Elliptic curve data - 12138.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': '12138w', 'Clabel': '12138w3', 'Cnumber': 3, 'abc_quality': 1.07814467781823, 'absD': 13335258025968770331349056, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 136, 'ainvs': [1, 0, 0, -248263722, -1495363594140], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 12138, 'degree': 4423680, 'elladic_images': ['8.96.0.110'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6491620510711531479509583693', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2, 4], 'jinv': [70108386184777836280897, 552468975892674624], 'lmfdb_iso': '12138.ba', 'lmfdb_label': '12138.ba2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -859044, -304722459], 'min_quad_twist_disc': 17, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.96.0-8.f.1.2', '68.24.0-4.b.1.1', '136.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7919302403351336048582581719', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 2023], [7, 8, 1734], [17, 162, 42]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2325553790430451078261910604', 'prec': 100}, 'szpiro_ratio': 7.401413933680872, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 1, 1, 2, 1, -1, 1, 1, 2, -4, 1, -2, -1, 2, 1, 0, 1, 4, 2], 'aplist': [1, 1, 2, -1, -4, -2, 0, 4, -8, -6, 0, 2, -10, -4, 0, 6, -4, -6, -12, 8, 6, 0, -12, -6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 12138, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '12138.ba', 'trace_hash': 728659878416027624}
• 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': '0.00067667185838062200211423969509', 'prec': 113}, 'conductor': 12138, 'gens': [[-9198, 104634, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.7919302403351336048582581719', 'prec': 100}], 'lmfdb_label': '12138.ba2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.038052010781995546916856521541', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.7524438962465447853615523107910739147', 'prec': 130}, 'tamagawa_product': 768, 'torsion_generators': [[-8476, 4238, 1], [18180, -9090, 1]], 'xcoord_integral_points': [-9198, -8476, 18180]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [7, 2], '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '12138.ba2'}
• ec_torsion_growth •

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

  
  
  • id: 626380
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '12138.ba2', 'torsion': [2, 8]}
  • id: 626382
    {'degree': 4, 'field': [2, 12, -11, -2, 1], 'lmfdb_label': '12138.ba2', 'torsion': [2, 4]}
  • id: 626381
    {'degree': 4, 'field': [38, 4, -3, -2, 1], 'lmfdb_label': '12138.ba2', 'torsion': [2, 4]}
  • id: 626387
    {'degree': 8, 'field': [-17033, 8273, 595, -1400, 1592, -92, 73, -1, 1], 'lmfdb_label': '12138.ba2', 'torsion': [2, 6]}
  • id: 626386
    {'degree': 8, 'field': [256, 0, -288, 0, 130, 0, -18, 0, 1], 'lmfdb_label': '12138.ba2', 'torsion': [2, 16]}
  • id: 626383
    {'degree': 8, 'field': [256, 0, 0, 0, 49, 0, 0, 0, 1], 'lmfdb_label': '12138.ba2', 'torsion': [4, 8]}
  • id: 626385
    {'degree': 8, 'field': [5058, 5352, -5452, 216, -147, 44, -10, -4, 1], 'lmfdb_label': '12138.ba2', 'torsion': [2, 8]}
  • id: 626384
    {'degree': 8, 'field': [14662, -4840, 5132, -568, 245, 44, -10, -4, 1], 'lmfdb_label': '12138.ba2', 'torsion': [2, 8]}
  • id: 626389
    {'degree': 16, 'field': [589824, 0, 69264, 0, -142740, 0, 29849, 0, 16154, 0, 3929, 0, 541, 0, 34, 0, 1], 'lmfdb_label': '12138.ba2', 'torsion': [2, 24]}
  • id: 626388
    {'degree': 16, 'field': [4285458, 7255416, -1975252, 1775368, 6958058, -2771832, 2005296, -527744, 432883, -54152, 55464, -2520, 3378, -56, 92, 0, 1], 'lmfdb_label': '12138.ba2', 'torsion': [8, 8]}
• 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: 261825
    {'conductor': 12138, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '12138.ba2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 261826
    {'conductor': 12138, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '12138.ba2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 261827
    {'conductor': 12138, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12138.ba2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 261828
    {'conductor': 12138, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '12138.ba2', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1744411
    {'adelic_gens': [[31, 128, 124, 103], [7, 40, 22, 121], [3, 106, 98, 131], [1, 0, 8, 1], [129, 8, 128, 9], [5, 4, 132, 133], [1, 8, 0, 1]], 'adelic_image': '136.192.1.?', 'conductor': 12138, 'lmfdb_label': '12138.ba2', 'prime': 0}
  • id: 57841
    {'conductor': 12138, 'elladic_image': '8.96.0.110', 'lmfdb_label': '12138.ba2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 529467
    {'lmfdb_iso': '12138.ba', 'p': 5, 'prec': 20, 'unit': 5872449845983, 'val': 1}
  • id: 529473
    {'lmfdb_iso': '12138.ba', 'p': 11, 'prec': 20, 'unit': 51063433622685107501, 'val': 1}
  • id: 529471
    {'lmfdb_iso': '12138.ba', 'p': 13, 'prec': 20, 'unit': 1320893866353322105760, 'val': 1}
  • id: 529474
    {'lmfdb_iso': '12138.ba', 'p': 19, 'prec': 20, 'unit': 158103365200493991106610, 'val': 1}
  • id: 529477
    {'lmfdb_iso': '12138.ba', 'p': 23, 'prec': 20, 'unit': 24032546495920510194450506, 'val': 1}
  • id: 529472
    {'lmfdb_iso': '12138.ba', 'p': 29, 'prec': 20, 'unit': 3144352717997778615090221429, 'val': 1}
  • id: 529481
    {'lmfdb_iso': '12138.ba', 'p': 37, 'prec': 20, 'unit': 539783097986254318594777956687, 'val': 1}
  • id: 529469
    {'lmfdb_iso': '12138.ba', 'p': 41, 'prec': 20, 'unit': 3577812160141769544446545985162, 'val': 1}
  • id: 529470
    {'lmfdb_iso': '12138.ba', 'p': 43, 'prec': 20, 'unit': 5799665645553987656585285881302, 'val': 1}
  • id: 529475
    {'lmfdb_iso': '12138.ba', 'p': 53, 'prec': 20, 'unit': 38968770562796453592238044494662, 'val': 1}
  • id: 529479
    {'lmfdb_iso': '12138.ba', 'p': 59, 'prec': 20, 'unit': 4144583501427782820165520241814484, 'val': 1}
  • id: 529480
    {'lmfdb_iso': '12138.ba', 'p': 61, 'prec': 20, 'unit': 4832172556220908159416246987431900, 'val': 1}
  • id: 529466
    {'lmfdb_iso': '12138.ba', 'p': 67, 'prec': 20, 'unit': 42779384278852903038133558214663369, 'val': 1}
  • id: 529468
    {'lmfdb_iso': '12138.ba', 'p': 71, 'prec': 20, 'unit': 8405542939582461370246466947181409, 'val': 1}
  • id: 529476
    {'lmfdb_iso': '12138.ba', 'p': 73, 'prec': 20, 'unit': 63039363459258388321209499799925860, 'val': 1}
  • id: 529465
    {'lmfdb_iso': '12138.ba', 'p': 83, 'prec': 20, 'unit': 1787982280738249634645126873876099928, 'val': 1}
  • id: 529478
    {'lmfdb_iso': '12138.ba', 'p': 89, 'prec': 20, 'unit': 9606488007479662753716786322793566062, 'val': 1}
  • id: 529464
    {'lmfdb_iso': '12138.ba', 'p': 97, 'prec': 20, 'unit': 44493923432353393605338066452128065344, 'val': 1}