data:
- - Lvalue:
      __RealLiteral__: 0
      data: '3.28537990874532'
      prec: 54
    abs_disc: 19821
    ainvs: 1,1,0,0;3,0,-1,0;-3,3,2/3,-1/3;-21,-75,1/3,28/3;-103,-292,4,37
    analytic_rank: 0
    bad_primes:
    - (-1/3*w^3-1/3*w^2+3*w+2)
    - (-1/3*w^3-1/3*w^2+2*w)
    base_change: []
    class_deg: 6
    class_label: 4.4.19821.1-21.1-a
    class_size: 4
    cm: 0
    cm_type: 0
    conductor_ideal: (-1/3*w^3-1/3*w^2+4*w-1)
    conductor_label: '21.1'
    conductor_norm: 21
    conductor_norm_factors:
    - 3
    - 7
    degree: 4
    disc: (7/3*w^3-8/3*w^2-20*w+13)
    equation: '{y}^2+\left(a+1\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+3a-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(\frac{28}{3}a^{3}+\frac{1}{3}a^{2}-75a-21\right){x}+37a^{3}+4a^{2}-292a-103'
    field_label: 4.4.19821.1
    galois_images:
    - 2B
    - 3B.1.2
    gens: []
    heights: []
    id: 569997
    iso_label: a
    iso_nlabel: 0
    isodeg:
    - 1
    - 2
    - 3
    - 6
    isogeny_matrix:
    - - 1
      - 2
      - 3
      - 6
    - - 2
      - 1
      - 6
      - 3
    - - 3
      - 6
      - 1
      - 2
    - - 6
      - 3
      - 2
      - 1
    jinv: -4497131/189,-2609822/63,5279251/63,-3858185/189
    label: 4.4.19821.1-21.1-a3
    local_data:
    - cp: 6
      kod: 10
      normp: 3
      ord_cond: 1
      ord_den_j: 6
      ord_disc: 6
      p: (-1/3*w^3-1/3*w^2+3*w+2)
      red: 1
      rootno: -1
    - cp: 1
      kod: 5
      normp: 7
      ord_cond: 1
      ord_den_j: 1
      ord_disc: 1
      p: (-1/3*w^3-1/3*w^2+2*w)
      red: 1
      rootno: -1
    minD: (7/3*w^3-8/3*w^2-20*w+13)
    n_bad_primes: 2
    ngens: 0
    non_min_p: []
    nonmax_primes:
    - 2
    - 3
    nonmax_rad: 6
    normdisc: -5103
    number: 3
    omega:
      __RealLiteral__: 0
      data: '308.35934795540212891511679873437917362'
      prec: 130
    potential_good_reduction: false
    q_curve: false
    rank: 0
    rank_bounds:
    - 0
    - 0
    reducible_primes:
    - 2
    - 3
    reg: 1
    root_analytic_conductor: 18.40681918345954
    semistable: true
    sha: 1
    short_class_label: 21.1-a
    short_label: 21.1-a3
    signature:
    - 4
    - 0
    tamagawa_product: 6
    torsion_gens:
    - '[[-2,-3,1/3,1/3],[3,2,-1/3,-1/3],[1,0,0,0]]'
    torsion_order: 2
    torsion_primes:
    - 2
    torsion_structure:
    - 2
    trace_hash: 717926711534010101
label_cols:
- label
labels:
- 4.4.19821.1-21.1-a3
tables:
- ec_nfcurves
timestamp: '2024-05-22T18:28:29.621287'