Elliptic curve data - 475.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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '475a', 'Clabel': '475a2', 'Cnumber': 2, 'abc_quality': 1.0331037033479094, 'absD': 107171875, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 5130, 'ainvs': [0, -1, 1, -233, -1382], 'analytic_rank': 0, 'bad_primes': [5, 19], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 475, 'degree': 108, 'elladic_images': ['9.36.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.28885196887431314512285193174', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [-89915392, 6859], 'lmfdb_iso': '475.b', 'lmfdb_label': '475.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -9, -15], 'min_quad_twist_disc': 5, 'modell_images': ['3Cs'], 'modm_images': ['3.12.0.a.1', '9.36.0.b.1', '15.24.0-3.a.1.1', '38.2.0.a.1', '45.72.0-9.b.1.1', '114.24.1.?', '171.108.4.?', '342.216.13.?', '513.324.16.?', '570.48.1.?', '855.216.4.?', '1026.648.43.?', '1710.432.13.?', '2565.648.16.?', '5130.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.51586698734273704217752773487', 'prec': 107}, 'szpiro_ratio': 4.558396272652278, '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, 0, 2, -2, 0, 0, 1, 0, 1, 0, 3, -4, 4, 0, 0, 4, 3, 0, 1, 0], 'aplist': [0, 2, 0, 1, 3, 4, 3, 1, 0, 6, -4, -2, -6, 1, 3, -12, -6, -1, 4, 6, 7, 8, -12, 12, -8], 'class_deg': 9, 'class_size': 3, 'conductor': 475, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '475.b', 'trace_hash': 2118555155025302141}
• 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': '0.56118540506430701375283633277', 'prec': 103}, 'conductor': 475, 'gens': [], 'heights': [], 'lmfdb_label': '475.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.60810303942937204242007529230', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8243091182881161272602258768887862438', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 3, 0], '3': [0, 1], '5': 'a', '7': [4, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [1, 0], '23': [0, 0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [2, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '475.b2'}
• ec_torsion_growth •

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

  
  
  • id: 21377
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '475.b2', 'torsion': [3]}
  • id: 21378
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '475.b2', 'torsion': [3]}
  • id: 21379
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '475.b2', 'torsion': [2]}
  • id: 21380
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '475.b2', 'torsion': [3, 3]}
  • id: 21382
    {'degree': 6, 'field': [-4, 4, 4, -8, -6, 0, 1], 'lmfdb_label': '475.b2', 'torsion': [6]}
  • id: 21381
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '475.b2', 'torsion': [2, 2]}
  • id: 21383
    {'degree': 6, 'field': [6, -18, 52, -11, 17, -1, 1], 'lmfdb_label': '475.b2', 'torsion': [6]}
  • id: 21384
    {'degree': 12, 'field': [-16616, 31936, -27024, 11672, -3212, 1600, -1576, 968, -326, 40, 12, -6, 1], 'lmfdb_label': '475.b2', 'torsion': [4]}
  • id: 21386
    {'degree': 12, 'field': [1, 3, 3, 0, 17, -3, -6, 3, 17, 0, 3, -3, 1], 'lmfdb_label': '475.b2', 'torsion': [2, 6]}
  • id: 21385
    {'degree': 12, 'field': [16, 16, 32, 48, 24, -16, 80, -52, 32, -16, 6, 0, 1], 'lmfdb_label': '475.b2', 'torsion': [3, 6]}
  • id: 21387
    {'degree': 12, 'field': [3481, 0, 3191, 0, 2142, 0, 991, 0, 222, 0, 23, 0, 1], 'lmfdb_label': '475.b2', 'torsion': [2, 6]}
  • id: 21388
    {'degree': 18, 'field': [-1, -3, -3, -12, 31, -1, 39, 43, -172, 96, -50, -36, 106, -21, 8, 5, -10, -1, 1], 'lmfdb_label': '475.b2', 'torsion': [9]}
  • id: 21389
    {'degree': 18, 'field': [54439939, 0, 0, 576600, 0, 0, -429654, 0, 0, -15316, 0, 0, 2211, 0, 0, -12, 0, 0, 1], 'lmfdb_label': '475.b2', 'torsion': [9]}
• 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: 5214
    {'conductor': 475, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '475.b2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5215
    {'conductor': 475, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '475.b2', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1667920
    {'adelic_gens': [[4103, 0, 0, 5129], [1, 27, 27, 730], [1961, 790, 1740, 3631], [19, 54, 2844, 4573], [4996, 3105, 15, 676], [1, 54, 0, 1], [1, 0, 54, 1], [5077, 54, 5076, 55], [43, 30, 840, 2137]], 'adelic_image': '5130.1296.43.?', 'conductor': 475, 'lmfdb_label': '475.b2', 'prime': 0}
  • id: 2132
    {'conductor': 475, 'elladic_image': '9.36.0.2', 'lmfdb_label': '475.b2', 'modell_image': '3Cs', 'prime': 3}
• lmfdb_iso 475.b does not appear in ec_padic