Elliptic curve data - 8190.bg2

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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': '8190bc', 'Clabel': '8190bc1', 'Cnumber': 1, 'abc_quality': 0.9748403597757912, 'absD': 261660672000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 5460, 'ainvs': [1, -1, 1, -3383, -70769], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 8190, 'degree': 12288, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.94290110631172087278872709731', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2], 'jinv': [158542456758867, 9691136000], 'lmfdb_iso': '8190.bg', 'lmfdb_label': '8190.bg2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -30444, 1941200], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '156.6.0.?', '210.6.0.?', '1820.6.0.?', '5460.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.62508010989734615833983513744', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 105], [3, 6, 182], [5, 6, 1638], [7, 8, 1170], [13, 14, 630]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.66824803414469344993991578808', 'prec': 103}, 'szpiro_ratio': 3.9944736288677265, '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, 1, 0, 1, -1, 0, 1, 1, 0, -1, 2, 0, -1, 1, 0, 1, 4, 0, -4, -1], 'aplist': [1, 0, -1, 1, 2, -1, 4, -4, -8, -4, -8, -8, -6, 6, -2, -2, 0, 10, -16, -6, -2, 4, 2, 10, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 8190, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '8190.bg', 'trace_hash': 1950405608056621891}
• 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': '0.15170730908271287024591470148', 'prec': 103}, 'conductor': 8190, 'gens': [[-37, 70, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.62508010989734615833983513744', 'prec': 103}], 'lmfdb_label': '8190.bg2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.62840897745341723331783122726', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.2848952429929754945420224750125804331', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[67, -34, 1]], 'xcoord_integral_points': [-37, -29, 67, 131, 223]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 0], '7': [4, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 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': '8190.bg2'}
• ec_torsion_growth •

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

  
  
  • id: 428249
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '8190.bg2', 'torsion': [2, 2]}
  • id: 428250
    {'degree': 4, 'field': [16, -8, -30, -2, 1], 'lmfdb_label': '8190.bg2', 'torsion': [4]}
  • id: 428252
    {'degree': 8, 'field': [-62039, -126556, -54872, 6164, 6118, 236, -152, -4, 1], 'lmfdb_label': '8190.bg2', 'torsion': [2, 4]}
  • id: 428253
    {'degree': 8, 'field': [-12, 0, 3, 0, 3, 0, -15, 0, 1], 'lmfdb_label': '8190.bg2', 'torsion': [6]}
  • id: 428251
    {'degree': 8, 'field': [9216, 0, 5148, 0, -681, 0, 12, 0, 1], 'lmfdb_label': '8190.bg2', 'torsion': [2, 4]}
  • id: 428255
    {'degree': 16, 'field': [11851030, 18840130, -29043486, -7549627, 11607326, 1733811, -2073221, -298856, 307911, 42136, -40976, 2805, 1700, -157, -45, -2, 1], 'lmfdb_label': '8190.bg2', 'torsion': [2, 6]}
  • id: 428254
    {'degree': 16, 'field': [64828798225, 0, -116581505432, 0, 24527021612, 0, -1913092808, 0, 70522870, 0, -1431400, 0, 18764, 0, -184, 0, 1], 'lmfdb_label': '8190.bg2', 'torsion': [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: 170069
    {'conductor': 8190, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '8190.bg2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 170070
    {'conductor': 8190, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '8190.bg2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 170071
    {'conductor': 8190, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '8190.bg2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 170072
    {'conductor': 8190, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8190.bg2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 170073
    {'conductor': 8190, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8190.bg2', 'prime': 13, 'reduction_type': -1, '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: 1718018
    {'adelic_gens': [[3644, 1, 1819, 0], [1, 2, 2, 5], [1, 4, 0, 1], [4682, 1, 3119, 0], [1369, 4096, 1364, 4095], [1094, 1, 2183, 0], [1, 0, 4, 1], [3, 4, 8, 11], [5457, 4, 5456, 5], [4201, 4, 2942, 9]], 'adelic_image': '5460.12.0.?', 'conductor': 8190, 'lmfdb_label': '8190.bg2', 'prime': 0}
  • id: 40064
    {'conductor': 8190, 'elladic_image': '2.3.0.1', 'lmfdb_label': '8190.bg2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 337242
    {'lmfdb_iso': '8190.bg', 'p': 11, 'prec': 20, 'unit': 18614627170165862589, 'val': 1}
  • id: 337243
    {'lmfdb_iso': '8190.bg', 'p': 17, 'prec': 20, 'unit': 233133595573543335859640, 'val': 1}
  • id: 337244
    {'lmfdb_iso': '8190.bg', 'p': 19, 'prec': 20, 'unit': 1717879320632638266373629, 'val': 1}
  • id: 337247
    {'lmfdb_iso': '8190.bg', 'p': 23, 'prec': 20, 'unit': 67600697684887695820661754, 'val': 1}
  • id: 337240
    {'lmfdb_iso': '8190.bg', 'p': 29, 'prec': 20, 'unit': 1311500660291499847446949326, 'val': 1}
  • id: 337251
    {'lmfdb_iso': '8190.bg', 'p': 31, 'prec': 20, 'unit': 2386741049745551402240520934, 'val': 1}
  • id: 337236
    {'lmfdb_iso': '8190.bg', 'p': 37, 'prec': 20, 'unit': 549340080447312913355617417341, 'val': 1}
  • id: 337238
    {'lmfdb_iso': '8190.bg', 'p': 41, 'prec': 20, 'unit': 3452297584027738851476618821942, 'val': 1}
  • id: 337239
    {'lmfdb_iso': '8190.bg', 'p': 43, 'prec': 20, 'unit': 331306689353445154868191057583, 'val': 1}
  • id: 337241
    {'lmfdb_iso': '8190.bg', 'p': 47, 'prec': 20, 'unit': 3095506791588623977006819956448, 'val': 1}
  • id: 337245
    {'lmfdb_iso': '8190.bg', 'p': 53, 'prec': 20, 'unit': 152374495970666444595467086297472, 'val': 1}
  • id: 337250
    {'lmfdb_iso': '8190.bg', 'p': 61, 'prec': 20, 'unit': 7936147911453761676720281565351962, 'val': 1}
  • id: 337235
    {'lmfdb_iso': '8190.bg', 'p': 67, 'prec': 20, 'unit': 10190362216977297946917341983728269, 'val': 1}
  • id: 337237
    {'lmfdb_iso': '8190.bg', 'p': 71, 'prec': 20, 'unit': 91797028307302764317698269979920913, 'val': 1}
  • id: 337246
    {'lmfdb_iso': '8190.bg', 'p': 73, 'prec': 20, 'unit': 194737344634971565612453257031679798, 'val': 1}
  • id: 337249
    {'lmfdb_iso': '8190.bg', 'p': 79, 'prec': 20, 'unit': 3259963421487459392962933794166276, 'val': 1}
  • id: 337234
    {'lmfdb_iso': '8190.bg', 'p': 83, 'prec': 20, 'unit': 34352634838383808855745633204843841, 'val': 2}
  • id: 337248
    {'lmfdb_iso': '8190.bg', 'p': 89, 'prec': 20, 'unit': 7054026924934290365441572389715894852, 'val': 1}
  • id: 337233
    {'lmfdb_iso': '8190.bg', 'p': 97, 'prec': 20, 'unit': 48501008632067518148632298595250914070, 'val': 1}