Elliptic curve data - 102.b1

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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': '102c', 'Clabel': '102c3', 'Cnumber': 3, 'abc_quality': 1.0866579960559595, 'absD': 11591221248, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 408, 'ainvs': [1, 0, 1, -751, -6046], 'analytic_rank': 0, 'bad_primes': [2, 3, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 102, 'degree': 72, 'elladic_images': ['8.6.0.4', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.64142632068141965454817785789', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [46753267515625, 11591221248], 'lmfdb_iso': '102.b', 'lmfdb_label': '102.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -751, -6046], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '6.24.0-6.a.1.2', '8.6.0.d.1', '24.48.0-24.bx.1.11', '34.6.0.a.1', '102.48.0.?', '136.12.0.?', '408.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 17], [3, 4, 1], [17, 18, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.64142632068141965454817785789', 'prec': 103}, 'szpiro_ratio': 6.805641142839843, '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, 1, 1, 0, -1, 2, -1, 1, 0, 0, 1, 2, -2, 0, 1, -1, -1, -4, 0], 'aplist': [-1, 1, 0, 2, 0, 2, -1, -4, -6, 0, -10, 8, 6, -4, 12, 6, -12, 8, -4, 6, 2, -10, 12, -18, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 102, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '102.b', 'trace_hash': 1834044102859205000}
• 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': '0.27724528994755945093548865341', 'prec': 103}, 'conductor': 102, 'gens': [], 'heights': [], 'lmfdb_label': '102.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.92868832812702231544493968953', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.92868832812702231544493968952761090912', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-9, 4, 1]], 'xcoord_integral_points': [-9]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [1, 1], '17': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '102.b1'}
• ec_torsion_growth •

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

  
  
  • id: 3874
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '102.b1', 'torsion': [2, 2]}
  • id: 3875
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '102.b1', 'torsion': [6]}
  • id: 3876
    {'degree': 3, 'field': [-3, 0, 0, 1], 'lmfdb_label': '102.b1', 'torsion': [6]}
  • id: 3877
    {'degree': 4, 'field': [3, -2, 1, -2, 1], 'lmfdb_label': '102.b1', 'torsion': [4]}
  • id: 3878
    {'degree': 4, 'field': [16, 4, 5, -1, 1], 'lmfdb_label': '102.b1', 'torsion': [2, 6]}
  • id: 3880
    {'degree': 6, 'field': [-16, -129, 45, 17, -9, -3, 1], 'lmfdb_label': '102.b1', 'torsion': [2, 6]}
  • id: 3879
    {'degree': 6, 'field': [3, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '102.b1', 'torsion': [3, 6]}
  • id: 3881
    {'degree': 8, 'field': [-152, -196, 127, 38, -114, 52, -8, -2, 1], 'lmfdb_label': '102.b1', 'torsion': [2, 4]}
  • id: 3882
    {'degree': 8, 'field': [9, -30, 59, -74, 50, -10, 1, -2, 1], 'lmfdb_label': '102.b1', 'torsion': [2, 4]}
  • id: 3883
    {'degree': 8, 'field': [9, -6, 1, 10, -6, 2, 3, -2, 1], 'lmfdb_label': '102.b1', 'torsion': [12]}
  • id: 3885
    {'degree': 12, 'field': [2187, 0, 0, -1188, 0, 0, 252, 0, 0, -24, 0, 0, 1], 'lmfdb_label': '102.b1', 'torsion': [12]}
  • id: 3884
    {'degree': 12, 'field': [4996, 4326, -99, -7180, 645, 2886, 47, -726, 15, 100, -9, -6, 1], 'lmfdb_label': '102.b1', 'torsion': [6, 6]}
  • id: 3888
    {'degree': 16, 'field': [172, -848, 1378, -452, -679, -68, 900, -188, -238, -112, 162, -40, 20, -4, 4, -4, 1], 'lmfdb_label': '102.b1', 'torsion': [2, 12]}
  • id: 3887
    {'degree': 16, 'field': [324, -1080, 1314, -4092, 9853, -9482, 7602, -6284, 3486, -1486, 558, -154, 78, -20, 12, -2, 1], 'lmfdb_label': '102.b1', 'torsion': [2, 12]}
  • id: 3886
    {'degree': 16, 'field': [2916, -11664, 27432, -40464, 44976, -36168, 22676, -9816, 3023, -336, 92, -152, 180, -96, 36, -8, 1], 'lmfdb_label': '102.b1', 'torsion': [8]}
  • id: 3889
    {'degree': 18, 'field': [27, 0, 0, -72, 0, 0, 363, 0, 0, 336, 0, 0, 121, 0, 0, -8, 0, 0, 1], 'lmfdb_label': '102.b1', 'torsion': [18]}
• 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: 658
    {'conductor': 102, 'conductor_valuation': 1, 'discriminant_valuation': 18, 'j_denominator_valuation': 18, 'kodaira_symbol': 22, 'lmfdb_label': '102.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 659
    {'conductor': 102, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '102.b1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 660
    {'conductor': 102, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '102.b1', 'prime': 17, '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: 1666177
    {'adelic_gens': [[370, 3, 21, 400], [397, 12, 396, 13], [1, 0, 12, 1], [11, 2, 358, 399], [137, 12, 340, 1], [1, 6, 6, 37], [1, 12, 0, 1], [327, 394, 38, 101], [205, 12, 6, 73]], 'adelic_image': '408.96.1.?', 'conductor': 102, 'lmfdb_label': '102.b1', 'prime': 0}
  • id: 360
    {'conductor': 102, 'elladic_image': '8.6.0.4', 'lmfdb_label': '102.b1', 'modell_image': '2B', 'prime': 2}
  • id: 361
    {'conductor': 102, 'elladic_image': '3.8.0.2', 'lmfdb_label': '102.b1', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 102.b does not appear in ec_padic