Elliptic curve data - 171.b1

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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': '171b', 'Clabel': '171b3', 'Cnumber': 3, 'abc_quality': 1.104947099482495, 'absD': 13851, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 1026, 'ainvs': [0, 0, 1, -6924, 221760], 'analytic_rank': 1, 'bad_primes': [3, 19], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 171, 'degree': 72, 'elladic_images': ['27.72.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.58274530132537264921771750205', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3, 9], 'jinv': [-50357871050752, 19], 'lmfdb_iso': '171.b', 'lmfdb_label': '171.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -769, -8470], 'min_quad_twist_disc': -3, 'modell_images': ['3B.1.1'], 'modm_images': ['3.8.0-3.a.1.2', '9.24.0-9.a.1.2', '27.72.0-27.a.1.2', '38.2.0.a.1', '114.16.0.?', '171.72.0.?', '342.144.3.?', '513.648.16.?', '1026.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0337018194312539087610363840', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.033439156991317803520094883589', 'prec': 107}, 'szpiro_ratio': 7.418192451356714, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, -2, -3, 0, -1, 0, 0, 0, -3, 0, -4, 0, 0, 4, 3, 0, 1, 6], 'aplist': [0, 0, -3, -1, -3, -4, 3, 1, 0, -6, -4, 2, 6, -1, 3, -12, 6, -1, -4, -6, -7, 8, -12, -12, 8], 'class_deg': 9, 'class_size': 3, 'conductor': 171, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '171.b', 'trace_hash': 356985413515069152}
• 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': '0.31176966948017056319602018487', 'prec': 103}, 'conductor': 171, 'gens': [[62, 175, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0337018194312539087610363840', 'prec': 100}], 'lmfdb_label': '171.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.3827779033284052041975492616', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0768577238443480228145386666163038742', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[48, 0, 1]], 'xcoord_integral_points': [48, 62]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 5, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 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': '171.b1'}
• ec_torsion_growth •

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

  
  
  • id: 6841
    {'degree': 3, 'field': [-19, -57, 0, 1], 'lmfdb_label': '171.b1', 'torsion': [9]}
  • id: 6840
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '171.b1', 'torsion': [6]}
  • id: 6842
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '171.b1', 'torsion': [2, 6]}
  • id: 6843
    {'degree': 6, 'field': [12, 6, -5, -3, 4, -3, 1], 'lmfdb_label': '171.b1', 'torsion': [3, 3]}
  • id: 6844
    {'degree': 6, 'field': [19, 0, 0, -1, 0, 0, 1], 'lmfdb_label': '171.b1', 'torsion': [9]}
  • id: 6845
    {'degree': 9, 'field': [-71117, -107217, -55233, -5928, 4218, 1197, -95, -57, 0, 1], 'lmfdb_label': '171.b1', 'torsion': [18]}
  • id: 6846
    {'degree': 12, 'field': [-419, 1870, -1812, 338, 747, -860, 264, 172, -145, 22, 12, -6, 1], 'lmfdb_label': '171.b1', 'torsion': [12]}
  • id: 6848
    {'degree': 18, 'field': [324, -1224, 2932, -3908, 3514, -1906, 827, -675, 931, -756, 285, -31, -6, 21, 3, -10, 5, -3, 1], 'lmfdb_label': '171.b1', 'torsion': [3, 6]}
  • id: 6849
    {'degree': 18, 'field': [6859, 0, 0, 3819, 0, 0, 608, 0, 0, 1, 0, 0, 40, 0, 0, -5, 0, 0, 1], 'lmfdb_label': '171.b1', 'torsion': [18]}
  • id: 6850
    {'degree': 18, 'field': [6859, 0, 94880547, 0, -181592025, 0, 63313624, 0, 21482388, 0, 2500647, 0, 155629, 0, 5643, 0, 114, 0, 1], 'lmfdb_label': '171.b1', 'torsion': [2, 18]}
  • id: 6847
    {'degree': 18, 'field': [19683, 0, 0, -13851, 0, 0, 2700, 0, 0, -171, 0, 0, 100, 0, 0, -19, 0, 0, 1], 'lmfdb_label': '171.b1', 'torsion': [3, 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: 1331
    {'conductor': 171, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '171.b1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1332
    {'conductor': 171, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '171.b1', 'prime': 19, '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: 1666463
    {'adelic_gens': [[31, 36, 334, 421], [89, 951, 399, 934], [1, 54, 0, 1], [973, 54, 972, 55], [1, 0, 54, 1], [28, 27, 729, 703], [70, 45, 385, 472]], 'adelic_image': '1026.1296.43.?', 'conductor': 171, 'lmfdb_label': '171.b1', 'prime': 0}
  • id: 688
    {'conductor': 171, 'elladic_image': '27.72.0.1', 'lmfdb_label': '171.b1', 'modell_image': '3B.1.1', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1134
    {'lmfdb_iso': '171.b', 'p': 5, 'prec': 20, 'unit': 6606530844037, 'val': 1}
  • id: 1135
    {'lmfdb_iso': '171.b', 'p': 7, 'prec': 20, 'unit': 10693765253762460, 'val': 1}
  • id: 1133
    {'lmfdb_iso': '171.b', 'p': 11, 'prec': 20, 'unit': 41453725288552787363, 'val': 1}
  • id: 1140
    {'lmfdb_iso': '171.b', 'p': 13, 'prec': 20, 'unit': 1331264124875008502391, 'val': 1}
  • id: 1142
    {'lmfdb_iso': '171.b', 'p': 17, 'prec': 20, 'unit': 138089033310851898974715, 'val': 1}
  • id: 1139
    {'lmfdb_iso': '171.b', 'p': 29, 'prec': 20, 'unit': 2876148562547719769056753196, 'val': 1}
  • id: 1136
    {'lmfdb_iso': '171.b', 'p': 31, 'prec': 20, 'unit': 17285881914420179898018433763, 'val': 1}
  • id: 1151
    {'lmfdb_iso': '171.b', 'p': 37, 'prec': 20, 'unit': 561407382301817475591769151693, 'val': 1}
  • id: 1137
    {'lmfdb_iso': '171.b', 'p': 41, 'prec': 20, 'unit': 1488440327052097957312225177632, 'val': 1}
  • id: 1138
    {'lmfdb_iso': '171.b', 'p': 43, 'prec': 20, 'unit': 4615083635681369449380981222569, 'val': 1}
  • id: 1149
    {'lmfdb_iso': '171.b', 'p': 47, 'prec': 20, 'unit': 21145677225732888609962847901456, 'val': 1}
  • id: 1144
    {'lmfdb_iso': '171.b', 'p': 53, 'prec': 20, 'unit': 50282643553881823157775762343253, 'val': 1}
  • id: 1145
    {'lmfdb_iso': '171.b', 'p': 59, 'prec': 20, 'unit': 2656982913406994527964997506645286, 'val': 1}
  • id: 1150
    {'lmfdb_iso': '171.b', 'p': 61, 'prec': 20, 'unit': 4021149885466154011342630062687778, 'val': 1}
  • id: 1143
    {'lmfdb_iso': '171.b', 'p': 67, 'prec': 20, 'unit': 26140166439327746255986101773687777, 'val': 1}
  • id: 1148
    {'lmfdb_iso': '171.b', 'p': 71, 'prec': 20, 'unit': 57350391138230287483542907250928029, 'val': 1}
  • id: 1146
    {'lmfdb_iso': '171.b', 'p': 73, 'prec': 20, 'unit': 162273213908365866130081459660089822, 'val': 1}
  • id: 1141
    {'lmfdb_iso': '171.b', 'p': 79, 'prec': 20, 'unit': 623257711504741171689277851792077070, 'val': 1}
  • id: 1132
    {'lmfdb_iso': '171.b', 'p': 83, 'prec': 20, 'unit': 2604004849490406349084253774253236750, 'val': 1}
  • id: 1147
    {'lmfdb_iso': '171.b', 'p': 89, 'prec': 20, 'unit': 2768532963416802084582055614826562664, 'val': 1}
  • id: 1131
    {'lmfdb_iso': '171.b', 'p': 97, 'prec': 20, 'unit': 49707083005464869359339572430176927061, 'val': 1}