Elliptic curve data - 1140.b1

Formats: - HTML - YAML - JSON - 2024-05-12T05:14:49.195634

• 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': '1140d', 'Clabel': '1140d2', 'Cnumber': 2, 'abc_quality': 0.8904892774586586, 'absD': 27360000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 228, 'ainvs': [0, 1, 0, -76, -76], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1140, 'degree': 384, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.11741507984889356071344335684', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [192143824, 106875], 'lmfdb_iso': '1140.b', 'lmfdb_label': '1140.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -76, -76], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '76.6.0.?', '228.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.34468304052440331223137805747', 'prec': 107}, 'szpiro_ratio': 3.497611772349727, '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, 2, 0, 6, 0, -1, 0, -2, 0, 1, 0], 'aplist': [0, 1, -1, -4, 2, 6, -2, 1, 6, 8, -8, 10, -4, 4, 6, 12, -8, 2, 4, 12, -10, -8, 2, -12, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 1140, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1140.b', 'trace_hash': 794417791412348690}
• 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': '0.79070513182369868462811745900', 'prec': 103}, 'conductor': 1140, 'gens': [], 'heights': [], 'lmfdb_label': '1140.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.7322680034463230856454674774', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7322680034463230856454674773780453291', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-1, 0, 1]], 'xcoord_integral_points': [-1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [0, 0], '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1140.b1'}
• ec_torsion_growth •

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

  
  
  • id: 56193
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '1140.b1', 'torsion': [2, 2]}
  • id: 56194
    {'degree': 4, 'field': [19, 0, -8, 0, 1], 'lmfdb_label': '1140.b1', 'torsion': [4]}
  • id: 56197
    {'degree': 8, 'field': [-72, 180, -198, 35, -14, -7, 7, -4, 1], 'lmfdb_label': '1140.b1', 'torsion': [6]}
  • id: 56195
    {'degree': 8, 'field': [81, -54, 144, 108, 123, 36, 16, -2, 1], 'lmfdb_label': '1140.b1', 'torsion': [2, 4]}
  • id: 56196
    {'degree': 8, 'field': [216, -1296, -120, 1056, 208, -88, -4, -4, 1], 'lmfdb_label': '1140.b1', 'torsion': [2, 4]}
  • id: 56199
    {'degree': 16, 'field': [259860, 81696, -1278360, 3645704, -5190142, 4719606, -2756471, 1119808, -416190, 97440, -26055, 3504, -493, -70, 30, -8, 1], 'lmfdb_label': '1140.b1', 'torsion': [2, 6]}
  • id: 56198
    {'degree': 16, 'field': [2030625, 0, -3249000, 0, 2037750, 0, -522120, 0, 106411, 0, -15496, 0, 1542, 0, -64, 0, 1], 'lmfdb_label': '1140.b1', 'torsion': [8]}
• 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: 16517
    {'conductor': 1140, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '1140.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 16518
    {'conductor': 1140, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1140.b1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 16519
    {'conductor': 1140, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1140.b1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 16520
    {'conductor': 1140, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1140.b1', 'prime': 19, '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: 1671742
    {'adelic_gens': [[172, 61, 57, 172], [194, 1, 131, 0], [1, 4, 0, 1], [225, 4, 224, 5], [1, 0, 4, 1], [77, 4, 154, 9], [3, 4, 8, 11], [1, 2, 2, 5]], 'adelic_image': '228.12.0.?', 'conductor': 1140, 'lmfdb_label': '1140.b1', 'prime': 0}
  • id: 5414
    {'conductor': 1140, 'elladic_image': '2.3.0.1', 'lmfdb_label': '1140.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1140.b does not appear in ec_padic