Elliptic curve data - 72128.bd3

Formats: - HTML - YAML - JSON - 2024-05-03T15:45:52.429189

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '72128b', 'Clabel': '72128b1', 'Cnumber': 1, 'abc_quality': 0.7946684976008203, 'absD': 4965397692416, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1288, 'ainvs': [0, 0, 0, -11564, 466480], 'analytic_rank': 0, 'bad_primes': [2, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 72128, 'degree': 122880, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2138948176141840451325122297', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 29, 'isogeny_degrees': [1, 2, 4], 'jinv': [5545233, 161], 'lmfdb_iso': '72128.bd', 'lmfdb_label': '72128.bd3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -4, -2], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.4', '56.24.0-56.z.1.11', '184.24.0.?', '322.6.0.?', '644.12.0.?', '1288.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.79878102775339057154601232421', 'prec': 107}, 'szpiro_ratio': 3.547278599061871, '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, 2, 0, 0, 0, -3, 0, -4, 0, 6, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, 2, 0, -4, 6, 2, 4, -1, 2, 4, 2, 6, -12, 12, 10, 0, 2, -12, 8, 14, 8, -4, -6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 72128, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '72128.bd', 'trace_hash': 2092223911921837990}
• 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': '0.088231641315584293039344219518', 'prec': 107}, 'conductor': 72128, 'gens': [], 'heights': [], 'lmfdb_label': '72128.bd3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.76522818395723206739469841883', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0609127358289282695787936753400710301', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[70, 0, 1]], 'xcoord_integral_points': [70]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '7': 'a', '23': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '72128.bd3'}
• ec_torsion_growth •

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

  
  
  • id: 3419115
    {'degree': 2, 'field': [-322, 0, 1], 'lmfdb_label': '72128.bd3', 'torsion': [4]}
  • id: 3419114
    {'degree': 2, 'field': [-40, -1, 1], 'lmfdb_label': '72128.bd3', 'torsion': [2, 2]}
  • id: 3419116
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '72128.bd3', 'torsion': [4]}
  • id: 3419117
    {'degree': 4, 'field': [1442, 84, -83, -2, 1], 'lmfdb_label': '72128.bd3', 'torsion': [2, 4]}
  • id: 3419121
    {'degree': 8, 'field': [-2352, 0, 504, 0, 168, 0, 0, 0, 1], 'lmfdb_label': '72128.bd3', 'torsion': [6]}
  • id: 3419120
    {'degree': 8, 'field': [497, -224, 266, -84, 43, -4, 6, -4, 1], 'lmfdb_label': '72128.bd3', 'torsion': [8]}
  • id: 3419119
    {'degree': 8, 'field': [784, 0, -3472, 0, 844, 0, -60, 0, 1], 'lmfdb_label': '72128.bd3', 'torsion': [8]}
  • id: 3419118
    {'degree': 8, 'field': [399512, -454928, 203484, -40952, 1638, 772, -111, -2, 1], 'lmfdb_label': '72128.bd3', 'torsion': [2, 4]}
  • id: 3419126
    {'degree': 16, 'field': [-4822247, -8948048, -3701298, -1026046, -2216875, -689832, 591901, 155074, -18498, 26416, -6227, 1242, -436, 98, 24, -8, 1], 'lmfdb_label': '72128.bd3', 'torsion': [12]}
  • id: 3419127
    {'degree': 16, 'field': [1033, -4972, -7594, 8370, 8363, -7232, -407, 1074, -242, -996, 1531, -610, -64, 66, 8, -8, 1], 'lmfdb_label': '72128.bd3', 'torsion': [12]}
  • id: 3419124
    {'degree': 16, 'field': [1225, 0, -22162, 0, 61693, 0, -64654, 0, 31524, 0, -7746, 0, 957, 0, -54, 0, 1], 'lmfdb_label': '72128.bd3', 'torsion': [2, 8]}
  • id: 3419125
    {'degree': 16, 'field': [2304, 0, 67968, 0, -76032, 0, 33984, 0, 480, 0, -1416, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '72128.bd3', 'torsion': [2, 6]}
  • id: 3419123
    {'degree': 16, 'field': [9025, 0, -11782, 0, 29773, 0, -27754, 0, 10524, 0, -1326, 0, -3, 0, 6, 0, 1], 'lmfdb_label': '72128.bd3', 'torsion': [2, 8]}
  • id: 3419122
    {'degree': 16, 'field': [87578116096, 0, 0, 0, 140177664, 0, 0, 0, -197600, 0, 0, 0, 8289, 0, 0, 0, 1], 'lmfdb_label': '72128.bd3', 'torsion': [4, 4]}
• 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: 1748227
    {'conductor': 72128, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '72128.bd3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1748228
    {'conductor': 72128, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '72128.bd3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1748229
    {'conductor': 72128, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '72128.bd3', '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: 2140691
    {'adelic_gens': [[1, 0, 8, 1], [1096, 1285, 363, 1286], [1281, 8, 1280, 9], [1, 8, 0, 1], [1, 4, 4, 17], [169, 164, 166, 807], [157, 158, 470, 1117], [1124, 1, 23, 6], [7, 6, 1282, 1283]], 'adelic_image': '1288.48.0.?', 'conductor': 72128, 'lmfdb_label': '72128.bd3', 'prime': 0}
  • id: 299456
    {'conductor': 72128, 'elladic_image': '8.12.0.8', 'lmfdb_label': '72128.bd3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 72128.bd does not appear in ec_padic