Elliptic curve data - 174570.b2

Formats: - HTML - YAML - JSON - 2024-06-14T04:43:33.074732

• 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': '174570co', 'Clabel': '174570co2', 'Cnumber': 2, 'abc_quality': 0.9928122853972299, 'absD': 24562681259341171422326400, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 30360, 'ainvs': [1, 1, 0, 66419907, -115937563203], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 174570, 'degree': 66769920, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5600799340057402648230181953', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [17991524611989937, 13637201212800], 'lmfdb_iso': '174570.b', 'lmfdb_label': '174570.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 125558, 9583444], 'min_quad_twist_disc': -23, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '1320.6.0.?', '1380.6.0.?', '2024.6.0.?', '30360.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '38.150489149073296402117861520', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2084592720588779967179535714', 'prec': 100}, 'szpiro_ratio': 5.4389133478816065, '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, -1, -1, 1, -1, 1, -4, -1, 1, 1, 1, -1, 2, 4, 1, 1, -2, -1, 0, -1], 'aplist': [-1, -1, -1, -4, 1, 2, -2, 0, 0, -6, 0, 10, -8, -4, 8, 6, 8, 12, 0, -14, 16, -10, -12, 14, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 174570, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '174570.b', 'trace_hash': 1811689328476379490}
• 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': '0.00080863746552644878184438428242', 'prec': 113}, 'conductor': 174570, 'gens': [[34626031520847397, 6490830835203193254235771, 770956]], 'heights': [{'__RealLiteral__': 0, 'data': '38.150489149073296402117861520', 'prec': 100}], 'lmfdb_label': '174570.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.037574128561572964141472952547', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8669427679483487905746145093398134748', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[6699, -6699, 2]], 'xcoord_integral_points': []}
• lmfdb_label 174570.b2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7742004
    {'degree': 2, 'field': [506, 0, 1], 'lmfdb_label': '174570.b2', 'torsion': [2, 2]}
  • id: 7742005
    {'degree': 4, 'field': [-18216, 0, 69, 0, 1], 'lmfdb_label': '174570.b2', 'torsion': [4]}
  • id: 7742008
    {'degree': 8, 'field': [-177994, -55775, 31668, 2921, 487, -437, 7, 0, 1], 'lmfdb_label': '174570.b2', 'torsion': [6]}
  • id: 7742006
    {'degree': 8, 'field': [183358681, 0, 5450874, 0, 46082, 0, 186, 0, 1], 'lmfdb_label': '174570.b2', 'torsion': [2, 4]}
  • id: 7742007
    {'degree': 8, 'field': [415915236, 0, 16974848, 0, 244310, 0, 352, 0, 1], 'lmfdb_label': '174570.b2', 'torsion': [2, 4]}
  • id: 7742010
    {'degree': 16, 'field': [32936651130, 69774705228, 51765760451, 10629024776, -5068130078, -2772814390, -273589391, 93001792, 31672809, 2214502, 355415, 20360, 15741, -1402, -162, 0, 1], 'lmfdb_label': '174570.b2', 'torsion': [2, 6]}
  • id: 7742009
    {'degree': 16, 'field': [499041900932256, -472218867090432, 128780017190352, 6631589164464, -8406525209964, 892240276008, 136514971140, -30703364088, 542447659, 278342516, -20876510, -902584, 155611, 1952, -602, -4, 1], 'lmfdb_label': '174570.b2', '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: 4318505
    {'conductor': 174570, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '174570.b2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4318506
    {'conductor': 174570, 'conductor_valuation': 1, 'discriminant_valuation': 18, 'j_denominator_valuation': 18, 'kodaira_symbol': 22, 'lmfdb_label': '174570.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4318507
    {'conductor': 174570, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '174570.b2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4318508
    {'conductor': 174570, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '174570.b2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4318509
    {'conductor': 174570, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '174570.b2', 'prime': 23, 'reduction_type': 0, '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: 2788734
    {'adelic_gens': [[1, 2, 2, 5], [2, 1, 15179, 0], [1, 4, 0, 1], [3796, 26569, 11385, 18976], [10121, 4, 20242, 9], [18217, 4, 6074, 9], [30357, 4, 30356, 5], [1, 0, 4, 1], [15844, 1, 26399, 0], [3, 4, 8, 11], [24842, 1, 2759, 0]], 'adelic_image': '30360.12.0.?', 'conductor': 174570, 'lmfdb_label': '174570.b2', 'prime': 0}
  • id: 657042
    {'conductor': 174570, 'elladic_image': '2.3.0.1', 'lmfdb_label': '174570.b2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 174570.b does not appear in ec_padic