Elliptic curve data - 3192.j2

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '3192l', 'Clabel': '3192l2', 'Cnumber': 2, 'abc_quality': 0.9130336334003399, 'absD': 3772790784, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 3192, 'ainvs': [0, -1, 0, 128, 2860], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 3192, 'degree': 2304, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.51814095119007294401402884219', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2], 'jinv': [112363774, 1842183], 'lmfdb_iso': '3192.j', 'lmfdb_label': '3192.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 128, 2860], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '56.6.0.b.1', '228.6.0.?', '3192.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.1706689233051909251848358408', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 7], [3, 4, 1064], [7, 8, 456], [19, 20, 168]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.11724396432321025628510060248', 'prec': 107}, 'szpiro_ratio': 3.6525028456086743, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, -1, 0, 2, 0, -1, 0, 1, 0, 6, 0, -2, 0, -2, 0, -8, 0, 1, 0], 'aplist': [0, -1, 2, -1, 6, -2, -8, 1, -8, -2, -6, -4, -2, 4, -6, 6, 4, 2, 14, -8, -14, 4, -8, 6, -12], 'class_deg': 2, 'class_size': 2, 'conductor': 3192, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '3192.j', 'trace_hash': 68451720985513418}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.35477130712416494842793219665', 'prec': 103}, 'conductor': 3192, 'gens': [[5, 60, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.1706689233051909251848358408', 'prec': 100}], 'lmfdb_label': '3192.j2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0399575566330636610272595837', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2973611063728530731615442315641110103', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-11, 0, 1]], 'xcoord_integral_points': [-11, 5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [5, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '3192.j2'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 166641
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '3192.j2', 'torsion': [2, 2]}
  • id: 166642
    {'degree': 4, 'field': [-56, 0, 17, 0, 1], 'lmfdb_label': '3192.j2', 'torsion': [4]}
  • id: 166645
    {'degree': 8, 'field': [121, -154, 252, -174, 70, -30, -12, -2, 1], 'lmfdb_label': '3192.j2', 'torsion': [6]}
  • id: 166644
    {'degree': 8, 'field': [1404, -1648, 2220, -1128, 525, 44, -10, -4, 1], 'lmfdb_label': '3192.j2', 'torsion': [2, 4]}
  • id: 166643
    {'degree': 8, 'field': [51202, 20412, -7950, -1344, 587, -84, -6, 0, 1], 'lmfdb_label': '3192.j2', 'torsion': [2, 4]}
  • id: 166647
    {'degree': 16, 'field': [43112356, 0, 47827920, 0, -5435668, 0, 219912, 0, 49392, 0, 7980, 0, 308, 0, -42, 0, 1], 'lmfdb_label': '3192.j2', 'torsion': [2, 6]}
  • id: 166646
    {'degree': 16, 'field': [1058618554, -2055812768, -850828436, -418355984, -119387175, -35850974, -467945, 2736840, 58489, 193860, 4346, -4344, 1043, -478, -1, 0, 1], 'lmfdb_label': '3192.j2', 'torsion': [8]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 57727
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '3192.j2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 57728
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '3192.j2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57729
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.j2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 57730
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3192.j2', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1684744
    {'adelic_gens': [[2, 1, 1595, 0], [401, 2794, 2792, 399], [1, 2, 2, 5], [2129, 4, 1066, 9], [1, 4, 0, 1], [1009, 4, 2018, 9], [1826, 1, 2279, 0], [3189, 4, 3188, 5], [1, 0, 4, 1], [3, 4, 8, 11]], 'adelic_image': '3192.12.0.?', 'conductor': 3192, 'lmfdb_label': '3192.j2', 'prime': 0}
  • id: 16015
    {'conductor': 3192, 'elladic_image': '2.3.0.1', 'lmfdb_label': '3192.j2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 104881
    {'lmfdb_iso': '3192.j', 'p': 5, 'prec': 20, 'unit': 2233979649012, 'val': 2}
  • id: 104880
    {'lmfdb_iso': '3192.j', 'p': 11, 'prec': 20, 'unit': 40703313348486918633, 'val': 1}
  • id: 104887
    {'lmfdb_iso': '3192.j', 'p': 13, 'prec': 20, 'unit': 754461210025095633618, 'val': 1}
  • id: 104889
    {'lmfdb_iso': '3192.j', 'p': 17, 'prec': 20, 'unit': 180401920634266188600734, 'val': 1}
  • id: 104894
    {'lmfdb_iso': '3192.j', 'p': 23, 'prec': 20, 'unit': 68701018638579588913792658, 'val': 1}
  • id: 104886
    {'lmfdb_iso': '3192.j', 'p': 29, 'prec': 20, 'unit': 1749243521189904846770524202, 'val': 1}
  • id: 104883
    {'lmfdb_iso': '3192.j', 'p': 31, 'prec': 20, 'unit': 2440578116276634576838709313, 'val': 1}
  • id: 104898
    {'lmfdb_iso': '3192.j', 'p': 37, 'prec': 20, 'unit': 144053776049559934861459851207, 'val': 1}
  • id: 104884
    {'lmfdb_iso': '3192.j', 'p': 41, 'prec': 20, 'unit': 532497754917900257744227083393, 'val': 1}
  • id: 104885
    {'lmfdb_iso': '3192.j', 'p': 43, 'prec': 20, 'unit': 3060148027343462554297735394265, 'val': 1}
  • id: 104896
    {'lmfdb_iso': '3192.j', 'p': 47, 'prec': 20, 'unit': 32788368847822110613233675965546, 'val': 1}
  • id: 104891
    {'lmfdb_iso': '3192.j', 'p': 53, 'prec': 20, 'unit': 393249050818948603515802793401981, 'val': 1}
  • id: 104892
    {'lmfdb_iso': '3192.j', 'p': 59, 'prec': 20, 'unit': 1626288442994365335195398044543313, 'val': 1}
  • id: 104897
    {'lmfdb_iso': '3192.j', 'p': 61, 'prec': 20, 'unit': 3740447794492051590139373286696237, 'val': 1}
  • id: 104890
    {'lmfdb_iso': '3192.j', 'p': 67, 'prec': 20, 'unit': 23028338105228211756528224187029329, 'val': 1}
  • id: 104882
    {'lmfdb_iso': '3192.j', 'p': 71, 'prec': 20, 'unit': 58487069053398929870791440157698829, 'val': 1}
  • id: 104893
    {'lmfdb_iso': '3192.j', 'p': 73, 'prec': 20, 'unit': 172824905178050184532110388923537799, 'val': 1}
  • id: 104888
    {'lmfdb_iso': '3192.j', 'p': 79, 'prec': 20, 'unit': 900599433892955066109652995730314510, 'val': 1}
  • id: 104879
    {'lmfdb_iso': '3192.j', 'p': 83, 'prec': 20, 'unit': 503326248410557651203775828008243663, 'val': 1}
  • id: 104895
    {'lmfdb_iso': '3192.j', 'p': 89, 'prec': 20, 'unit': 3739269834517797338699795608911865901, 'val': 1}
  • id: 104878
    {'lmfdb_iso': '3192.j', 'p': 97, 'prec': 20, 'unit': 23762242627887590271881239949621627259, 'val': 1}