
    dirichlet_group: []
    disc_abs: 33045608803078144
    disc_rad: 182
    disc_sign: 1
    frobs:
    - - 2
      - - 0
    - - 3
      - - - 6
          - 2
    - - 5
      - - - 6
          - 2
    - - 7
      - - 0
    - - 11
      - - - 3
          - 4
    - - 13
      - - 0
    - - 17
      - - - 6
          - 2
    - - 19
      - - - 6
          - 2
    - - 23
      - - - 3
          - 4
    - - 29
      - - - 2
          - 4
        - - 1
          - 4
    - - 31
      - - - 6
          - 2
    - - 37
      - - - 3
          - 4
    - - 41
      - - - 2
          - 6
    - - 43
      - - - 2
          - 4
        - - 1
          - 4
    - - 47
      - - - 6
          - 2
    - - 53
      - - - 3
          - 4
    - - 59
      - - - 6
          - 2
    gal_is_abelian: false
    gal_is_cyclic: false
    gal_is_solvable: true
    galois_disc_exponents:
    - 36
    - 20
    - 12
    galois_label: 12T7
    galt: 7
    grd: 51.61370512661073
    id: 18380585
    index: 1
    inessentialp: []
    is_galois: false
    is_minimal_sibling: false
    iso_number: 1
    label: 12.0.33045608803078144.1
    local_algs:
    - 2.6.6.1
    - 2.6.6.1
    - 7.6.5.5
    - 7.6.5.5
    - 13.2.0.1
    - 13.2.0.1
    - 13.4.2.1
    - 13.4.2.1
    minimal_sibling:
    - 1183
    - 0
    - 364
    - 0
    - 35
    - 0
    - 1
    monogenic: 0
    num_ram: 3
    r2: 6
    ramps:
    - 2
    - 7
    - 13
    rd: 23.8008689519
    regulator:
      __RealLiteral__: 0
      data: '1615.30314445'
      prec: 44
    res:
      gal:
      - 1,-50,1794,26200,149593,483852,1081836,1829292,2386593,2499518,2736312,2278450,2507033,1428978,744652,206120,72609,8282,1566,-110,1,-10,32,-8,1
      sib:
      - 1183,0,364,0,35,0,1
      - 3266,312,-138,494,253,-26,-24,0,1
      - 9317,35574,38962,1890,2674,-2338,2780,96,557,-22,44,-4,1
    subfield_mults:
    - 1
    - 1
    - 1
    - 1
    - 1
    subfields:
    - 2.-1.1
    - 1.-2.-1.1
    - 1.-1.1.-1.1.-1.1
    - 1183.0.364.0.35.0.1
    - -169.0.104.0.-19.0.1
    torsion_gen: \( -\frac{1142}{65670527} a^{10} - \frac{73105}{131341054} a^{8}
      - \frac{506174}{65670527} a^{6} - \frac{613833}{10103158} a^{4} - \frac{113585}{777166}
      a^{2} + \frac{3902}{29891} \)
    torsion_order: 14
    units:
    - \( \frac{1219}{65670527} a^{10} + \frac{6862}{65670527} a^{8} - \frac{16371}{65670527}
      a^{6} - \frac{107314}{5051579} a^{4} - \frac{54401}{388583} a^{2} + \frac{3059}{29891}
      \)
    - \( \frac{12451}{131341054} a^{10} + \frac{98799}{65670527} a^{8} + \frac{311829}{65670527}
      a^{6} - \frac{183571}{10103158} a^{4} + \frac{174379}{777166} a^{2} + \frac{30117}{59782}
      \)
    - \( \frac{11798}{65670527} a^{11} - \frac{10656}{65670527} a^{10} + \frac{474869}{131341054}
      a^{9} - \frac{200882}{65670527} a^{8} + \frac{3332729}{131341054} a^{7} - \frac{2320381}{131341054}
      a^{6} + \frac{579507}{10103158} a^{5} + \frac{17163}{5051579} a^{4} + \frac{51957}{388583}
      a^{3} + \frac{9671}{777166} a^{2} - \frac{72195}{59782} a + \frac{183955}{59782}
      \)
    - \( \frac{3281}{65670527} a^{11} - \frac{12187}{131341054} a^{10} + \frac{59591}{65670527}
      a^{9} - \frac{149697}{65670527} a^{8} + \frac{1255497}{131341054} a^{7} - \frac{3136895}{131341054}
      a^{6} + \frac{292035}{5051579} a^{5} - \frac{792553}{10103158} a^{4} + \frac{200147}{777166}
      a^{3} - \frac{160378}{388583} a^{2} + \frac{13647}{59782} a + \frac{7550}{29891}
      \)
    - \( \frac{31479}{131341054} a^{11} - \frac{4203}{10103158} a^{10} + \frac{526257}{131341054}
      a^{9} - \frac{23232}{5051579} a^{8} + \frac{1931691}{131341054} a^{7} + \frac{49789}{5051579}
      a^{6} - \frac{415865}{5051579} a^{5} + \frac{2348435}{10103158} a^{4} + \frac{51123}{777166}
      a^{3} - \frac{690709}{777166} a^{2} + \frac{16656}{29891} a + \frac{103143}{59782}
      \)
    used_grh: false
    zk:
    - '1'
    - a
    - a^2
    - a^3
    - a^4
    - a^5
    - 1/26*a^6 - 4/13*a^4 - 3/26*a^2 - 1/2
    - 1/26*a^7 - 4/13*a^5 - 3/26*a^3 - 1/2*a
    - 1/338*a^8 + 5/338*a^6 + 49/338*a^4 + 5/13*a^2 - 1/2
    - 1/338*a^9 + 5/338*a^7 + 49/338*a^5 + 5/13*a^3 - 1/2*a
    - 1/131341054*a^10 + 52603/131341054*a^8 - 2136423/131341054*a^6 - 1232588/5051579*a^4
      + 359383/777166*a^2 + 7615/29891
    - 1/131341054*a^11 + 52603/131341054*a^9 - 2136423/131341054*a^7 - 1232588/5051579*a^5
      + 359383/777166*a^3 + 7615/29891*a
label_cols:
- label
labels:
- 12.0.33045608803078144.1
tables:
- nf_fields
timestamp: '2024-05-12T16:31:20.479097'