Elliptic curve data - 31850.bo1

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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': '31850ce', 'Clabel': '31850ce3', 'Cnumber': 3, 'abc_quality': 0.9543225417743602, 'absD': 82711952960000000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 10920, 'ainvs': [1, 0, 0, -254213, 47332417], 'analytic_rank': 2, 'bad_primes': [2, 5, 7, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 31850, 'degree': 497664, 'elladic_images': ['4.6.0.3', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0081234332223704254428924830', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 40, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [988345570681, 44994560], 'lmfdb_iso': '31850.bo', 'lmfdb_label': '31850.bo1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -208, -1122], 'min_quad_twist_disc': -35, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.b.1', '6.12.0.a.1', '12.24.0.f.1', '24.48.0.br.2', '105.8.0.?', '130.6.0.?', '210.24.0.?', '260.24.0.?', '280.12.0.?', '390.24.0.?', '420.48.0.?', '546.24.0.?', '728.12.0.?', '780.96.3.?', '840.96.0.?', '1092.48.0.?', '1560.192.9.?', '2184.96.0.?', '2730.48.0.?', '3640.48.0.?', '5460.192.3.?', '10920.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 49, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.17956284394004275265798826279', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 15925], [3, 2, 1225], [5, 18, 1274], [7, 26, 650], [13, 14, 2450]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.23044940247766358558983644466', 'prec': 103}, 'szpiro_ratio': 4.721030520215792, '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, 1, -2, 1, 0, -2, 0, 1, 1, 0, -6, -2, 1, 0, 0, 1, -6, 1, -2, 0], 'aplist': [1, -2, 0, 0, -6, 1, -6, -2, -6, -6, -2, -2, 6, -2, -12, -6, -6, -2, 4, -6, -10, -4, 0, 6, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 31850, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '31850.bo', 'trace_hash': 524212996540487656}
• 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': '0.018020471415802998318073634936', 'prec': 107}, 'conductor': 31850, 'gens': [[82, 5159, 1], [186, 2455, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.30888780878522380239476850110', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.60099997281277374839095446901', 'prec': 103}], 'lmfdb_label': '31850.bo1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.33806795511413323307984398688', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999999', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '8.7414398590015416849905458499277352284', 'prec': 130}, 'tamagawa_product': 576, 'torsion_generators': [[242, -121, 1]], 'xcoord_integral_points': [-568, -542, -318, -118, -108, 46, 82, 186, 232, 242, 342, 368, 382, 466, 498, 642, 732, 1642, 4866, 5282, 8082, 8992, 96282, 143056, 2984482]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [6, 0], '5': 'a', '7': 'a', '11': [2, 0], '13': [3, 0], '17': [4, 0], '19': [2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '31850.bo1'}
• ec_torsion_growth •

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

  
  
  • id: 1587742
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '31850.bo1', 'torsion': [6]}
  • id: 1587741
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '31850.bo1', 'torsion': [2, 2]}
  • id: 1587744
    {'degree': 4, 'field': [-26, -143, -55, -1, 1], 'lmfdb_label': '31850.bo1', 'torsion': [2, 6]}
  • id: 1587743
    {'degree': 4, 'field': [200, -28, -3, 0, 1], 'lmfdb_label': '31850.bo1', 'torsion': [4]}
  • id: 1587745
    {'degree': 6, 'field': [135, 0, 0, -20, 0, 0, 1], 'lmfdb_label': '31850.bo1', 'torsion': [6]}
  • id: 1587747
    {'degree': 8, 'field': [256, 0, -7744, 0, 356, 0, -29, 0, 1], 'lmfdb_label': '31850.bo1', 'torsion': [2, 4]}
  • id: 1587748
    {'degree': 8, 'field': [1114, -1454, 3627, -2014, 245, 110, -27, -2, 1], 'lmfdb_label': '31850.bo1', 'torsion': [12]}
  • id: 1587746
    {'degree': 8, 'field': [1600, 0, 3120, 0, 76, 0, 13, 0, 1], 'lmfdb_label': '31850.bo1', 'torsion': [2, 4]}
  • id: 1587749
    {'degree': 12, 'field': [1024, -4992, 10032, -9360, 5940, -2892, 1051, -156, -30, 0, 12, -6, 1], 'lmfdb_label': '31850.bo1', 'torsion': [3, 6]}
  • id: 1587750
    {'degree': 12, 'field': [390625, 0, 0, 0, 0, 0, 990, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '31850.bo1', 'torsion': [2, 6]}
  • id: 1587752
    {'degree': 16, 'field': [140816, -553488, 1046188, -1240148, 968765, -464566, 101017, 11894, -1525, -13402, 9738, -2798, 95, 144, -23, -4, 1], 'lmfdb_label': '31850.bo1', 'torsion': [8]}
  • id: 1587751
    {'degree': 16, 'field': [203840, 407680, 582400, -873600, -304464, -657760, 2233312, -1877344, 865564, -252616, 50784, -6168, 17, 198, -26, -2, 1], 'lmfdb_label': '31850.bo1', 'torsion': [4, 4]}
  • id: 1587754
    {'degree': 16, 'field': [16777216, 0, 76746752, 0, -578880, 0, -3587828, 0, 130799, 0, 35818, 0, -1680, 0, -22, 0, 1], 'lmfdb_label': '31850.bo1', 'torsion': [2, 12]}
  • id: 1587753
    {'degree': 16, 'field': [56310016, 0, 28598528, 0, 6346372, 0, 676768, 0, 62553, 0, 6224, 0, 418, 0, 16, 0, 1], 'lmfdb_label': '31850.bo1', 'torsion': [2, 12]}
  • id: 1587755
    {'degree': 18, 'field': [-10559160861696, -7213161113856, 629008464960, 985793438928, -58266463824, -60529441152, 10943802016, 3165630504, -772826688, -178258709, 30606165, 7193088, -910056, -156474, 18114, 1696, -192, -9, 1], 'lmfdb_label': '31850.bo1', 'torsion': [18]}
• 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: 744305
    {'conductor': 31850, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '31850.bo1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 744306
    {'conductor': 31850, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '31850.bo1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 744307
    {'conductor': 31850, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '31850.bo1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 744308
    {'conductor': 31850, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '31850.bo1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1876826
    {'adelic_gens': [[8191, 4704, 7812, 1849], [1, 12, 12, 145], [3858, 1561, 4823, 8], [7, 24, 492, 1687], [3641, 4704, 3640, 1], [3119, 0, 0, 10919], [5461, 4704, 5460, 1], [10897, 24, 10896, 25], [1, 24, 0, 1], [608, 6237, 8883, 4766], [21, 4, 10820, 10901], [1, 0, 24, 1]], 'adelic_image': '10920.384.9.?', 'conductor': 31850, 'lmfdb_label': '31850.bo1', 'prime': 0}
  • id: 142433
    {'conductor': 31850, 'elladic_image': '4.6.0.3', 'lmfdb_label': '31850.bo1', 'modell_image': '2B', 'prime': 2}
  • id: 142434
    {'conductor': 31850, 'elladic_image': '3.4.0.1', 'lmfdb_label': '31850.bo1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1550445
    {'lmfdb_iso': '31850.bo', 'p': 11, 'prec': 20, 'unit': 10308580779293951860, 'val': 2}
  • id: 1550446
    {'lmfdb_iso': '31850.bo', 'p': 17, 'prec': 20, 'unit': 5598564000212770899417, 'val': 3}
  • id: 1550447
    {'lmfdb_iso': '31850.bo', 'p': 19, 'prec': 20, 'unit': 1870638532571540639787451, 'val': 2}
  • id: 1550451
    {'lmfdb_iso': '31850.bo', 'p': 23, 'prec': 20, 'unit': 56662101985398512328267389, 'val': 2}
  • id: 1550443
    {'lmfdb_iso': '31850.bo', 'p': 29, 'prec': 20, 'unit': 4870163436798579865510940959, 'val': 2}
  • id: 1550455
    {'lmfdb_iso': '31850.bo', 'p': 31, 'prec': 20, 'unit': 18897743283520252169729291438, 'val': 2}
  • id: 1550439
    {'lmfdb_iso': '31850.bo', 'p': 37, 'prec': 20, 'unit': 334805284955537389358294001850, 'val': 2}
  • id: 1550441
    {'lmfdb_iso': '31850.bo', 'p': 41, 'prec': 20, 'unit': 1049654404952588562226332537423, 'val': 2}
  • id: 1550442
    {'lmfdb_iso': '31850.bo', 'p': 43, 'prec': 20, 'unit': 7455094939289474828954819574531, 'val': 2}
  • id: 1550453
    {'lmfdb_iso': '31850.bo', 'p': 47, 'prec': 20, 'unit': 18665499008532618907845876331958, 'val': 2}
  • id: 1550448
    {'lmfdb_iso': '31850.bo', 'p': 53, 'prec': 20, 'unit': 558050199028510821673818611684842, 'val': 2}
  • id: 1550449
    {'lmfdb_iso': '31850.bo', 'p': 59, 'prec': 20, 'unit': 3936377533645833156929374734088393, 'val': 2}
  • id: 1550454
    {'lmfdb_iso': '31850.bo', 'p': 61, 'prec': 20, 'unit': 163964973055719212064331354861161, 'val': 2}
  • id: 1550438
    {'lmfdb_iso': '31850.bo', 'p': 67, 'prec': 20, 'unit': 13422744064089347385485644610187846, 'val': 2}
  • id: 1550440
    {'lmfdb_iso': '31850.bo', 'p': 71, 'prec': 20, 'unit': 115456167896094782537359625317166785, 'val': 2}
  • id: 1550450
    {'lmfdb_iso': '31850.bo', 'p': 73, 'prec': 20, 'unit': 3618432157831402659130524970723517, 'val': 2}
  • id: 1550444
    {'lmfdb_iso': '31850.bo', 'p': 79, 'prec': 20, 'unit': 379188151269312917967078309716855299, 'val': 2}
  • id: 1550452
    {'lmfdb_iso': '31850.bo', 'p': 89, 'prec': 20, 'unit': 5911026956136206838276951718591782420, 'val': 2}
  • id: 1550437
    {'lmfdb_iso': '31850.bo', 'p': 97, 'prec': 20, 'unit': 5704024311808055231091715281556517519, 'val': 2}