Elliptic curve data - 221760.b2

Formats: - HTML - YAML - JSON - 2024-04-28T02:17:03.901141

• 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': '221760hg', 'Clabel': '221760hg2', 'Cnumber': 2, 'abc_quality': 0.8034076491587089, 'absD': 6828646809600, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4620, 'ainvs': [0, 0, 0, 2052, 120528], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 221760, 'degree': 516096, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1442891744582111292761199227', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [2963088, 21175], 'lmfdb_iso': '221760.b', 'lmfdb_label': '221760.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 57, 558], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '84.6.0.?', '660.6.0.?', '1540.6.0.?', '4620.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, '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': '-0.48834175269614066692375148003', 'prec': 107}, 'szpiro_ratio': 2.999542404208454, '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, -1, 0, -6, 0, 0, 0, -2, 0, 8, 0], 'aplist': [0, 0, -1, -1, -1, -6, -2, 8, -8, 6, 0, 2, 6, 8, 8, 2, 6, 8, 10, 8, 14, -10, 18, -14, 0], 'class_deg': 2, 'class_size': 2, 'conductor': 221760, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '221760.b', 'trace_hash': 1158438329413950286}
• 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': '0.10141052981202791831459195731', 'prec': 103}, 'conductor': 221760, 'gens': [], 'heights': [], 'lmfdb_label': '221760.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.54448299581958405293934117263', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1779319832783362117573646905325344452', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-36, 0, 1]], 'xcoord_integral_points': [-36]}
• lmfdb_label 221760.b2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9647875
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '221760.b2', 'torsion': [2, 2]}
  • id: 9647876
    {'degree': 4, 'field': [-756, 0, 54, 0, 1], 'lmfdb_label': '221760.b2', 'torsion': [4]}
  • id: 9647879
    {'degree': 8, 'field': [-12288, 0, 3744, 0, -384, 0, 0, 0, 1], 'lmfdb_label': '221760.b2', 'torsion': [6]}
  • id: 9647878
    {'degree': 8, 'field': [275625, 0, 18900, 0, 2739, 0, -36, 0, 1], 'lmfdb_label': '221760.b2', 'torsion': [2, 4]}
  • id: 9647877
    {'degree': 8, 'field': [810793, 161228, 43702, 3800, -1064, 296, 46, -4, 1], 'lmfdb_label': '221760.b2', 'torsion': [2, 4]}
  • id: 9647881
    {'degree': 16, 'field': [148048912, 98359264, 69758648, 14976888, 8589929, 3383912, 2122144, 373944, 139807, 41736, 22990, 1288, 1229, 12, 50, -4, 1], 'lmfdb_label': '221760.b2', 'torsion': [2, 6]}
  • id: 9647880
    {'degree': 16, 'field': [7646657337081, 0, 2424827353284, 0, -536710627530, 0, -22508795484, 0, -279856701, 0, 497556, 0, 42570, 0, 384, 0, 1], 'lmfdb_label': '221760.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: 5498600
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '221760.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5498601
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '221760.b2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5498602
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221760.b2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5498603
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.b2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5498604
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221760.b2', 'prime': 11, '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: 3079327
    {'adelic_gens': [[1156, 3469, 3465, 1156], [1, 2, 2, 5], [3697, 4, 2774, 9], [1, 4, 0, 1], [1544, 1, 3079, 0], [2521, 4, 422, 9], [1322, 1, 3959, 0], [1, 0, 4, 1], [4617, 4, 4616, 5], [3, 4, 8, 11]], 'adelic_image': '4620.12.0.?', 'conductor': 221760, 'lmfdb_label': '221760.b2', 'prime': 0}
  • id: 812176
    {'conductor': 221760, 'elladic_image': '2.3.0.1', 'lmfdb_label': '221760.b2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 221760.b does not appear in ec_padic