data:
- - Ciso: 19a
    Clabel: 19a3
    Cnumber: 3
    abc_quality: 1.3175706029138485
    absD: 19
    adelic_genus: 43
    adelic_index: 1296
    adelic_level: 1026
    ainvs:
    - 0
    - 1
    - 1
    - 1
    - 0
    analytic_rank: 0
    bad_primes:
    - 19
    class_deg: 9
    class_size: 3
    cm: 0
    conductor: 19
    degree: 3
    elladic_images:
    - 27.72.0.1
    faltings_height:
      __RealLiteral__: 0
      data: '-1.0651731316767918878751503533'
      prec: 103
    faltings_index: 0
    faltings_ratio: 1
    id: 23
    iso_nlabel: 0
    isogeny_degrees:
    - 1
    - 3
    - 9
    jinv:
    - 32768
    - 19
    lmfdb_iso: 19.a
    lmfdb_label: 19.a3
    lmfdb_number: 3
    manin_constant: 3
    min_quad_twist_ainvs:
    - 0
    - 1
    - 1
    - 1
    - 0
    min_quad_twist_disc: 1
    modell_images:
    - 3B.1.1
    modm_images:
    - 3.8.0-3.a.1.2
    - 9.24.0-9.a.1.2
    - 27.72.0-27.a.1.2
    - 38.2.0.a.1
    - 114.16.0.?
    - 171.72.0.?
    - 342.144.3.?
    - 513.648.16.?
    - 1026.1296.43.?
    nonmax_primes:
    - 3
    nonmax_rad: 3
    num_bad_primes: 1
    num_int_pts: 2
    optimality: 0
    potential_good_reduction: false
    rank: 0
    regulator: 1
    semistable: true
    sha: 1
    sha_primes: []
    signD: -1
    stable_faltings_height:
      __RealLiteral__: 0
      data: '-1.0651731316767918878751503533'
      prec: 103
    szpiro_ratio: 3.5311337004995735
    torsion: 3
    torsion_primes:
    - 3
    torsion_structure:
    - 3
- - anlist:
    - 0
    - 1
    - 0
    - -2
    - -2
    - 3
    - 0
    - -1
    - 0
    - 1
    - 0
    - 3
    - 4
    - -4
    - 0
    - -6
    - 4
    - -3
    - 0
    - 1
    - -6
    aplist:
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    - 3
    - -1
    - 3
    - -4
    - -3
    - 1
    - 0
    - 6
    - -4
    - 2
    - -6
    - -1
    - -3
    - 12
    - -6
    - -1
    - -4
    - 6
    - -7
    - 8
    - 12
    - 12
    - 8
    class_deg: 9
    class_size: 3
    conductor: 19
    id: 4
    isogeny_matrix:
    - - 1
      - 3
      - 9
    - - 3
      - 1
      - 3
    - - 9
      - 3
      - 1
    lmfdb_iso: 19.a
    trace_hash: 409437620317032020
- - area:
      __RealLiteral__: 0
      data: '8.4177810759646052062925449915'
      prec: 100
    conductor: 19
    gens: []
    heights: []
    id: 23
    lmfdb_label: 19.a3
    ngens: 0
    rank_bounds:
    - 0
    - 0
    real_period:
      __RealLiteral__: 0
      data: '4.0792792004649324322095526836'
      prec: 100
    sha_an:
      __RealLiteral__: 0
      data: '1.0000000000000000000000000000'
      prec: 100
    special_value:
      __RealLiteral__: 0
      data: '0.45325324449610360357883918706482153450'
      prec: 133
    tamagawa_product: 1
    torsion_generators:
    - - 0
      - 0
      - 1
    xcoord_integral_points:
    - 0
- - id: 23
    iwdata:
      '19':
      - 1
      - 0
      '2':
      - 0
      - 3
      - 0
      '3':
      - 0
      - 0
    iwp0: 5
    lmfdb_label: 19.a3
- - degree: 3
    field:
    - -2
    - -2
    - 0
    - 1
    id: 335
    lmfdb_label: 19.a3
    torsion:
    - 6
  - degree: 3
    field:
    - 7
    - -6
    - -1
    - 1
    id: 336
    lmfdb_label: 19.a3
    torsion:
    - 9
  - degree: 6
    field:
    - 1
    - -3
    - 4
    - -3
    - 4
    - -3
    - 1
    id: 337
    lmfdb_label: 19.a3
    torsion:
    - 2
    - 6
  - degree: 6
    field:
    - 1
    - -3
    - 4
    - -2
    - 1
    - -1
    - 1
    id: 339
    lmfdb_label: 19.a3
    torsion:
    - 9
  - degree: 6
    field:
    - 12
    - 6
    - -5
    - -3
    - 4
    - -3
    - 1
    id: 338
    lmfdb_label: 19.a3
    torsion:
    - 3
    - 3
  - degree: 9
    field:
    - 1
    - -8
    - 23
    - -23
    - -7
    - 16
    - 2
    - -5
    - -1
    - 1
    id: 340
    lmfdb_label: 19.a3
    torsion:
    - 18
  - degree: 12
    field:
    - -2
    - -4
    - -4
    - -4
    - 6
    - 8
    - -4
    - 0
    - -4
    - -10
    - -2
    - 0
    - 1
    id: 341
    lmfdb_label: 19.a3
    torsion:
    - 12
  - degree: 18
    field:
    - 1
    - -10
    - 36
    - -50
    - -4
    - 83
    - -89
    - 14
    - 100
    - -152
    - 121
    - -54
    - 11
    - 4
    - 6
    - -9
    - 7
    - -3
    - 1
    id: 344
    lmfdb_label: 19.a3
    torsion:
    - 18
  - degree: 18
    field:
    - 1
    - -3
    - 5
    - 0
    - -3
    - -17
    - 31
    - -5
    - -4
    - -12
    - 26
    - -18
    - 12
    - -9
    - 12
    - -1
    - 4
    - -1
    - 1
    id: 342
    lmfdb_label: 19.a3
    torsion:
    - 3
    - 9
  - degree: 18
    field:
    - 83
    - -173
    - 348
    - 5
    - -526
    - 692
    - 46
    - -1329
    - 1007
    - 567
    - -970
    - 223
    - 260
    - -181
    - 13
    - 29
    - -11
    - -1
    - 1
    id: 345
    lmfdb_label: 19.a3
    torsion:
    - 2
    - 18
  - degree: 18
    field:
    - 324
    - -1224
    - 2932
    - -3908
    - 3514
    - -1906
    - 827
    - -675
    - 931
    - -756
    - 285
    - -31
    - -6
    - 21
    - 3
    - -10
    - 5
    - -3
    - 1
    id: 343
    lmfdb_label: 19.a3
    torsion:
    - 3
    - 6
- - conductor: 19
    conductor_valuation: 1
    discriminant_valuation: 1
    id: 37
    j_denominator_valuation: 1
    kodaira_symbol: 5
    lmfdb_label: 19.a3
    prime: 19
    reduction_type: 1
    root_number: -1
    tamagawa_number: 1
- - adelic_gens:
    - - 31
      - 36
      - 334
      - 421
    - - 994
      - 9
      - 689
      - 790
    - - 1
      - 54
      - 0
      - 1
    - - 973
      - 54
      - 972
      - 55
    - - 149
      - 681
      - 271
      - 448
    - - 1
      - 0
      - 54
      - 1
    - - 28
      - 27
      - 729
      - 703
    adelic_image: 1026.1296.43.?
    conductor: 19
    id: 1665911
    lmfdb_label: 19.a3
    prime: 0
  - conductor: 19
    elladic_image: 27.72.0.1
    id: 29
    lmfdb_label: 19.a3
    modell_image: 3B.1.1
    prime: 3
- []
label_cols:
- lmfdb_label
- lmfdb_iso
- lmfdb_label
- lmfdb_label
- lmfdb_label
- lmfdb_label
- lmfdb_label
- lmfdb_iso
labels:
- 19.a3
- 19.a
- 19.a3
- 19.a3
- 19.a3
- 19.a3
- 19.a3
- 19.a
tables:
- ec_curvedata
- ec_classdata
- ec_mwbsd
- ec_iwasawa
- ec_torsion_growth
- ec_localdata
- ec_galrep
- ec_padic
timestamp: '2024-04-23T14:16:44.996469'