Elliptic curve data - 22320.bi4

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• 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': '22320bv', 'Clabel': '22320bv1', 'Cnumber': 1, 'abc_quality': 1.1472356070759668, 'absD': 1156730291654492160, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1860, 'ainvs': [0, 0, 0, 200013, -38629006], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 31], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 22320, 'degree': 276480, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1518922240094549649511334947', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 34, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [296354077829711, 387386634240], 'lmfdb_iso': '22320.bi', 'lmfdb_label': '22320.bi4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1389, -22239], 'min_quad_twist_disc': 12, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0-6.a.1.9', '30.24.0.b.1', '60.48.0-30.b.1.7', '124.6.0.?', '372.48.0.?', '1860.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.90943889911545480983627875478', 'prec': 103}, 'szpiro_ratio': 4.83981021202923, '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, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -6, 0, -8, 0], 'aplist': [0, 0, 1, -2, 0, -4, -6, -8, 0, 0, -1, -4, 6, -8, -12, 6, -6, 2, -2, -6, 8, -8, 12, 0, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 22320, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '22320.bi', 'trace_hash': 1403702406175420342}
• 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': '0.013517306548240595991674800406', 'prec': 107}, 'conductor': 22320, 'gens': [], 'heights': [], 'lmfdb_label': '22320.bi4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14643882989305740851918694876', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.58575531957222963407674779505297255587', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[169, 0, 1]], 'xcoord_integral_points': [169]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '31': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '22320.bi4'}
• ec_torsion_growth •

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

  
  
  • id: 1133965
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '22320.bi4', 'torsion': [6]}
  • id: 1133964
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '22320.bi4', 'torsion': [2, 2]}
  • id: 1133967
    {'degree': 4, 'field': [4, 0, 1, 0, 1], 'lmfdb_label': '22320.bi4', 'torsion': [2, 6]}
  • id: 1133966
    {'degree': 4, 'field': [100, -20, -10, -2, 1], 'lmfdb_label': '22320.bi4', 'torsion': [4]}
  • id: 1133968
    {'degree': 6, 'field': [17424, 0, 2968, 0, -103, 0, 1], 'lmfdb_label': '22320.bi4', 'torsion': [6]}
  • id: 1133971
    {'degree': 8, 'field': [-23, 90, -80, -26, 29, -22, 12, -4, 1], 'lmfdb_label': '22320.bi4', 'torsion': [12]}
  • id: 1133969
    {'degree': 8, 'field': [256, 0, 116, 0, -9, 0, -4, 0, 1], 'lmfdb_label': '22320.bi4', 'torsion': [2, 4]}
  • id: 1133970
    {'degree': 8, 'field': [1249, 2184, 199, -490, 536, -92, 15, -2, 1], 'lmfdb_label': '22320.bi4', 'torsion': [2, 4]}
  • id: 1133973
    {'degree': 12, 'field': [33856, 0, -17431, 0, 4335, 0, -575, 0, 105, 0, -1, 0, 1], 'lmfdb_label': '22320.bi4', 'torsion': [2, 6]}
  • id: 1133972
    {'degree': 12, 'field': [492307344, 0, 11471196, 0, 245101, 0, -43859, 0, -516, 0, 1, 0, 1], 'lmfdb_label': '22320.bi4', 'torsion': [3, 6]}
  • id: 1133976
    {'degree': 16, 'field': [16, 0, 668, 0, 8009, 0, 4212, 0, 4424, 0, 1422, 0, 272, 0, 20, 0, 1], 'lmfdb_label': '22320.bi4', 'torsion': [2, 12]}
  • id: 1133975
    {'degree': 16, 'field': [576, 864, -360, -1440, 2064, -2316, 1872, -900, 361, -296, 112, 148, -146, 28, 16, -8, 1], 'lmfdb_label': '22320.bi4', 'torsion': [2, 12]}
  • id: 1133974
    {'degree': 16, 'field': [2624400, 0, -2529600, 0, 1193020, 0, 1294560, 0, 260169, 0, 6944, 0, -1734, 0, 0, 0, 1], 'lmfdb_label': '22320.bi4', 'torsion': [8]}
  • id: 1133977
    {'degree': 18, 'field': [9915526, 28395480, 28347318, 5794366, -7762026, -3175998, 1567283, 636534, -453102, -129578, 124293, 35934, -16018, -4554, 1137, 262, -48, -6, 1], 'lmfdb_label': '22320.bi4', '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: 509914
    {'conductor': 22320, 'conductor_valuation': 4, 'discriminant_valuation': 24, 'j_denominator_valuation': 12, 'kodaira_symbol': -20, 'lmfdb_label': '22320.bi4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 509915
    {'conductor': 22320, 'conductor_valuation': 2, 'discriminant_valuation': 15, 'j_denominator_valuation': 9, 'kodaira_symbol': -13, 'lmfdb_label': '22320.bi4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 509916
    {'conductor': 22320, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '22320.bi4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 509917
    {'conductor': 22320, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '22320.bi4', 'prime': 31, '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: 1813209
    {'adelic_gens': [[1701, 1082, 754, 139], [1, 0, 12, 1], [1, 6, 6, 37], [1234, 1849, 1251, 20], [11, 2, 1810, 1851], [1, 12, 0, 1], [1801, 12, 1506, 73], [1849, 12, 1848, 13], [10, 3, 1461, 1852]], 'adelic_image': '1860.96.1.?', 'conductor': 22320, 'lmfdb_label': '22320.bi4', 'prime': 0}
  • id: 103175
    {'conductor': 22320, 'elladic_image': '2.3.0.1', 'lmfdb_label': '22320.bi4', 'modell_image': '2B', 'prime': 2}
  • id: 103176
    {'conductor': 22320, 'elladic_image': '3.4.0.1', 'lmfdb_label': '22320.bi4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 22320.bi does not appear in ec_padic