Elliptic curve data - 912.b4

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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': '912g', 'Clabel': '912g4', 'Cnumber': 4, 'abc_quality': 0.9747386105988611, 'absD': 1601384448, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, -1, 0, 136, -1872], 'analytic_rank': 1, 'bad_primes': [2, 3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 912, 'degree': 384, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.44813851835711921574779975159', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [67419143, 390963], 'lmfdb_iso': '912.b', 'lmfdb_label': '912.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 8, 29], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '6.6.0.a.1', '12.24.0-12.g.1.2', '152.24.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.6018939134308192452519184243', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 4, 304], [19, 20, 48]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.24500866220282609366943236987', 'prec': 107}, 'szpiro_ratio': 4.187973963278707, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, -2, 0, 0, 0, 1, 0, 0, 0, 6, 0, 2, 0, -6, 0, 1, 0], 'aplist': [0, -1, -2, 0, 0, 6, -6, 1, -4, 2, -8, -10, -2, 4, -12, -6, 12, -2, 4, 0, 10, 0, -16, -2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 912, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '912.b', 'trace_hash': 533216063535067348}
• 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': '0.40808612477717129413820357150', 'prec': 103}, 'conductor': 912, 'gens': [[18, 78, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.6018939134308192452519184243', 'prec': 100}], 'lmfdb_label': '912.b4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.75202298051859802360121969732', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9566840157714437537809644231301686452', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[28, 152, 1]], 'xcoord_integral_points': [9, 18, 28, 484]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [3, 0], '7': [1, 5, 0], '11': [1, 1, 0], '13': [3, 0], '17': [1, 0], '19': [2, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '912.b4'}
• ec_torsion_growth •

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

  
  
  • id: 43810
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '912.b4', 'torsion': [2, 4]}
  • id: 43811
    {'degree': 4, 'field': [-3, 0, -8, 0, 1], 'lmfdb_label': '912.b4', 'torsion': [8]}
  • id: 43815
    {'degree': 8, 'field': [-3, 0, -11, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '912.b4', 'torsion': [12]}
  • id: 43812
    {'degree': 8, 'field': [1, -4, 8, -10, 7, -2, 2, -2, 1], 'lmfdb_label': '912.b4', 'torsion': [4, 4]}
  • id: 43814
    {'degree': 8, 'field': [9, 0, -24, 0, 67, 0, 8, 0, 1], 'lmfdb_label': '912.b4', 'torsion': [2, 8]}
  • id: 43813
    {'degree': 8, 'field': [2304, 0, 288, 0, 84, 0, -6, 0, 1], 'lmfdb_label': '912.b4', 'torsion': [2, 8]}
  • id: 43817
    {'degree': 16, 'field': [9, 0, -33, 0, 103, 0, -66, 0, 39, 0, -22, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '912.b4', 'torsion': [2, 12]}
  • id: 43816
    {'degree': 16, 'field': [81, 0, 864, 0, 612, 0, -648, 0, 459, 0, 216, 0, 68, 0, -32, 0, 1], 'lmfdb_label': '912.b4', 'torsion': [16]}
• 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: 12331
    {'conductor': 912, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '912.b4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 12332
    {'conductor': 912, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '912.b4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12333
    {'conductor': 912, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '912.b4', 'prime': 19, 'reduction_type': 1, '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: 1670340
    {'adelic_gens': [[277, 284, 238, 51], [7, 6, 450, 451], [97, 8, 388, 33], [1, 0, 8, 1], [449, 8, 448, 9], [403, 402, 298, 67], [160, 3, 157, 2], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '456.48.0.?', 'conductor': 912, 'lmfdb_label': '912.b4', 'prime': 0}
  • id: 4266
    {'conductor': 912, 'elladic_image': '4.12.0.7', 'lmfdb_label': '912.b4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 19824
    {'lmfdb_iso': '912.b', 'p': 5, 'prec': 20, 'unit': 594306628214, 'val': 3}
  • id: 19829
    {'lmfdb_iso': '912.b', 'p': 13, 'prec': 20, 'unit': 10079255436344950647, 'val': 2}
  • id: 19831
    {'lmfdb_iso': '912.b', 'p': 17, 'prec': 20, 'unit': 9743168496651584535083, 'val': 1}
  • id: 19835
    {'lmfdb_iso': '912.b', 'p': 23, 'prec': 20, 'unit': 72325998281911738157998860, 'val': 1}
  • id: 19828
    {'lmfdb_iso': '912.b', 'p': 29, 'prec': 20, 'unit': 4280963881037479817669070355, 'val': 1}
  • id: 19825
    {'lmfdb_iso': '912.b', 'p': 31, 'prec': 20, 'unit': 15975241345922943904386170643, 'val': 1}
  • id: 19839
    {'lmfdb_iso': '912.b', 'p': 37, 'prec': 20, 'unit': 413110138472948509961824021958, 'val': 1}
  • id: 19826
    {'lmfdb_iso': '912.b', 'p': 41, 'prec': 20, 'unit': 1578562254486023014006033906231, 'val': 1}
  • id: 19827
    {'lmfdb_iso': '912.b', 'p': 43, 'prec': 20, 'unit': 9343907059388428139322501378105, 'val': 1}
  • id: 19830
    {'lmfdb_iso': '912.b', 'p': 47, 'prec': 20, 'unit': 32482468547130912559054670515566, 'val': 1}
  • id: 19833
    {'lmfdb_iso': '912.b', 'p': 53, 'prec': 20, 'unit': 537123319550951089452200748944569, 'val': 1}
  • id: 19837
    {'lmfdb_iso': '912.b', 'p': 59, 'prec': 20, 'unit': 2638573714631780780317251097970554, 'val': 1}
  • id: 19838
    {'lmfdb_iso': '912.b', 'p': 61, 'prec': 20, 'unit': 1451282075123468873458145553733343, 'val': 1}
  • id: 19823
    {'lmfdb_iso': '912.b', 'p': 67, 'prec': 20, 'unit': 30162670498116543687958175886790633, 'val': 1}
  • id: 19834
    {'lmfdb_iso': '912.b', 'p': 73, 'prec': 20, 'unit': 115727764606211097765511129610232826, 'val': 1}
  • id: 19832
    {'lmfdb_iso': '912.b', 'p': 83, 'prec': 20, 'unit': 1783777105194779346216725534249896423, 'val': 1}
  • id: 19836
    {'lmfdb_iso': '912.b', 'p': 89, 'prec': 20, 'unit': 10759220141170901378008041442887154210, 'val': 1}
  • id: 19822
    {'lmfdb_iso': '912.b', 'p': 97, 'prec': 20, 'unit': 27502810699347716195892852317627882066, 'val': 1}