data:
- - class_group: []
    class_number: 1
    cm: false
    coeffs:
    - -137
    - 0
    - 0
    - 0
    - 0
    - 1
    conductor: 0
    degree: 5
    dirichlet_group: []
    disc_abs: 1100860503125
    disc_rad: 685
    disc_sign: 1
    frobs:
    - - 2
      - - - 4
          - 1
        - - 1
          - 1
    - - 3
      - - - 4
          - 1
        - - 1
          - 1
    - - 5
      - - 0
    - - 7
      - - - 4
          - 1
        - - 1
          - 1
    - - 11
      - - - 5
          - 1
    - - 13
      - - - 4
          - 1
        - - 1
          - 1
    - - 17
      - - - 4
          - 1
        - - 1
          - 1
    - - 19
      - - - 2
          - 2
        - - 1
          - 1
    - - 23
      - - - 4
          - 1
        - - 1
          - 1
    - - 29
      - - - 2
          - 2
        - - 1
          - 1
    - - 31
      - - - 5
          - 1
    - - 37
      - - - 4
          - 1
        - - 1
          - 1
    - - 41
      - - - 1
          - 5
    - - 43
      - - - 4
          - 1
        - - 1
          - 1
    - - 47
      - - - 4
          - 1
        - - 1
          - 1
    - - 53
      - - - 4
          - 1
        - - 1
          - 1
    - - 59
      - - - 2
          - 2
        - - 1
          - 1
    gal_is_abelian: false
    gal_is_cyclic: false
    gal_is_solvable: true
    galois_disc_exponents:
    - 23
    - 16
    galois_label: 5T3
    galt: 3
    grd: 325.980753070161
    id: 5703056
    index: 1
    inessentialp: []
    is_galois: false
    is_minimal_sibling: true
    iso_number: 1
    label: 5.1.1100860503125.1
    local_algs:
    - 5.5.5.2
    - 137.5.4.1
    monogenic: 1
    num_ram: 2
    r2: 2
    ramps:
    - 5
    - 137
    rd: 256.062781103
    regulator:
      __RealLiteral__: 0
      data: '27287.363999'
      prec: 40
    res:
      gal:
      - 362673936,-13140360,-25804620,-24393570,-9434435,3576538,3351890,1373855,-33245,-402460,217389,-50370,6485,2485,-1870,427,70,-35,15,-5,1
      sib:
      - 17261,4790,-5485,4120,-670,263,-15,10,5,-5,1
    subfield_mults: []
    subfields: []
    torsion_gen: \( -1 \)
    torsion_order: 2
    units:
    - \( 581125409227391 a^{4} + 1554506715753368 a^{3} + 4158659361329535 a^{2} +
      11125745351264340 a + 29762962715247001 \)
    - \( 407837316588286933855747129284564047778166357302955255642095658830284707
      a^{4} - 1487293396021188578613461484805313389187287178355438878925716358277061749
      a^{3} - 5377573486318640504996135730977472701980129831941072595666444152243399535
      a^{2} + 1752669433549774815545197061066282986377974257683751405598250567308930660
      a + 41381221986693667482935543419308238650730348508604476057963125483158909276
      \)
    used_grh: false
    zk:
    - '1'
    - a
    - a^2
    - a^3
    - a^4
label_cols:
- label
labels:
- 5.1.1100860503125.1
tables:
- nf_fields
timestamp: '2024-05-24T00:43:23.813790'