Elliptic curve data - 240.b6

Formats: - HTML - YAML - JSON - 2024-05-11T16:54:10.547295

• 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': '240b', 'Clabel': '240b2', 'Cnumber': 2, 'abc_quality': 1.0045688963827404, 'absD': 298598400, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, -1, 0, -296, -1680], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 240, 'degree': 96, 'elladic_images': ['8.12.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.36143343116226948930023576383', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [702595369, 72900], 'lmfdb_iso': '240.b', 'lmfdb_label': '240.b6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -19, 26], 'min_quad_twist_disc': -4, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1', '8.12.0-2.a.1.1', '12.96.0-12.a.2.7', '20.12.0-2.a.1.1', '24.192.1-24.cp.4.3', '40.24.0-40.a.1.2', '60.192.1-60.h.1.3', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33171374939767582011699635763', 'prec': 107}, 'szpiro_ratio': 5.234436764494534, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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': '0.48535880262978992387393752081', 'prec': 103}, 'conductor': 240, 'gens': [], 'heights': [], 'lmfdb_label': '240.b6', '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': 16, 'torsion_generators': [[-7, 0, 1], [20, 0, 1]], 'xcoord_integral_points': [-12, -7, 20]}
• 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.b6'}
• ec_torsion_growth •

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

  
  
  • id: 10226
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 6]}
  • id: 10229
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 4]}
  • id: 10228
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 4]}
  • id: 10227
    {'degree': 4, 'field': [9, 0, -4, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 4]}
  • id: 10230
    {'degree': 6, 'field': [-3, 0, 7, 0, -1, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 6]}
  • id: 10233
    {'degree': 8, 'field': [1, 0, -3, 0, 8, 0, -3, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 12]}
  • id: 10231
    {'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 12]}
  • id: 10232
    {'degree': 8, 'field': [1, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 12]}
  • id: 10234
    {'degree': 12, 'field': [9, 0, 21, 0, 46, 0, 1, 0, -6, 0, 1, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [6, 6]}
  • id: 10235
    {'degree': 12, 'field': [121, 0, -68, 0, -49, 0, 28, 0, 11, 0, -8, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 12]}
  • id: 10236
    {'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 48, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [4, 12]}
  • id: 10239
    {'degree': 16, 'field': [4, 0, -48, 0, 220, 0, -384, 0, 189, 0, -60, 0, 40, 0, -12, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 8]}
  • id: 10237
    {'degree': 16, 'field': [36, 0, 48, 0, 100, 0, 288, 0, 389, 0, 252, 0, 80, 0, 12, 0, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 8]}
  • id: 10238
    {'degree': 16, 'field': [225, 0, -225, 0, 165, -270, 30, 210, -14, -138, 166, -114, 69, -42, 19, -6, 1], 'lmfdb_label': '240.b6', 'torsion': [2, 8]}
  • id: 10240
    {'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.b6', 'torsion': [2, 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: 2167
    {'conductor': 240, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '240.b6', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2168
    {'conductor': 240, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '240.b6', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2169
    {'conductor': 240, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '240.b6', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1666789
    {'adelic_gens': [[89, 108, 54, 47], [67, 6, 114, 115], [109, 12, 108, 13], [97, 6, 0, 1], [9, 4, 104, 113], [81, 4, 22, 9], [1, 0, 12, 1], [1, 12, 0, 1]], 'adelic_image': '120.384.5.?', 'conductor': 240, 'lmfdb_label': '240.b6', 'prime': 0}
  • id: 1012
    {'conductor': 240, 'elladic_image': '8.12.0.1', 'lmfdb_label': '240.b6', 'modell_image': '2Cs', 'prime': 2}
  • id: 1013
    {'conductor': 240, 'elladic_image': '3.4.0.1', 'lmfdb_label': '240.b6', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 240.b does not appear in ec_padic