Elliptic curve data - 85176.b2

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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': '85176y', 'Clabel': '85176y1', 'Cnumber': 1, 'abc_quality': 1.0348177494302118, 'absD': 25222355278848, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 56, 'ainvs': [0, 0, 0, -507, 241670], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 85176, 'degree': 225792, 'elladic_images': ['8.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2505383972247079103044254391', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [-4, 7], 'lmfdb_iso': '85176.b', 'lmfdb_label': '85176.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 0, -4], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.c.1', '14.6.0.b.1', '56.12.0.n.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 10647], [3, 6, 9464], [7, 8, 12168], [13, 86, 504]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1588650763067363946009676680', 'prec': 103}, 'szpiro_ratio': 3.3749294732078003, '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, -4, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0], 'aplist': [0, 0, -4, -1, 0, 0, 2, 2, -8, -2, -4, 6, -2, 8, -4, 10, 6, 4, 12, 0, 14, -8, 6, 10, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 85176, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '85176.b', 'trace_hash': 965643769758790850}
• 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': '0.081996657524139071596191961563', 'prec': 107}, 'conductor': 85176, 'gens': [], 'heights': [], 'lmfdb_label': '85176.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.54014624144158608138757510153', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0802924828831721627751502030645361262', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-65, 0, 1]], 'xcoord_integral_points': [-65]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': [0, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '85176.b2'}
• ec_torsion_growth •

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

  
  
  • id: 3993527
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '85176.b2', 'torsion': [2, 2]}
  • id: 3993528
    {'degree': 4, 'field': [-641, -58, -19, -2, 1], 'lmfdb_label': '85176.b2', 'torsion': [4]}
  • id: 3993531
    {'degree': 8, 'field': [-14759, -15608, -9104, -1840, -52, -58, 40, -2, 1], 'lmfdb_label': '85176.b2', 'torsion': [6]}
  • id: 3993530
    {'degree': 8, 'field': [45081, 15174, -2883, -1062, 262, 86, -13, -2, 1], 'lmfdb_label': '85176.b2', 'torsion': [2, 4]}
  • id: 3993529
    {'degree': 8, 'field': [594442, 81118, 40217, 1342, 1653, 78, 39, -2, 1], 'lmfdb_label': '85176.b2', 'torsion': [2, 4]}
  • id: 3993533
    {'degree': 16, 'field': [21154592, 103453504, 234803408, 193813312, 78048384, 1798216, -5566268, -962906, 583465, 53270, -22254, -4564, 2276, -28, -46, 0, 1], 'lmfdb_label': '85176.b2', 'torsion': [2, 6]}
  • id: 3993532
    {'degree': 16, 'field': [2873174404, 0, -394872592, 0, -25647816, 0, 3553936, 0, -7192, 0, -4616, 0, -108, 0, -16, 0, 1], 'lmfdb_label': '85176.b2', '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: 2077159
    {'conductor': 85176, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '85176.b2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2077160
    {'conductor': 85176, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '85176.b2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2077161
    {'conductor': 85176, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '85176.b2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2077162
    {'conductor': 85176, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '85176.b2', 'prime': 13, 'reduction_type': 0, '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: 2225070
    {'adelic_gens': [[1, 2, 2, 5], [29, 4, 2, 9], [3, 4, 8, 11], [9, 50, 48, 7], [34, 1, 39, 0], [53, 4, 52, 5], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '56.12.0.?', 'conductor': 85176, 'lmfdb_label': '85176.b2', 'prime': 0}
  • id: 347635
    {'conductor': 85176, 'elladic_image': '8.6.0.1', 'lmfdb_label': '85176.b2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 85176.b does not appear in ec_padic