Elliptic curve data - 85176.n5

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '85176bw', 'Clabel': '85176bw2', 'Cnumber': 2, 'abc_quality': 0.9686459833518319, 'absD': 45031944984295758338304, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2184, 'ainvs': [0, 0, 0, -17163471, 25393123730], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 85176, 'degree': 6193152, 'elladic_images': ['8.24.0.14'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0899223692334831764069512788', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 4], 'jinv': [620742479063632, 49991146569], 'lmfdb_iso': '85176.n', 'lmfdb_label': '85176.n5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -11284, -424316], 'min_quad_twist_disc': -39, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0-4.b.1.10', '12.24.0.c.1', '24.48.0-12.c.1.5', '52.24.0-4.b.1.2', '56.48.0-56.h.1.25', '104.48.0.?', '156.48.0.?', '168.96.0.?', '312.96.0.?', '728.96.0.?', '2184.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.5185536236286439256278480876', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1521], [3, 6, 9464], [7, 8, 12168], [13, 98, 504]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.79604342579536308973776352525', 'prec': 103}, 'szpiro_ratio': 5.425115213895803, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -2, 0, -1, 0, 0, 0, -4, 0, 0, 0, 0, 0, 6, 0, -4, 0], 'aplist': [0, 0, -2, -1, -4, 0, 6, -4, 0, -6, 0, -6, -6, 4, 0, 2, 4, -2, -4, 0, 6, 8, 12, 10, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 85176, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '85176.n', 'trace_hash': 824928315652309540}
• 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': '0.0020707493373993141048259775620', 'prec': 110}, 'conductor': 85176, 'gens': [[1603, 44712, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.5185536236286439256278480876', 'prec': 100}], 'lmfdb_label': '85176.n5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.11110272260306634994870947501', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0161888785047479852420843331621349548', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[1846, 0, 1], [2899, 0, 1]], 'xcoord_integral_points': [-4745, 1603, 1846, 2899, 30407]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '85176.n5'}
• ec_torsion_growth •

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

  
  
  • id: 3993905
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '85176.n5', 'torsion': [2, 4]}
  • id: 3993907
    {'degree': 4, 'field': [-3, 12, -11, -2, 1], 'lmfdb_label': '85176.n5', 'torsion': [2, 4]}
  • id: 3993906
    {'degree': 4, 'field': [169, 0, -13, 0, 1], 'lmfdb_label': '85176.n5', 'torsion': [2, 4]}
  • id: 3993908
    {'degree': 8, 'field': [81, 0, -63, 0, 40, 0, -7, 0, 1], 'lmfdb_label': '85176.n5', 'torsion': [4, 4]}
  • id: 3993909
    {'degree': 8, 'field': [79524, 0, -10788, 0, 1093, 0, -46, 0, 1], 'lmfdb_label': '85176.n5', 'torsion': [2, 8]}
  • id: 3993911
    {'degree': 8, 'field': [84594, 9240, 4170, 4230, -204, 168, 32, -2, 1], 'lmfdb_label': '85176.n5', 'torsion': [2, 6]}
  • id: 3993910
    {'degree': 8, 'field': [614656, 0, 0, 0, -343, 0, 0, 0, 1], 'lmfdb_label': '85176.n5', 'torsion': [2, 8]}
  • id: 3993913
    {'degree': 16, 'field': [4356, 0, -20880, 0, -2220, 0, -4980, 0, 11893, 0, -4300, 0, 606, 0, -40, 0, 1], 'lmfdb_label': '85176.n5', 'torsion': [2, 8]}
  • id: 3993912
    {'degree': 16, 'field': [994009, 0, 1447620, 0, 1235578, 0, 556032, 0, 136371, 0, 18912, 0, 1474, 0, 60, 0, 1], 'lmfdb_label': '85176.n5', 'torsion': [2, 8]}
  • id: 3993915
    {'degree': 16, 'field': [2898208, -1358112, 5321984, -2520064, 3668368, -2604368, 1396824, -870976, 434868, -170488, 62148, -14948, 1468, 104, -10, -6, 1], 'lmfdb_label': '85176.n5', 'torsion': [2, 12]}
  • id: 3993914
    {'degree': 16, 'field': [16008001, -7409852, -4588100, -1374824, 3007115, -23768, -137952, -167312, 45872, -9628, 4566, 452, 47, -40, 22, -4, 1], 'lmfdb_label': '85176.n5', 'torsion': [4, 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: 2077339
    {'conductor': 85176, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '85176.n5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2077340
    {'conductor': 85176, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '85176.n5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2077341
    {'conductor': 85176, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '85176.n5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2077342
    {'conductor': 85176, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '85176.n5', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2225155
    {'adelic_gens': [[2177, 8, 2176, 9], [1, 0, 8, 1], [721, 2182, 18, 5], [1, 8, 0, 1], [3, 1642, 8, 557], [5, 4, 2180, 2181], [167, 2176, 668, 2151], [1249, 4, 0, 1], [1097, 548, 548, 1093]], 'adelic_image': '2184.192.1.?', 'conductor': 85176, 'lmfdb_label': '85176.n5', 'prime': 0}
  • id: 347699
    {'conductor': 85176, 'elladic_image': '8.24.0.14', 'lmfdb_label': '85176.n5', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 4397786
    {'lmfdb_iso': '85176.n', 'p': 5, 'prec': 20, 'unit': 4537848235938, 'val': 1}
  • id: 4397778
    {'lmfdb_iso': '85176.n', 'p': 11, 'prec': 20, 'unit': 32110987228232459300, 'val': 1}
  • id: 4397779
    {'lmfdb_iso': '85176.n', 'p': 17, 'prec': 20, 'unit': 38245637054516292265487, 'val': 1}
  • id: 4397780
    {'lmfdb_iso': '85176.n', 'p': 19, 'prec': 20, 'unit': 15323987267107235633350, 'val': 2}
  • id: 4397776
    {'lmfdb_iso': '85176.n', 'p': 29, 'prec': 20, 'unit': 5274993261497372621884013078, 'val': 1}
  • id: 4397773
    {'lmfdb_iso': '85176.n', 'p': 37, 'prec': 20, 'unit': 442406867151114872475404493229, 'val': 1}
  • id: 4397774
    {'lmfdb_iso': '85176.n', 'p': 41, 'prec': 20, 'unit': 3212100296508341497388750298738, 'val': 1}
  • id: 4397775
    {'lmfdb_iso': '85176.n', 'p': 43, 'prec': 20, 'unit': 9492640784575877407997397942937, 'val': 1}
  • id: 4397781
    {'lmfdb_iso': '85176.n', 'p': 53, 'prec': 20, 'unit': 508154796920566071422693924908942, 'val': 1}
  • id: 4397784
    {'lmfdb_iso': '85176.n', 'p': 59, 'prec': 20, 'unit': 816985959044578117713616331957063, 'val': 1}
  • id: 4397785
    {'lmfdb_iso': '85176.n', 'p': 61, 'prec': 20, 'unit': 88139772768352783521021512095159, 'val': 1}
  • id: 4397772
    {'lmfdb_iso': '85176.n', 'p': 67, 'prec': 20, 'unit': 23870860741585579477166541659872133, 'val': 1}
  • id: 4397782
    {'lmfdb_iso': '85176.n', 'p': 73, 'prec': 20, 'unit': 170036093371145048667249531737413528, 'val': 1}
  • id: 4397777
    {'lmfdb_iso': '85176.n', 'p': 79, 'prec': 20, 'unit': 668463576170474208747222422834106317, 'val': 1}
  • id: 4397771
    {'lmfdb_iso': '85176.n', 'p': 83, 'prec': 20, 'unit': 1942402013486540694764596743297215522, 'val': 1}
  • id: 4397783
    {'lmfdb_iso': '85176.n', 'p': 89, 'prec': 20, 'unit': 1161383552235724518874812191830907280, 'val': 1}
  • id: 4397770
    {'lmfdb_iso': '85176.n', 'p': 97, 'prec': 20, 'unit': 3056725011575656431881316221307319169, 'val': 1}