Elliptic curve data - 54.b2

Formats: - HTML - YAML - JSON - 2026-07-28T20:40:20.859848

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '54b', 'Clabel': '54b3', 'Cnumber': 3, 'abc_quality': 1.0496550478531228, 'absD': 124416, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 72, 'ainvs': [1, -1, 1, -14, 29], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 54, 'degree': 6, 'elladic_images': ['9.72.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.31520442809991116702386968500', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3, 9], 'jinv': [-1167051, 512], 'lmfdb_iso': '54.b', 'lmfdb_label': '54.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -123, -667], 'min_quad_twist_disc': -3, 'modell_images': ['3B.1.1'], 'modm_images': ['3.8.0-3.a.1.2', '9.72.0-9.d.1.2', '24.16.0-24.d.1.8', '72.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 27], [3, 8, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.77295954837829020510522186705', 'prec': 107}, 'szpiro_ratio': 5.020647585518826, 'torsion': 9, 'torsion_primes': [3], 'torsion_structure': [9]}
• 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, -3, 0, -1, 1, 0, -3, 3, 0, -4, -1, 0, 1, 0, 0, 2, -3], 'aplist': [1, 0, -3, -1, 3, -4, 0, 2, 6, -6, 5, 2, 6, -10, -6, -9, -12, 8, 14, 0, -7, 8, 3, 18, -1], 'class_deg': 9, 'class_size': 3, 'conductor': 54, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '54.b', 'trace_hash': 689246320802081722}
• 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': '1.8783784089457941130346815604', 'prec': 100}, 'conductor': 54, 'gens': [], 'heights': [], 'lmfdb_label': '54.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.0915655491030075566523150028', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0305218497010025188841050009479161922', 'prec': 130}, 'tamagawa_product': 27, 'torsion_generators': [[3, 1, 1]], 'xcoord_integral_points': [-3, 1, 3, 9]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': 'a'}, 'iwp0': 5, 'lmfdb_label': '54.b2'}
• ec_torsion_growth •

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

  
  
  • id: 1890
    {'degree': 3, 'field': [-2, 3, 0, 1], 'lmfdb_label': '54.b2', 'torsion': [18]}
  • id: 1892
    {'degree': 6, 'field': [3, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '54.b2', 'torsion': [3, 9]}
  • id: 1891
    {'degree': 6, 'field': [6, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '54.b2', 'torsion': [2, 18]}
  • id: 1893
    {'degree': 9, 'field': [-4, 0, 0, -27, 0, 27, 0, -9, 0, 1], 'lmfdb_label': '54.b2', 'torsion': [27]}
  • id: 1894
    {'degree': 12, 'field': [-6, 0, 27, 0, -39, 0, -6, 0, 24, 0, -9, 0, 1], 'lmfdb_label': '54.b2', 'torsion': [36]}
  • id: 1895
    {'degree': 18, 'field': [1, 0, 0, -12, 0, 0, 63, 0, 0, -52, 0, 0, 15, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '54.b2', 'torsion': [3, 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: 266
    {'conductor': 54, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '54.b2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 267
    {'conductor': 54, 'conductor_valuation': 3, 'discriminant_valuation': 5, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '54.b2', 'prime': 3, 'reduction_type': 0, '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: 1666011
    {'adelic_gens': [[10, 9, 9, 1], [55, 18, 0, 1], [1, 18, 10, 37], [65, 54, 63, 19], [1, 18, 0, 1], [55, 18, 54, 19], [1, 0, 18, 1], [37, 18, 45, 19]], 'adelic_image': '72.144.3.?', 'conductor': 54, 'lmfdb_label': '54.b2', 'prime': 0}
  • id: 164
    {'conductor': 54, 'elladic_image': '9.72.0.5', 'lmfdb_label': '54.b2', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 54.b does not appear in ec_padic