Elliptic curve data - 240.b5

Formats: - HTML - YAML - JSON - 2025-09-30T16:34:04.334170

• 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': '240b', 'Clabel': '240b5', 'Cnumber': 5, 'abc_quality': 1.0339287621454463, 'absD': 21767823360, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, -1, 0, -1096, 12400], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 240, 'degree': 192, 'elladic_images': ['8.12.0.8', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.70800702144224214400885182456', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [35578826569, 5314410], 'lmfdb_iso': '240.b', 'lmfdb_label': '240.b5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -69, -194], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '8.12.0-4.c.1.4', '12.48.0-12.g.1.8', '20.12.0-4.c.1.2', '24.192.1-24.dj.4.7', '40.24.0-40.v.1.2', '60.96.0-60.c.4.12', '120.384.5.?'], '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': False, 'serre_invariants': [[2, 4, 5], [3, 4, 80], [5, 6, 48]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703102', 'prec': 107}, 'szpiro_ratio': 5.950543935012571, '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, -1, 0, -1, 0, 4, 0, 1, 0, 0, 0, 2, 0, 1, 0, 6, 0, 4, 0], 'aplist': [0, -1, -1, 4, 0, 2, 6, 4, 0, -6, -8, 2, -6, 4, 0, -6, 0, -10, 4, 0, 2, -8, -12, 18, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 240, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '240.b', 'trace_hash': 1065312699390175217}
• 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': '0.24267940131489496193696876040', 'prec': 103}, 'conductor': 240, 'gens': [], 'heights': [], 'lmfdb_label': '240.b5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1583921113140821333424743276', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1583921113140821333424743275907317437', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[25, 0, 1]], 'xcoord_integral_points': [25]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '240.b5'}
• ec_torsion_growth •

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

  
  
  • id: 10278
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [2, 2]}
  • id: 10279
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [4]}
  • id: 10280
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '240.b5', 'torsion': [4]}
  • id: 10281
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [6]}
  • id: 10284
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [12]}
  • id: 10285
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [12]}
  • id: 10282
    {'degree': 4, 'field': [4, 0, -6, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [2, 4]}
  • id: 10283
    {'degree': 4, 'field': [25, 0, 0, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [2, 6]}
  • id: 10286
    {'degree': 6, 'field': [-3, 0, 7, 0, -1, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [6]}
  • id: 10290
    {'degree': 8, 'field': [1, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [2, 12]}
  • id: 10289
    {'degree': 8, 'field': [16, -36, 39, -27, 14, -9, 6, -3, 1], 'lmfdb_label': '240.b5', 'torsion': [8]}
  • id: 10288
    {'degree': 8, 'field': [25, 0, -60, 0, 44, 0, -12, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [8]}
  • id: 10287
    {'degree': 8, 'field': [36, 0, 272, 0, 4, 0, 8, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [2, 4]}
  • id: 10294
    {'degree': 12, 'field': [1, -4, 1, 10, -20, -4, 41, -4, -20, 10, 1, -4, 1], 'lmfdb_label': '240.b5', 'torsion': [12]}
  • id: 10291
    {'degree': 12, 'field': [9, 0, 21, 0, 46, 0, 1, 0, -6, 0, 1, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [3, 6]}
  • id: 10293
    {'degree': 12, 'field': [121, 0, -68, 0, -49, 0, 28, 0, 11, 0, -8, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [12]}
  • id: 10292
    {'degree': 12, 'field': [1369, 0, -2702, 0, 855, 0, 80, 0, -45, 0, -2, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [2, 6]}
  • id: 10296
    {'degree': 16, 'field': [1, -18, 143, -630, 1595, -2292, 2244, -1620, 824, -240, 36, -24, 35, -30, 17, -6, 1], 'lmfdb_label': '240.b5', 'torsion': [2, 8]}
  • id: 10297
    {'degree': 16, 'field': [1, 0, -20, 0, 128, 0, -360, 0, 503, 0, -360, 0, 128, 0, -20, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [2, 8]}
  • id: 10299
    {'degree': 16, 'field': [256, 0, 48, 0, 25, 0, 93, 0, -6, 0, -3, 0, 10, 0, -3, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [24]}
  • id: 10298
    {'degree': 16, 'field': [625, 0, -1500, 0, 2500, 0, -2040, 0, 1191, 0, -408, 0, 100, 0, -12, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [24]}
  • id: 10295
    {'degree': 16, 'field': [625, 0, 0, 0, 0, 0, 0, 0, 850, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '240.b5', 'torsion': [4, 12]}
  • id: 10300
    {'degree': 18, 'field': [256, 0, 2304, 0, 3456, 0, 3888, 0, 2592, 0, 1008, 0, 177, 0, 18, 0, 9, 0, 1], 'lmfdb_label': '240.b5', '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: 2176
    {'conductor': 240, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '240.b5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2177
    {'conductor': 240, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '240.b5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2178
    {'conductor': 240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '240.b5', 'prime': 5, '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: 1666788
    {'adelic_gens': [[89, 96, 90, 119], [1, 12, 12, 25], [1, 24, 0, 1], [97, 24, 96, 25], [42, 79, 77, 92], [1, 0, 24, 1], [15, 106, 14, 11], [61, 24, 92, 29], [112, 3, 117, 34]], 'adelic_image': '120.384.5.?', 'conductor': 240, 'lmfdb_label': '240.b5', 'prime': 0}
  • id: 1010
    {'conductor': 240, 'elladic_image': '8.12.0.8', 'lmfdb_label': '240.b5', 'modell_image': '2B', 'prime': 2}
  • id: 1011
    {'conductor': 240, 'elladic_image': '3.4.0.1', 'lmfdb_label': '240.b5', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 240.b does not appear in ec_padic