Elliptic curve data - 87120.bn1

Formats: - HTML - YAML - JSON - 2025-10-19T06:46:52.428280

• 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': '87120t', 'Clabel': '87120t4', 'Cnumber': 4, 'abc_quality': 1.0052432979893915, 'absD': 3273096420633600, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2640, 'ainvs': [0, 0, 0, -57499563, -167820468662], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 87120, 'degree': 3932160, 'elladic_images': ['16.24.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8236419115093643446542781561', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [15897679904620804, 2475], 'lmfdb_iso': '87120.bn', 'lmfdb_label': '87120.bn1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -52800, 4687452], 'min_quad_twist_disc': -132, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '12.12.0-4.c.1.2', '16.24.0.f.1', '24.24.0-8.n.1.1', '40.24.0.cb.1', '44.12.0.h.1', '48.48.0-16.f.1.2', '80.48.0.?', '88.24.0.?', '120.48.0.?', '132.24.0.?', '176.48.0.?', '240.96.0.?', '264.48.0.?', '440.48.0.?', '528.96.0.?', '880.96.1.?', '1320.96.0.?', '2640.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '26.596457103026712334922292667', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1089], [3, 8, 9680], [5, 6, 17424], [11, 72, 720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49776548030950313574465698078', 'prec': 103}, 'szpiro_ratio': 5.733206799555542, '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, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, -1, 0, 0, 2, -6, -4, 0, 6, 8, 6, 10, -4, -8, 10, -12, -6, 4, 0, 14, 0, -4, 6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 87120, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '87120.bn', 'trace_hash': 2128710495134730086}
• 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': '0.0035270839602097035305917706430', 'prec': 110}, 'conductor': 87120, 'gens': [[941490708161, 887006318964059169, 5336]], 'heights': [{'__RealLiteral__': 0, 'data': '26.596457103026712334922292667', 'prec': 100}], 'lmfdb_label': '87120.bn1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.054825603215116098972467511259', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.8326672162335949094453337926878698221', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-4378, 0, 1]], 'xcoord_integral_points': [-4378]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '87120.bn1'}
• ec_torsion_growth •

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

  
  
  • id: 4078524
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [2, 2]}
  • id: 4078525
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '87120.bn1', 'torsion': [4]}
  • id: 4078526
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [4]}
  • id: 4078527
    {'degree': 4, 'field': [121, 0, 11, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [2, 4]}
  • id: 4078529
    {'degree': 4, 'field': [1225, 0, -40, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [8]}
  • id: 4078528
    {'degree': 4, 'field': [1849, 0, 46, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [8]}
  • id: 4078532
    {'degree': 8, 'field': [1, 0, 42, 0, 1763, 0, 42, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [2, 8]}
  • id: 4078531
    {'degree': 8, 'field': [1936, 0, 0, 0, -44, 0, 0, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [8]}
  • id: 4078530
    {'degree': 8, 'field': [4486, 688, -824, 274, -141, 2, 4, -4, 1], 'lmfdb_label': '87120.bn1', 'torsion': [2, 4]}
  • id: 4078533
    {'degree': 8, 'field': [305628, -328568, 43168, -2028, 1216, 16, 6, -2, 1], 'lmfdb_label': '87120.bn1', 'torsion': [6]}
  • id: 4078538
    {'degree': 16, 'field': [-215728524, 729369960, -386312432, -446363192, 83851108, 68211968, -5160592, -3165244, -125164, -33760, 8648, 5356, 1948, -428, -26, -2, 1], 'lmfdb_label': '87120.bn1', 'torsion': [2, 6]}
  • id: 4078535
    {'degree': 16, 'field': [17689, 0, 34052, 0, 20624, 0, 4164, 0, -58, 0, -324, 0, 32, 0, -4, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [2, 8]}
  • id: 4078534
    {'degree': 16, 'field': [22667121, -657018, 9522, -2571216, 651433, -82674, 147954, -54938, 15668, -3176, 2216, -842, 153, -12, 8, -4, 1], 'lmfdb_label': '87120.bn1', 'torsion': [4, 4]}
  • id: 4078536
    {'degree': 16, 'field': [74822500, 0, 41440000, 0, 151725500, 0, 27223000, 0, 3358525, 0, -132100, 0, 3980, 0, -100, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [16]}
  • id: 4078540
    {'degree': 16, 'field': [392951329, 0, 255924508, 0, 68462068, 0, 6220892, 0, 276662, 0, -15580, 0, -1052, 0, 4, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [12]}
  • id: 4078539
    {'degree': 16, 'field': [1929229929, 0, 158474184, 0, -18870434, 0, 2619408, 0, 570999, 0, 7216, 0, 726, 0, 0, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [12]}
  • id: 4078537
    {'degree': 16, 'field': [5719140625, 0, 4575312500, 0, 2778462500, 0, 672155000, 0, 122569975, 0, 2444200, 0, 36740, 0, 220, 0, 1], 'lmfdb_label': '87120.bn1', 'torsion': [2, 16]}
• 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: 2126347
    {'conductor': 87120, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '87120.bn1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2126348
    {'conductor': 87120, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '87120.bn1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2126349
    {'conductor': 87120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '87120.bn1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2126350
    {'conductor': 87120, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '87120.bn1', 'prime': 11, 'reduction_type': 0, '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: 2237744
    {'adelic_gens': [[974, 2409, 2277, 266], [1, 16, 0, 1], [13, 1776, 924, 985], [15, 2, 2542, 2627], [1, 0, 16, 1], [541, 1776, 2208, 565], [5, 4, 2636, 2637], [2625, 16, 2624, 17], [1832, 879, 1041, 2630], [1759, 0, 0, 2639]], 'adelic_image': '2640.192.1.?', 'conductor': 87120, 'lmfdb_label': '87120.bn1', 'prime': 0}
  • id: 354725
    {'conductor': 87120, 'elladic_image': '16.24.0.7', 'lmfdb_label': '87120.bn1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4503011
    {'lmfdb_iso': '87120.bn', 'p': 13, 'prec': 20, 'unit': 658542608189531064849, 'val': 1}
  • id: 4503013
    {'lmfdb_iso': '87120.bn', 'p': 17, 'prec': 20, 'unit': 198064861410581601385277, 'val': 1}
  • id: 4503014
    {'lmfdb_iso': '87120.bn', 'p': 19, 'prec': 20, 'unit': 448151277879599712497000, 'val': 1}
  • id: 4503010
    {'lmfdb_iso': '87120.bn', 'p': 29, 'prec': 20, 'unit': 4646952762273331332829209235, 'val': 1}
  • id: 4503020
    {'lmfdb_iso': '87120.bn', 'p': 31, 'prec': 20, 'unit': 4578205937014112592356908030, 'val': 1}
  • id: 4503007
    {'lmfdb_iso': '87120.bn', 'p': 37, 'prec': 20, 'unit': 21034866403273083493115469002, 'val': 1}
  • id: 4503008
    {'lmfdb_iso': '87120.bn', 'p': 41, 'prec': 20, 'unit': 947329895872395358130267971927, 'val': 1}
  • id: 4503009
    {'lmfdb_iso': '87120.bn', 'p': 43, 'prec': 20, 'unit': 6690242444204556591359211209827, 'val': 1}
  • id: 4503012
    {'lmfdb_iso': '87120.bn', 'p': 47, 'prec': 20, 'unit': 58529994235496314802149005214715, 'val': 1}
  • id: 4503015
    {'lmfdb_iso': '87120.bn', 'p': 53, 'prec': 20, 'unit': 402729126407630531385668269082677, 'val': 1}
  • id: 4503018
    {'lmfdb_iso': '87120.bn', 'p': 59, 'prec': 20, 'unit': 4119587324178776702470781727759399, 'val': 1}
  • id: 4503019
    {'lmfdb_iso': '87120.bn', 'p': 61, 'prec': 20, 'unit': 2915151358123257132909766866536320, 'val': 1}
  • id: 4503006
    {'lmfdb_iso': '87120.bn', 'p': 67, 'prec': 20, 'unit': 48029456839507325757954348912051555, 'val': 1}
  • id: 4503016
    {'lmfdb_iso': '87120.bn', 'p': 73, 'prec': 20, 'unit': 44182812447277209061166818874525904, 'val': 1}
  • id: 4503005
    {'lmfdb_iso': '87120.bn', 'p': 83, 'prec': 20, 'unit': 2084946923143835096817611275325021635, 'val': 1}
  • id: 4503017
    {'lmfdb_iso': '87120.bn', 'p': 89, 'prec': 20, 'unit': 4635390246054356549506728901095558141, 'val': 1}
  • id: 4503004
    {'lmfdb_iso': '87120.bn', 'p': 97, 'prec': 20, 'unit': 1467451468770804046222903832180684842, 'val': 1}