Elliptic curve data - 72128.bb2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '72128k', 'Clabel': '72128k1', 'Cnumber': 1, 'abc_quality': 0.9038338202074565, 'absD': 177335631872, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 184, 'ainvs': [0, 0, 0, 980, -16464], 'analytic_rank': 1, 'bad_primes': [2, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 72128, 'degree': 55296, 'elladic_images': ['8.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.84340773832824860628295142572', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 27, 'isogeny_degrees': [1, 2], 'jinv': [13500, 23], 'lmfdb_iso': '72128.bb', 'lmfdb_label': '72128.bb2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 5, 6], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.c.1', '46.6.0.a.1', '184.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.3417933326817735853691504594', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1127], [7, 26, 1472], [23, 24, 3136]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0537435769460017921593677746', 'prec': 103}, 'szpiro_ratio': 2.9447905033801525, '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, 0, 0, 0, 0, 0, 0, -3, 0, -6, 0, -2, 0, 0, 0, -6, 0, -6, 0], 'aplist': [0, 0, 0, 0, -6, -2, -6, -6, 1, 6, 0, 8, -6, 2, 8, 8, 4, -4, -2, -8, -6, 12, 10, -10, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 72128, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '72128.bb', 'trace_hash': 1010338424291589416}
• 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': '0.18510806734211658712903356289', 'prec': 103}, 'conductor': 72128, 'gens': [[142, 1728, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.3417933326817735853691504594', 'prec': 100}], 'lmfdb_label': '72128.bb2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.53319815723253413087484976488', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5636760936757811027772741769836994387', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[14, 0, 1]], 'xcoord_integral_points': [14, 142]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [1, 1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [2, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '72128.bb2'}
• ec_torsion_growth •

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

  
  
  • id: 3419252
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '72128.bb2', 'torsion': [2, 2]}
  • id: 3419253
    {'degree': 4, 'field': [-73, 10, -9, -2, 1], 'lmfdb_label': '72128.bb2', 'torsion': [4]}
  • id: 3419256
    {'degree': 8, 'field': [-460992, 0, -32928, 0, -2352, 0, 0, 0, 1], 'lmfdb_label': '72128.bb2', 'torsion': [6]}
  • id: 3419255
    {'degree': 8, 'field': [639, -1614, 1121, -194, 146, -22, -11, -2, 1], 'lmfdb_label': '72128.bb2', 'torsion': [2, 4]}
  • id: 3419254
    {'degree': 8, 'field': [86976, -65280, 19640, -4688, 2132, -268, 61, -2, 1], 'lmfdb_label': '72128.bb2', 'torsion': [2, 4]}
  • id: 3419257
    {'degree': 16, 'field': [8836, 0, 14128, 0, -33928, 0, 13392, 0, -3032, 0, 24, 0, -12, 0, -16, 0, 1], 'lmfdb_label': '72128.bb2', 'torsion': [8]}
  • id: 3419258
    {'degree': 16, 'field': [114310507200, 27265211520, -23875665696, -7277784192, 4897871664, -1545063744, 572144496, -48903504, 12125905, 106504, -60452, 20440, -2618, -392, 76, -8, 1], 'lmfdb_label': '72128.bb2', '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: 1748278
    {'conductor': 72128, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '72128.bb2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1748279
    {'conductor': 72128, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '72128.bb2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1748280
    {'conductor': 72128, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '72128.bb2', 'prime': 23, '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: 2140686
    {'adelic_gens': [[1, 2, 2, 5], [25, 162, 160, 23], [10, 1, 87, 0], [3, 4, 8, 11], [93, 4, 2, 9], [181, 4, 180, 5], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '184.12.0.?', 'conductor': 72128, 'lmfdb_label': '72128.bb2', 'prime': 0}
  • id: 299451
    {'conductor': 72128, 'elladic_image': '8.6.0.1', 'lmfdb_label': '72128.bb2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3700627
    {'lmfdb_iso': '72128.bb', 'p': 11, 'prec': 20, 'unit': 30729350625592378851, 'val': 1}
  • id: 3700633
    {'lmfdb_iso': '72128.bb', 'p': 13, 'prec': 20, 'unit': 351076044785603574949, 'val': 1}
  • id: 3700635
    {'lmfdb_iso': '72128.bb', 'p': 17, 'prec': 20, 'unit': 153015181455722585541386, 'val': 1}
  • id: 3700636
    {'lmfdb_iso': '72128.bb', 'p': 19, 'prec': 20, 'unit': 288814593190164840944439, 'val': 1}
  • id: 3700632
    {'lmfdb_iso': '72128.bb', 'p': 29, 'prec': 20, 'unit': 823137162123938458680928947, 'val': 1}
  • id: 3700628
    {'lmfdb_iso': '72128.bb', 'p': 37, 'prec': 20, 'unit': 8333956522294713169382755436, 'val': 1}
  • id: 3700630
    {'lmfdb_iso': '72128.bb', 'p': 41, 'prec': 20, 'unit': 1803919932663352130988513999556, 'val': 1}
  • id: 3700631
    {'lmfdb_iso': '72128.bb', 'p': 43, 'prec': 20, 'unit': 9329519115068701345519518599349, 'val': 1}
  • id: 3700642
    {'lmfdb_iso': '72128.bb', 'p': 47, 'prec': 20, 'unit': 8751247835757039129817246670059, 'val': 1}
  • id: 3700637
    {'lmfdb_iso': '72128.bb', 'p': 53, 'prec': 20, 'unit': 19524448729713479550970256588268, 'val': 1}
  • id: 3700638
    {'lmfdb_iso': '72128.bb', 'p': 59, 'prec': 20, 'unit': 580533692836457130637898032553990, 'val': 1}
  • id: 3700643
    {'lmfdb_iso': '72128.bb', 'p': 61, 'prec': 20, 'unit': 4829580231748278985618798461600995, 'val': 1}
  • id: 3700626
    {'lmfdb_iso': '72128.bb', 'p': 67, 'prec': 20, 'unit': 19131853911983334286844482841153493, 'val': 1}
  • id: 3700629
    {'lmfdb_iso': '72128.bb', 'p': 71, 'prec': 20, 'unit': 102028328317289872413541138913028124, 'val': 1}
  • id: 3700639
    {'lmfdb_iso': '72128.bb', 'p': 73, 'prec': 20, 'unit': 169077033767549726110004239274299746, 'val': 1}
  • id: 3700634
    {'lmfdb_iso': '72128.bb', 'p': 79, 'prec': 20, 'unit': 1059631282737100999589287832342220602, 'val': 1}
  • id: 3700640
    {'lmfdb_iso': '72128.bb', 'p': 83, 'prec': 20, 'unit': 455278663761727822035794965124181282, 'val': 1}
  • id: 3700641
    {'lmfdb_iso': '72128.bb', 'p': 89, 'prec': 20, 'unit': 8214992401161144338250742651229822377, 'val': 1}
  • id: 3700625
    {'lmfdb_iso': '72128.bb', 'p': 97, 'prec': 20, 'unit': 38612164618260467024182139644212475561, 'val': 1}