Elliptic curve data - 172062.bi1

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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': '172062h', 'Clabel': '172062h1', 'Cnumber': 1, 'abc_quality': 1.0291197136249353, 'absD': 107928298368, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 632, 'ainvs': [1, -1, 1, 340, 15535], 'analytic_rank': 2, 'bad_primes': [2, 3, 11, 79], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 172062, 'degree': 215040, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.79724306847695733997402853871', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 34, 'isogeny_degrees': [1], 'jinv': [408375, 10112], 'lmfdb_iso': '172062.bi', 'lmfdb_label': '172062.bi1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 38, -588], 'min_quad_twist_disc': -3, 'modell_images': [], 'modm_images': ['632.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 20, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.28430914534015550547205416549', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 86031], [3, 6, 19118], [7, 2, 86031], [11, 52, 1422], [79, 80, 2178]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.55136150012322102041090860574', 'prec': 107}, 'szpiro_ratio': 2.723694941459487, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, -2, 1, 0, 0, 0, 0, 4, -2, 0, 1, -8, 0, -8, 0], 'aplist': [1, 0, 0, -2, 0, 4, -8, -8, 1, 3, 0, 7, -12, -11, -6, -5, -9, -11, -16, 10, -11, -1, -4, -5, -9], 'class_deg': 1, 'class_size': 1, 'conductor': 172062, 'isogeny_matrix': [[1]], 'lmfdb_iso': '172062.bi', 'trace_hash': 1221001404721323334}
• 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': '0.20301282249119546879310151047', 'prec': 103}, 'conductor': 172062, 'gens': [[25, 185, 1], [157, 1901, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.22492422039008151899219414620', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.2745820487958529351626750943', 'prec': 100}], 'lmfdb_label': '172062.bi1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.79325061193498487952075691689', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '18.944385895662436402471779757189452768', 'prec': 130}, 'tamagawa_product': 84, 'torsion_generators': [], 'xcoord_integral_points': [-19, -5, 1, 7, 25, 91, 157, 311, 1645, 1885]}
• lmfdb_label 172062.bi1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7639863
    {'degree': 3, 'field': [-317, -7, -1, 1], 'lmfdb_label': '172062.bi1', 'torsion': [2]}
  • id: 7639864
    {'degree': 6, 'field': [31608, 13864, 3562, 664, 91, -2, 1], 'lmfdb_label': '172062.bi1', 'torsion': [2, 2]}
  • id: 7639865
    {'degree': 8, 'field': [-326, 1112, -1088, -49, 28, -7, 7, -4, 1], 'lmfdb_label': '172062.bi1', 'torsion': [3]}
  • id: 7639866
    {'degree': 12, 'field': [-802128339, 714997368, -211706946, 21601728, -509913, -550800, 189396, 27648, -5621, -168, 14, 0, 1], 'lmfdb_label': '172062.bi1', 'torsion': [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: 4256265
    {'conductor': 172062, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '172062.bi1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 4256266
    {'conductor': 172062, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '172062.bi1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4256267
    {'conductor': 172062, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '172062.bi1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 4256268
    {'conductor': 172062, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '172062.bi1', 'prime': 79, '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

  
  {'adelic_gens': [[1, 1, 631, 0], [161, 2, 161, 3], [631, 2, 630, 3], [317, 2, 317, 3], [1, 0, 2, 1], [1, 2, 0, 1], [159, 2, 0, 1]], 'adelic_image': '632.2.0.?', 'conductor': 172062, 'lmfdb_label': '172062.bi1', 'prime': 0}
• lmfdb_iso 172062.bi does not appear in ec_padic