Elliptic curve data - 5040.bb1

Formats: - HTML - YAML - JSON - 2026-01-11T08:17:01.740549

• 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': '5040e', 'Clabel': '5040e1', 'Cnumber': 1, 'abc_quality': 1.1234589902323506, 'absD': 67512690000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 84, 'ainvs': [0, 0, 0, -2862, 57591], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 5040, 'degree': 4608, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.85968595335715073230226278610', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 27, 'isogeny_degrees': [1, 2], 'jinv': [8232302592, 214375], 'lmfdb_iso': '5040.bb', 'lmfdb_label': '5040.bb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -318, 2133], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '28.6.0.d.1', '42.6.0.a.1', '84.12.0.?'], '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, 21], [3, 2, 80], [5, 6, 1008], [7, 8, 720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.19532232333057997271658184874', 'prec': 107}, 'szpiro_ratio': 4.163138902585815, '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, 1, 0, -1, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 8, 0], 'aplist': [0, 0, 1, -1, 2, -2, 2, 8, 2, -8, 8, -6, 6, -4, -4, 0, 4, -2, 4, -6, -6, 0, 16, 6, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 5040, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '5040.bb', 'trace_hash': 1160307970333818119}
• 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': '0.17917865348499136270981974193', 'prec': 103}, 'conductor': 5040, 'gens': [], 'heights': [], 'lmfdb_label': '5040.bb1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0962865390831921352685799038', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1925730781663842705371598075177910705', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[27, 0, 1]], 'xcoord_integral_points': [27]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '5040.bb1'}
• ec_torsion_growth •

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

  
  
  • id: 262725
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '5040.bb1', 'torsion': [2, 2]}
  • id: 262726
    {'degree': 4, 'field': [21, 0, -9, 0, 1], 'lmfdb_label': '5040.bb1', 'torsion': [4]}
  • id: 262729
    {'degree': 8, 'field': [-3, 0, 12, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '5040.bb1', 'torsion': [6]}
  • id: 262727
    {'degree': 8, 'field': [9, 0, 9, 0, 12, 0, -3, 0, 1], 'lmfdb_label': '5040.bb1', 'torsion': [2, 4]}
  • id: 262728
    {'degree': 8, 'field': [49, 0, 49, 0, 0, 0, -14, 0, 1], 'lmfdb_label': '5040.bb1', 'torsion': [2, 4]}
  • id: 262730
    {'degree': 16, 'field': [49, -392, 1630, -4550, 9518, -15794, 20590, -19900, 13387, -6066, 2050, -780, 358, -122, 28, -6, 1], 'lmfdb_label': '5040.bb1', 'torsion': [8]}
  • id: 262731
    {'degree': 16, 'field': [7575, -55800, -19650, 64680, -3720, -22980, 9168, -1722, -1277, 1600, -488, 82, 4, -20, 4, -2, 1], 'lmfdb_label': '5040.bb1', 'torsion': [2, 6]}
• 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: 97538
    {'conductor': 5040, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '5040.bb1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 97539
    {'conductor': 5040, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '5040.bb1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 97540
    {'conductor': 5040, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '5040.bb1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 97541
    {'conductor': 5040, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5040.bb1', 'prime': 7, '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: 1696833
    {'adelic_gens': [[1, 2, 2, 5], [62, 1, 11, 0], [81, 4, 80, 5], [3, 4, 8, 11], [32, 1, 55, 0], [1, 4, 0, 1], [65, 22, 20, 63], [1, 0, 4, 1]], 'adelic_image': '84.12.0.?', 'conductor': 5040, 'lmfdb_label': '5040.bb1', 'prime': 0}
  • id: 24953
    {'conductor': 5040, 'elladic_image': '2.3.0.1', 'lmfdb_label': '5040.bb1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 5040.bb does not appear in ec_padic