data:
- - class_group: []
    class_number: 1
    cm: false
    coeffs:
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    - 0
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    - 0
    - 0
    - 0
    - 0
    - 0
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    - 0
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    conductor: 0
    degree: 34
    dirichlet_group: []
    disc_abs: 11885748945456377039253666531245020090157279092950049
    disc_rad: 11885748945456377039253666531245020090157279092950049
    disc_sign: 1
    frobs:
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        - - 1
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    - - 43
      - - - 17
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    - - 59
      - - - 28
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          - 1
        - - 1
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    gal_is_abelian: false
    gal_is_cyclic: false
    gal_is_solvable: false
    galois_disc_exponents:
    - 147616399519802070423809304821760000000
    - 147616399519802070423809304821760000000
    - 147616399519802070423809304821760000000
    - 147616399519802070423809304821760000000
    galois_label: 34T115
    galt: 115
    grd: 1.0902178197707272e+26
    id: 19853175
    index: 1
    inessentialp: []
    is_galois: false
    is_minimal_sibling: true
    iso_number: 1
    label: 34.2.11885748945456377039253666531245020090157279092950049.1
    local_algs:
    - 7.2.1.1
    - 7.2.0.1
    - 7.15.0.1
    - 7.15.0.1
    - 191.2.0.1
    - 191.2.0.1
    - 191.2.1.2
    - 191.11.0.1
    - 191.17.0.1
    - m607.1.1.0
    - m607.1.1.0
    - m607.1.1.0
    - m607.1.2.0
    - m607.2.1.1
    - m607.1.5.0
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    - m14645575916792712592989131451003587034531413111.2.1.1
    - m14645575916792712592989131451003587034531413111.1.11.0
    - m14645575916792712592989131451003587034531413111.1.21.0
    monogenic: 1
    num_ram: 4
    r2: 16
    ramps:
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    - 191
    - 607
    - 14645575916792712592989131451003587034531413111
    rd: 34.0109237751
    regulator:
      __RealLiteral__: 0
      data: '2995765078540.3994'
      prec: 60
    subfield_mults: []
    subfields: []
    torsion_gen: \( -1 \)
    torsion_order: 2
    units:
    - \( a^{33} - 1 \)
    - \( a^{33} - a^{32} - a^{15} - 1 \)
    - \( a^{14} - a^{3} \)
    - \( a^{21} - a^{20} \)
    - \( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} + a^{27} - a^{26} + a^{25}
      - a^{24} - a^{22} - 1 \)
    - \( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} + a^{27} \)
    - \( a^{31} - a^{30} + a^{29} - a^{28} + a^{27} \)
    - \( a^{33} - a^{32} + a^{31} - a^{30} + a^{27} - a^{26} - 1 \)
    - \( a^{12} - a^{9} + a^{6} \)
    - \( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} - a^{15} + a^{14} + a^{8}
      - a^{7} - 1 \)
    - \( 2 a^{33} - 3 a^{32} + 3 a^{31} - 3 a^{30} + 3 a^{29} - 3 a^{28} + 3 a^{27}
      - 3 a^{26} + 3 a^{25} - 3 a^{24} + 3 a^{23} - 2 a^{22} + 2 a^{21} - a^{20} +
      a^{19} - a^{18} - a^{16} + a^{12} - a^{11} + a^{10} - a^{9} + a^{8} - a^{7}
      + a^{6} + a^{4} - a^{3} + a^{2} - a - 2 \)
    - \( a^{32} - 2 a^{31} + a^{30} + a^{28} - a^{27} + a^{24} - a^{23} + a^{20} -
      a^{18} + a^{16} - a^{14} + a^{12} - a^{10} + a^{8} + a^{7} - a^{6} - a^{5} +
      a^{4} + a^{3} - a^{2} - a + 1 \)
    - \( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} + a^{27} - a^{26} + a^{25}
      - a^{24} + a^{12} + a^{10} - a^{5} - 1 \)
    - \( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} - a^{26} + a^{25} + a^{18}
      - a^{13} - a^{7} + a^{5} + a^{4} - 1 \)
    - \( 2 a^{33} - 2 a^{32} + 2 a^{31} - 2 a^{30} + a^{29} - a^{28} + 2 a^{27} -
      a^{26} + a^{25} - a^{24} + a^{23} + a^{19} + a^{14} - a^{9} + a^{6} - a^{4}
      - a^{3} - 2 \)
    - \( a^{33} - a^{27} + a^{26} + a^{12} - a^{11} + a^{6} - a^{2} - 1 \)
    - \( a^{33} - a^{32} - a^{30} - a^{27} + a^{26} + a^{23} + a^{20} - a^{18} + a^{17}
      - a^{16} - a^{14} - a^{12} - a^{9} + a^{8} + a^{7} + a^{5} + a^{4} + a^{2} -
      2 \)
    used_grh: true
    zk:
    - '1'
    - a
    - a^2
    - a^3
    - a^4
    - a^5
    - a^6
    - a^7
    - a^8
    - a^9
    - a^10
    - a^11
    - a^12
    - a^13
    - a^14
    - a^15
    - a^16
    - a^17
    - a^18
    - a^19
    - a^20
    - a^21
    - a^22
    - a^23
    - a^24
    - a^25
    - a^26
    - a^27
    - a^28
    - a^29
    - a^30
    - a^31
    - a^32
    - a^33
label_cols:
- label
labels:
- 34.2.11885748945456377039253666531245020090157279092950049.1
tables:
- nf_fields
timestamp: '2024-05-18T16:32:30.508176'