Elliptic curve data - 81120.bs2

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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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '81120cb', 'Clabel': '81120cb3', 'Cnumber': 3, 'abc_quality': 1.0397263843855777, 'absD': 26064768600000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 1, 0, -83880, 5177628], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 81120, 'degree': 737280, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8481151189484322769037084684', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 44, 'isogeny_degrees': [1, 2, 4], 'jinv': [26410345352, 10546875], 'lmfdb_iso': '81120.bs', 'lmfdb_label': '81120.bs2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -496, -2204], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '24.24.0.bi.1', '104.24.0.?', '156.12.0.?', '312.48.0.?'], '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, 'serre_invariants': [[2, 4, 507], [3, 4, 27040], [5, 6, 16224], [13, 86, 480]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.045780054797704926814040656522', 'prec': 107}, 'szpiro_ratio': 4.036298175401815, '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, 4, 0, 0, 0, 1, 0, 2, 0, 4, 0], 'aplist': [0, 1, 1, -4, 4, 0, 2, 4, 0, 10, -4, 10, -2, 4, 8, 2, 12, -10, 12, 0, -10, 4, 4, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 81120, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '81120.bs', 'trace_hash': 478720591443156438}
• 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': '0.024816904178773055828461727216', 'prec': 107}, 'conductor': 81120, 'gens': [], 'heights': [], 'lmfdb_label': '81120.bs2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.34185509573860169617342864320', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1022611488632203540811437184035399839', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[251, 0, 1]], 'xcoord_integral_points': [251]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [3, 0], '13': 'a'}, 'iwp0': 5, 'lmfdb_label': '81120.bs2'}
• ec_torsion_growth •

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

  
  
  • id: 3814789
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [4]}
  • id: 3814790
    {'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [4]}
  • id: 3814788
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [2, 2]}
  • id: 3814791
    {'degree': 4, 'field': [25, 0, -16, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [2, 4]}
  • id: 3814795
    {'degree': 8, 'field': [-85683, 0, -35152, 0, 1014, 0, 0, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [6]}
  • id: 3814793
    {'degree': 8, 'field': [-3, 12, 120, -240, 61, 68, -18, -4, 1], 'lmfdb_label': '81120.bs2', 'torsion': [8]}
  • id: 3814792
    {'degree': 8, 'field': [4300, 3600, 1928, 384, 216, -24, 20, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [2, 4]}
  • id: 3814794
    {'degree': 8, 'field': [6137, 1240, -1456, -144, 222, -8, -16, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [8]}
  • id: 3814800
    {'degree': 16, 'field': [-6750, 51300, -44280, -41760, 183420, 17844, -21350, 119332, -10329, -12324, 4386, -1164, -288, -24, 36, -8, 1], 'lmfdb_label': '81120.bs2', 'torsion': [12]}
  • id: 3814797
    {'degree': 16, 'field': [433, 3132, -11028, -13500, 42976, 9648, -51336, 324, 26289, -1344, -6588, 252, 826, -12, -48, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [2, 8]}
  • id: 3814798
    {'degree': 16, 'field': [625, 0, 26400, 0, 1113736, 0, 60336, 0, 28455, 0, -3456, 0, 520, 0, -24, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [2, 8]}
  • id: 3814796
    {'degree': 16, 'field': [62500, -180000, 259200, -166080, -7604, 75168, 35712, 2112, 8541, 2856, 288, -432, -38, -24, 0, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [4, 4]}
  • id: 3814801
    {'degree': 16, 'field': [1102500, 0, -6066000, 0, 3061200, 0, -839816, 0, 140612, 0, -15776, 0, 1156, 0, -52, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [12]}
  • id: 3814799
    {'degree': 16, 'field': [485012529, 0, -153905184, 0, -35515908, 0, 956352, 0, 211830, 0, -9312, 0, 988, 0, 64, 0, 1], 'lmfdb_label': '81120.bs2', 'torsion': [2, 6]}
• 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: 1974086
    {'conductor': 81120, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '81120.bs2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1974087
    {'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '81120.bs2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1974088
    {'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '81120.bs2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 1974089
    {'conductor': 81120, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '81120.bs2', 'prime': 13, '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: 2198674
    {'adelic_gens': [[7, 6, 306, 307], [1, 0, 8, 1], [144, 65, 91, 222], [1, 8, 0, 1], [1, 4, 4, 17], [168, 247, 143, 12], [305, 8, 304, 9], [40, 195, 13, 170], [167, 0, 0, 311]], 'adelic_image': '312.48.0.?', 'conductor': 81120, 'lmfdb_label': '81120.bs2', 'prime': 0}
  • id: 332663
    {'conductor': 81120, 'elladic_image': '8.12.0.11', 'lmfdb_label': '81120.bs2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 81120.bs does not appear in ec_padic