Elliptic curve data - 267696.gb2

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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': '267696gb', 'Clabel': '267696gb1', 'Cnumber': 1, 'abc_quality': 0.9456942014037588, 'absD': 202624691931028224, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 1716, 'ainvs': [0, 0, 0, 137904, -8972548], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 267696, 'degree': 2419200, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0093705379046239405663330703', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 157, 'isogeny_degrees': [1, 3], 'jinv': [321978368, 224939], 'lmfdb_iso': '267696.gb', 'lmfdb_label': '267696.gb2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 91, -121], 'min_quad_twist_disc': 156, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '22.2.0.a.1', '66.8.0.a.1', '156.8.0.?', '1716.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '16.506180573920956856310363451', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 16731], [3, 2, 2704], [11, 12, 24336], [13, 98, 1584]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.28450840553349614610285468325', 'prec': 107}, 'szpiro_ratio': 3.7700450301614468, '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, 0, 0, 0, 3, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0], 'aplist': [0, 0, 3, 2, -1, 0, 0, 2, -3, 6, -1, 7, 6, -8, -12, 6, -9, 2, -7, 3, -8, 4, 12, -15, 13], 'class_deg': 3, 'class_size': 2, 'conductor': 267696, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '267696.gb', 'trace_hash': 985825094142404550}
• 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': '0.017975580594071291387069040835', 'prec': 107}, 'conductor': 267696, 'gens': [[298554698, 5700936906106, 629]], 'heights': [{'__RealLiteral__': 0, 'data': '16.506180573920956856310363451', 'prec': 100}], 'lmfdb_label': '267696.gb2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.17912059441365474633427814371', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.826387503599370557614991936704988116', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 267696.gb2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11450901
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '267696.gb2', 'torsion': [3]}
  • id: 11450902
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '267696.gb2', 'torsion': [2]}
  • id: 11450905
    {'degree': 6, 'field': [-13718, -1444, -76, -42, 42, -2, 1], 'lmfdb_label': '267696.gb2', 'torsion': [6]}
  • id: 11450903
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '267696.gb2', 'torsion': [2, 2]}
  • id: 11450904
    {'degree': 6, 'field': [53, -44, 31, 6, -7, -2, 1], 'lmfdb_label': '267696.gb2', 'torsion': [3]}
  • id: 11450906
    {'degree': 12, 'field': [-1353938, -1981564, -1074648, -310024, -63658, 8180, 13000, 3768, 1002, 218, -22, -2, 1], 'lmfdb_label': '267696.gb2', 'torsion': [4]}
  • id: 11450907
    {'degree': 12, 'field': [2809, -2332, 293, -2000, 1596, -536, 271, 38, 30, 2, 11, -2, 1], 'lmfdb_label': '267696.gb2', 'torsion': [3, 3]}
  • id: 11450908
    {'degree': 12, 'field': [232227121, -2956366, 1918255, 2097300, -1099510, 55814, -9667, -8146, 2650, -420, 95, -6, 1], 'lmfdb_label': '267696.gb2', 'torsion': [2, 6]}
  • id: 11450909
    {'degree': 18, 'field': [-17121767, 3780114, 46224204, -6995118, -39804947, 8348678, 8587023, -6279594, 1512685, 420306, -25352, 33792, -35538, -1022, 2021, 162, -69, -6, 1], 'lmfdb_label': '267696.gb2', 'torsion': [9]}
  • id: 11450910
    {'degree': 18, 'field': [2197, 0, 0, 0, 0, 0, -169, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '267696.gb2', 'torsion': [6]}
• 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: 6636020
    {'conductor': 267696, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '267696.gb2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6636021
    {'conductor': 267696, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '267696.gb2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6636022
    {'conductor': 267696, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '267696.gb2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6636023
    {'conductor': 267696, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '267696.gb2', 'prime': 13, '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: 3357697
    {'adelic_gens': [[4, 3, 9, 7], [937, 1326, 39, 547], [1711, 6, 1710, 7], [467, 390, 468, 389], [1, 6, 0, 1], [3, 4, 8, 11], [1572, 1391, 1001, 1143], [857, 0, 0, 1715], [1, 0, 6, 1], [791, 0, 0, 1715]], 'adelic_image': '1716.16.0.?', 'conductor': 267696, 'lmfdb_label': '267696.gb2', 'prime': 0}
  • id: 958144
    {'conductor': 267696, 'elladic_image': '3.4.0.1', 'lmfdb_label': '267696.gb2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 267696.gb does not appear in ec_padic