Elliptic curve data - 816.b2

Formats: - HTML - YAML - JSON - 2024-05-16T11:40:49.093723

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '816h', 'Clabel': '816h3', 'Cnumber': 3, 'abc_quality': 1.0315574162602832, 'absD': 110841053184, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 136, 'ainvs': [0, -1, 0, -27744, 1787904], 'analytic_rank': 1, 'bad_primes': [2, 3, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 816, 'degree': 1536, 'elladic_images': ['8.96.0.35'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1936518759214449089464431174', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [576615941610337, 27060804], 'lmfdb_iso': '816.b', 'lmfdb_label': '816.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1734, -27936], 'min_quad_twist_disc': -4, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '8.96.0-8.e.1.5', '136.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 11, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.8269817694884771133715028815', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.50050469536149959952921099594', 'prec': 103}, 'szpiro_ratio': 6.310165433577791, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
• 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, 0, 0, 1, 0, 4, 0, -2, 0, 2, 0, 1, 0, -4, 0], 'aplist': [0, -1, -2, 0, 4, -2, 1, -4, 0, -10, -8, -2, 10, -12, 0, 6, -12, -10, 12, 0, 10, 8, -4, -6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 816, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '816.b', 'trace_hash': 1491784977306846667}
• 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': '0.091877073605974043070090898313', 'prec': 107}, 'conductor': 816, 'gens': [[146, 910, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.8269817694884771133715028815', 'prec': 100}], 'lmfdb_label': '816.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.99348185850601324739329990214', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9010184804100217125383093577879546832', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[96, 0, 1], [80, 272, 1]], 'xcoord_integral_points': [-192, 80, 96, 97, 114, 146, 1185]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 3, 0], '11': [1, 0], '13': [1, 0], '17': [2, 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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '816.b2'}
• ec_torsion_growth •

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

  
  
  • id: 38489
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '816.b2', 'torsion': [4, 4]}
  • id: 38491
    {'degree': 4, 'field': [2, 12, -11, -2, 1], 'lmfdb_label': '816.b2', 'torsion': [2, 8]}
  • id: 38490
    {'degree': 4, 'field': [16, 0, 9, 0, 1], 'lmfdb_label': '816.b2', 'torsion': [2, 8]}
  • id: 38494
    {'degree': 8, 'field': [-507, 0, -392, 0, -78, 0, 0, 0, 1], 'lmfdb_label': '816.b2', 'torsion': [2, 12]}
  • id: 38493
    {'degree': 8, 'field': [81, 0, -108, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '816.b2', 'torsion': [4, 8]}
  • id: 38492
    {'degree': 8, 'field': [256, 0, 0, 0, 49, 0, 0, 0, 1], 'lmfdb_label': '816.b2', 'torsion': [4, 8]}
  • id: 38497
    {'degree': 16, 'field': [-318788, 2762256, -7090408, 4349472, 1556408, -3425880, 1518612, 477696, -276451, 66672, -24576, 0, 386, -72, 68, 0, 1], 'lmfdb_label': '816.b2', 'torsion': [2, 16]}
  • id: 38496
    {'degree': 16, 'field': [256, 0, -1984, 0, 7688, 0, -6968, 0, 3332, 0, -688, 0, 98, 0, -14, 0, 1], 'lmfdb_label': '816.b2', 'torsion': [2, 16]}
  • id: 38495
    {'degree': 16, 'field': [100258, 25688, -8524, -71592, 159290, -222416, 166912, -21384, -59117, 30648, 5416, -5320, 98, 336, -28, -8, 1], 'lmfdb_label': '816.b2', 'torsion': [8, 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: 10583
    {'conductor': 816, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '816.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 10584
    {'conductor': 816, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '816.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 10585
    {'conductor': 816, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '816.b2', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1669756
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [135, 94, 0, 33], [5, 4, 132, 133], [3, 110, 94, 115], [129, 8, 128, 9], [105, 8, 12, 33]], 'adelic_image': '136.192.1.?', 'conductor': 816, 'lmfdb_label': '816.b2', 'prime': 0}
  • id: 3754
    {'conductor': 816, 'elladic_image': '8.96.0.35', 'lmfdb_label': '816.b2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 16476
    {'lmfdb_iso': '816.b', 'p': 5, 'prec': 20, 'unit': 8825431677663, 'val': 1}
  • id: 16483
    {'lmfdb_iso': '816.b', 'p': 11, 'prec': 20, 'unit': 16571100867996405230, 'val': 1}
  • id: 16481
    {'lmfdb_iso': '816.b', 'p': 13, 'prec': 20, 'unit': 83421926776081939350, 'val': 1}
  • id: 16484
    {'lmfdb_iso': '816.b', 'p': 19, 'prec': 20, 'unit': 1968637796478763019645504, 'val': 1}
  • id: 16480
    {'lmfdb_iso': '816.b', 'p': 29, 'prec': 20, 'unit': 1416536744473640912886433598, 'val': 1}
  • id: 16477
    {'lmfdb_iso': '816.b', 'p': 31, 'prec': 20, 'unit': 13949341852340056356839637451, 'val': 1}
  • id: 16490
    {'lmfdb_iso': '816.b', 'p': 37, 'prec': 20, 'unit': 402105728074642883234028357862, 'val': 1}
  • id: 16478
    {'lmfdb_iso': '816.b', 'p': 41, 'prec': 20, 'unit': 610845358652900391846355078957, 'val': 1}
  • id: 16479
    {'lmfdb_iso': '816.b', 'p': 43, 'prec': 20, 'unit': 5101775100505261816206399713027, 'val': 1}
  • id: 16485
    {'lmfdb_iso': '816.b', 'p': 53, 'prec': 20, 'unit': 570118130808845491880591858665795, 'val': 1}
  • id: 16488
    {'lmfdb_iso': '816.b', 'p': 59, 'prec': 20, 'unit': 1343971496639300779317445283892111, 'val': 1}
  • id: 16489
    {'lmfdb_iso': '816.b', 'p': 61, 'prec': 20, 'unit': 1909776350045629744915529704152225, 'val': 1}
  • id: 16475
    {'lmfdb_iso': '816.b', 'p': 67, 'prec': 20, 'unit': 44967906305976396425444888505425268, 'val': 1}
  • id: 16486
    {'lmfdb_iso': '816.b', 'p': 73, 'prec': 20, 'unit': 202162725660225663181990047652091569, 'val': 1}
  • id: 16482
    {'lmfdb_iso': '816.b', 'p': 79, 'prec': 20, 'unit': 364450595174336498399006657995136672, 'val': 1}
  • id: 16474
    {'lmfdb_iso': '816.b', 'p': 83, 'prec': 20, 'unit': 293584274248935369431881873547976786, 'val': 1}
  • id: 16487
    {'lmfdb_iso': '816.b', 'p': 89, 'prec': 20, 'unit': 9586245386873343026757348963008400519, 'val': 1}
  • id: 16473
    {'lmfdb_iso': '816.b', 'p': 97, 'prec': 20, 'unit': 129012419303103802336052442018699313, 'val': 1}