Elliptic curve data - 8112.ba2

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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': '8112r', 'Clabel': '8112r1', 'Cnumber': 1, 'abc_quality': 0.9425741828608891, 'absD': 1527047909712, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 1, 0, -7323, 231336], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 8112, 'degree': 9984, 'elladic_images': ['4.6.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1087982124501417696587959960', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2], 'jinv': [256000, 9], 'lmfdb_iso': '8112.ba', 'lmfdb_label': '8112.ba2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -43, -92], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.d.1', '24.12.0.by.1', '26.6.0.b.1', '52.24.0-52.i.1.1', '312.48.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.5217023542912626461026597219', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 13], [3, 4, 2704], [13, 62, 48]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0459628658326592188537302923', 'prec': 103}, 'szpiro_ratio': 4.256153895608417, '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, 0, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 0, 0, -2, 0, -6, 0], 'aplist': [0, 1, 0, 2, 2, 0, -2, -6, 0, -2, -2, -4, -4, -4, -10, -10, -6, -2, 2, -6, 16, -8, 14, -12, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 8112, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '8112.ba', 'trace_hash': 1356684012408466399}
• 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': '0.10887047295285812743162592512', 'prec': 103}, 'conductor': 8112, 'gens': [[1404, 2358, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '6.5217023542912626461026597219', 'prec': 100}], 'lmfdb_label': '8112.ba2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.84199703076253486106870214398', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.4912540178302763016292962104660225340', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[56, 0, 1]], 'xcoord_integral_points': [56]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 3, 0], '7': [1, 0], '11': [1, 0], '13': 'a', '17': [1, 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, 0]}, 'iwp0': 0, 'lmfdb_label': '8112.ba2'}
• ec_torsion_growth •

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

  
  
  • id: 423938
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '8112.ba2', 'torsion': [2, 2]}
  • id: 423939
    {'degree': 4, 'field': [13, 0, -13, 0, 1], 'lmfdb_label': '8112.ba2', 'torsion': [2, 4]}
  • id: 423941
    {'degree': 8, 'field': [-507, 0, -676, 0, -78, 0, 0, 0, 1], 'lmfdb_label': '8112.ba2', 'torsion': [6]}
  • id: 423940
    {'degree': 8, 'field': [729, 0, -189, 0, 72, 0, -6, 0, 1], 'lmfdb_label': '8112.ba2', 'torsion': [2, 4]}
  • id: 423943
    {'degree': 16, 'field': [81, 54, -360, -582, 163, 1854, 1032, -1764, -1391, 128, 204, 82, 71, 6, -16, -2, 1], 'lmfdb_label': '8112.ba2', 'torsion': [2, 8]}
  • id: 423942
    {'degree': 16, 'field': [33489, 8784, 1152, 20682, -12449, 3124, 7634, -5464, 1857, 308, -374, 160, -21, -14, 8, -4, 1], 'lmfdb_label': '8112.ba2', 'torsion': [4, 4]}
  • id: 423944
    {'degree': 16, 'field': [10278225, 5375160, -4601268, -1492680, 587106, 255320, -204412, 126464, -61321, 19136, -3484, 208, -338, 112, 4, -8, 1], 'lmfdb_label': '8112.ba2', 'torsion': [2, 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: 168159
    {'conductor': 8112, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '8112.ba2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 168160
    {'conductor': 8112, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8112.ba2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 168161
    {'conductor': 8112, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '8112.ba2', '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: 1717528
    {'adelic_gens': [[1, 0, 8, 1], [22, 305, 259, 66], [1, 8, 0, 1], [7, 2, 266, 299], [1, 4, 4, 17], [309, 230, 304, 67], [3, 82, 86, 11], [305, 8, 304, 9], [209, 8, 212, 33]], 'adelic_image': '312.48.1.?', 'conductor': 8112, 'lmfdb_label': '8112.ba2', 'prime': 0}
  • id: 39690
    {'conductor': 8112, 'elladic_image': '4.6.0.2', 'lmfdb_label': '8112.ba2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 333904
    {'lmfdb_iso': '8112.ba', 'p': 7, 'prec': 20, 'unit': 6579360460808979, 'val': 1}
  • id: 333909
    {'lmfdb_iso': '8112.ba', 'p': 11, 'prec': 20, 'unit': 29051581684170328344, 'val': 1}
  • id: 333910
    {'lmfdb_iso': '8112.ba', 'p': 17, 'prec': 20, 'unit': 237227880398224343222484, 'val': 1}
  • id: 333911
    {'lmfdb_iso': '8112.ba', 'p': 19, 'prec': 20, 'unit': 1458653558639367065413459, 'val': 1}
  • id: 333907
    {'lmfdb_iso': '8112.ba', 'p': 29, 'prec': 20, 'unit': 2017966817546706017202968330, 'val': 1}
  • id: 333919
    {'lmfdb_iso': '8112.ba', 'p': 31, 'prec': 20, 'unit': 10967596170190231422264518910, 'val': 1}
  • id: 333903
    {'lmfdb_iso': '8112.ba', 'p': 37, 'prec': 20, 'unit': 559248999707199685047774839711, 'val': 1}
  • id: 333905
    {'lmfdb_iso': '8112.ba', 'p': 41, 'prec': 20, 'unit': 2448243936197826869576939917795, 'val': 1}
  • id: 333906
    {'lmfdb_iso': '8112.ba', 'p': 43, 'prec': 20, 'unit': 3237896963434829773044871268930, 'val': 1}
  • id: 333917
    {'lmfdb_iso': '8112.ba', 'p': 47, 'prec': 20, 'unit': 169146891845669236010783526492, 'val': 1}
  • id: 333912
    {'lmfdb_iso': '8112.ba', 'p': 53, 'prec': 20, 'unit': 191349650654456992002843997000247, 'val': 1}
  • id: 333913
    {'lmfdb_iso': '8112.ba', 'p': 59, 'prec': 20, 'unit': 774145833127331924000436929145910, 'val': 1}
  • id: 333918
    {'lmfdb_iso': '8112.ba', 'p': 61, 'prec': 20, 'unit': 101018098501189483203065153117422, 'val': 1}
  • id: 333902
    {'lmfdb_iso': '8112.ba', 'p': 67, 'prec': 20, 'unit': 28509023005954442099296389802642494, 'val': 1}
  • id: 333916
    {'lmfdb_iso': '8112.ba', 'p': 71, 'prec': 20, 'unit': 45832859255843972294537059968966769, 'val': 1}
  • id: 333914
    {'lmfdb_iso': '8112.ba', 'p': 73, 'prec': 20, 'unit': 247322216349175423824369057484450318, 'val': 1}
  • id: 333908
    {'lmfdb_iso': '8112.ba', 'p': 79, 'prec': 20, 'unit': 230070427787749978238215592990082093, 'val': 1}
  • id: 333901
    {'lmfdb_iso': '8112.ba', 'p': 83, 'prec': 20, 'unit': 2396032276051541926547780560606484368, 'val': 1}
  • id: 333915
    {'lmfdb_iso': '8112.ba', 'p': 89, 'prec': 20, 'unit': 7387706972415124273764815550633875610, 'val': 1}
  • id: 333900
    {'lmfdb_iso': '8112.ba', 'p': 97, 'prec': 20, 'unit': 37407289398705459572683066735185609130, 'val': 1}