Elliptic curve data - 54978.b2

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

  
  {'Ciso': '54978m', 'Clabel': '54978m1', 'Cnumber': 1, 'abc_quality': 0.9010252156857624, 'absD': 54337640556276, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 15708, 'ainvs': [1, 1, 0, 2376, 352836], 'analytic_rank': 2, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 54978, 'degree': 221184, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3154238436066493871319031555', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [12600539783, 461862324], 'lmfdb_iso': '54978.b', 'lmfdb_label': '54978.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 48, -1022], 'min_quad_twist_disc': -7, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '21.8.0-3.a.1.1', '2244.8.0.?', '5236.2.0.?', '15708.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 5, 'num_int_pts': 24, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.22870225152756423500900711009', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.34246876907899273457922678378', 'prec': 103}, 'szpiro_ratio': 3.5791259175353733, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 1, -3, 1, 0, -1, 1, 3, 1, -1, -5, 0, 3, 1, 1, -1, -2, -3], 'aplist': [-1, -1, -3, 0, 1, -5, 1, -2, 3, 9, -8, -4, -6, -7, 0, -9, -3, -8, -16, -3, 10, -4, 0, -6, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 54978, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '54978.b', 'trace_hash': 1370832894520630678}
• 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': '0.072017388137496596601883370899', 'prec': 107}, 'conductor': 54978, 'gens': [[-22, 550, 1], [27, 648, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.33341679354231288894151384282', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.69358110901245763824643912278', 'prec': 103}], 'lmfdb_label': '54978.b2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.47571988740203232774635152139', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2223140485736384226968576229449316659', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [], 'xcoord_integral_points': [-43, -22, 0, 27, 55, 143, 162, 272, 594, 2134, 2673, 188352]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [4, 0], '5': [4, 0], '7': 'a', '11': [3, 0], '13': [2, 0], '17': [3, 0], '19': [2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 2, 0]}, 'iwp0': 0, 'lmfdb_label': '54978.b2'}
• ec_torsion_growth •

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

  
  
  • id: 2656084
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '54978.b2', 'torsion': [3]}
  • id: 2656085
    {'degree': 3, 'field': [14, 0, -1, 1], 'lmfdb_label': '54978.b2', 'torsion': [2]}
  • id: 2656087
    {'degree': 6, 'field': [-15875, 8315, -678, 433, 78, -1, 1], 'lmfdb_label': '54978.b2', 'torsion': [3]}
  • id: 2656088
    {'degree': 6, 'field': [112, 0, 4, 0, 4, 0, 1], 'lmfdb_label': '54978.b2', 'torsion': [6]}
  • id: 2656086
    {'degree': 6, 'field': [5236, 0, 1, 0, -2, 0, 1], 'lmfdb_label': '54978.b2', 'torsion': [2, 2]}
  • id: 2656089
    {'degree': 12, 'field': [-18190502, 31959631, -23113183, -4065097, -161227, -298541, 20699, 2477, -1765, 85, -13, -1, 1], 'lmfdb_label': '54978.b2', 'torsion': [4]}
  • id: 2656091
    {'degree': 12, 'field': [200704, -175616, 94304, -108976, 64100, -10856, 776, 440, -367, 28, 14, -4, 1], 'lmfdb_label': '54978.b2', 'torsion': [2, 6]}
  • id: 2656090
    {'degree': 12, 'field': [65691025, 14078385, -226237, -264024, 244857, -25389, 21778, -3045, -159, 12, -1, -3, 1], 'lmfdb_label': '54978.b2', 'torsion': [3, 3]}
  • id: 2656093
    {'degree': 18, 'field': [-2860869001536, 0, 32244226560, 0, -8592270960, 0, 1140346180, 0, 19287392, 0, -1442808, 0, -31928, 0, 324, 0, -4, 0, 1], 'lmfdb_label': '54978.b2', 'torsion': [6]}
  • id: 2656092
    {'degree': 18, 'field': [90952894736, -100240783104, 55485322464, -23699495380, 8646426624, -4845047724, 4123041317, -2244572679, 882290448, -250171766, 65636595, -13944675, 2170918, -276903, 15999, 2426, -318, -3, 1], 'lmfdb_label': '54978.b2', 'torsion': [9]}
• 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: 1320458
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '54978.b2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1320459
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '54978.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1320460
    {'conductor': 54978, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '54978.b2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1320461
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '54978.b2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1320462
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '54978.b2', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 2029373
    {'adelic_gens': [[5545, 6, 927, 19], [3, 4, 8, 11], [4, 3, 9, 7], [1, 0, 6, 1], [15703, 6, 15702, 7], [6731, 15702, 4485, 15689], [7855, 6, 7857, 19], [7141, 6, 5715, 19], [6546, 9169, 1309, 2619], [1, 6, 0, 1]], 'adelic_image': '15708.16.0.?', 'conductor': 54978, 'lmfdb_label': '54978.b2', 'prime': 0}
  • id: 234331
    {'conductor': 54978, 'elladic_image': '3.4.0.1', 'lmfdb_label': '54978.b2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2781139
    {'lmfdb_iso': '54978.b', 'p': 5, 'prec': 20, 'unit': 171001900329, 'val': 4}
  • id: 2781145
    {'lmfdb_iso': '54978.b', 'p': 13, 'prec': 20, 'unit': 720383456531351890895, 'val': 2}
  • id: 2781147
    {'lmfdb_iso': '54978.b', 'p': 19, 'prec': 20, 'unit': 1914830182024025542887432, 'val': 2}
  • id: 2781150
    {'lmfdb_iso': '54978.b', 'p': 23, 'prec': 20, 'unit': 50238677140018535986950325, 'val': 2}
  • id: 2781144
    {'lmfdb_iso': '54978.b', 'p': 29, 'prec': 20, 'unit': 3110881289402762595897584989, 'val': 2}
  • id: 2781141
    {'lmfdb_iso': '54978.b', 'p': 31, 'prec': 20, 'unit': 14508173658425887977800207505, 'val': 2}
  • id: 2781154
    {'lmfdb_iso': '54978.b', 'p': 37, 'prec': 20, 'unit': 233485269420481857988886331292, 'val': 2}
  • id: 2781142
    {'lmfdb_iso': '54978.b', 'p': 41, 'prec': 20, 'unit': 4082702379719752952905018382814, 'val': 2}
  • id: 2781143
    {'lmfdb_iso': '54978.b', 'p': 43, 'prec': 20, 'unit': 6230854693160118346148039830740, 'val': 2}
  • id: 2781148
    {'lmfdb_iso': '54978.b', 'p': 53, 'prec': 20, 'unit': 174407383087315631635362651275640, 'val': 2}
  • id: 2781152
    {'lmfdb_iso': '54978.b', 'p': 59, 'prec': 20, 'unit': 2947331080971492956451917598537528, 'val': 2}
  • id: 2781153
    {'lmfdb_iso': '54978.b', 'p': 61, 'prec': 20, 'unit': 6840265019779790998437386864693334, 'val': 2}
  • id: 2781138
    {'lmfdb_iso': '54978.b', 'p': 67, 'prec': 20, 'unit': 1462854818022306843267389511777234, 'val': 2}
  • id: 2781140
    {'lmfdb_iso': '54978.b', 'p': 71, 'prec': 20, 'unit': 127561028589918456006476720095473337, 'val': 2}
  • id: 2781149
    {'lmfdb_iso': '54978.b', 'p': 73, 'prec': 20, 'unit': 205104019446579858129170756246172082, 'val': 2}
  • id: 2781146
    {'lmfdb_iso': '54978.b', 'p': 79, 'prec': 20, 'unit': 405006450036522902081636466114032948, 'val': 2}
  • id: 2781151
    {'lmfdb_iso': '54978.b', 'p': 89, 'prec': 20, 'unit': 5127002628250089680789192992209139597, 'val': 2}
  • id: 2781137
    {'lmfdb_iso': '54978.b', 'p': 97, 'prec': 20, 'unit': 36555295143410001482018478315824380808, 'val': 2}