Elliptic curve data - 20160.cz2

Formats: - HTML - YAML - JSON - 2025-09-18T14:08:57.438482

• 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': '20160ce', 'Clabel': '20160ce5', 'Cnumber': 5, 'abc_quality': 1.05504045380176, 'absD': 24787589110824960000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 1680, 'ainvs': [0, 0, 0, -69148812, 221322182384], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 20160, 'degree': 1572864, 'elladic_images': ['8.96.0.30'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0368827417895632020678929873', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 77, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [191342053882402567201, 129708022500], 'lmfdb_iso': '20160.cz', 'lmfdb_label': '20160.cz2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -120050, -16020000], 'min_quad_twist_disc': -24, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.2', '8.96.0-8.l.1.4', '24.192.1-24.ch.1.6', '80.192.2.?', '112.192.1.?', '240.384.5.?', '336.384.5.?', '560.384.5.?', '1680.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.5797976132659891807376011446', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 2240], [5, 6, 4032], [7, 8, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4478558266155903922444221867', 'prec': 100}, 'szpiro_ratio': 6.635646587530232, '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, 1, 0, -1, 0, 0, 0, -4, 0, 2, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, 1, -1, -4, 2, -2, -4, 8, -2, 0, -6, 6, 4, 0, -10, 12, -14, 12, 8, 10, 16, -12, -10, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 20160, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '20160.cz', 'trace_hash': 1092166393215764486}
• 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': '0.0023024868901910385165371755581', 'prec': 110}, 'conductor': 20160, 'gens': [[4813, 1395, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.5797976132659891807376011446', 'prec': 100}], 'lmfdb_label': '20160.cz2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.17591536181282028267544024892', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.0379311388348558694982160760296695746', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[4798, 0, 1], [4804, 0, 1]], 'xcoord_integral_points': [-9602, -962, 4798, 4804, 4813, 14408]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [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': '20160.cz2'}
• ec_torsion_growth •

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

  
  
  • id: 1028478
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 4]}
  • id: 1028479
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 4]}
  • id: 1028482
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 8]}
  • id: 1028480
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [4, 4]}
  • id: 1028481
    {'degree': 4, 'field': [150, 0, 0, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 8]}
  • id: 1028486
    {'degree': 8, 'field': [-3888, 0, 2022, 0, -216, 0, 0, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 6]}
  • id: 1028483
    {'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [4, 8]}
  • id: 1028484
    {'degree': 8, 'field': [22201, 0, 1804, 0, -294, 0, 4, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [4, 8]}
  • id: 1028485
    {'degree': 8, 'field': [22801, 0, -1796, 0, 306, 0, 4, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [4, 8]}
  • id: 1028490
    {'degree': 16, 'field': [-309599, 2999400, -3929780, -4602000, 6361504, 1878000, -3031660, -324000, 642681, 24000, -68480, -600, 3754, 0, -100, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 16]}
  • id: 1028488
    {'degree': 16, 'field': [54586, 170128, 216360, -799120, 483140, -154896, 153832, -111440, 61005, -27560, 11452, -3864, 1190, -280, 60, -8, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 16]}
  • id: 1028492
    {'degree': 16, 'field': [263169, 0, -1737936, 0, -397548, 0, -102492, 0, -2430, 0, 1152, 0, 208, 0, -4, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 12]}
  • id: 1028491
    {'degree': 16, 'field': [291600, 0, 1312200, 0, -140940, 0, 96984, 0, 4644, 0, 684, 0, 328, 0, 20, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 12]}
  • id: 1028489
    {'degree': 16, 'field': [4693726, -11221304, 20172156, -21205496, 19494698, -12506264, 7427204, -3201368, 1336503, -398104, 121676, -24728, 5638, -728, 124, -8, 1], 'lmfdb_label': '20160.cz2', 'torsion': [2, 16]}
  • id: 1028487
    {'degree': 16, 'field': [31640625, 0, -25312500, 0, 10125000, 0, -2700000, 0, 444375, 0, -36000, 0, 1800, 0, -60, 0, 1], 'lmfdb_label': '20160.cz2', 'torsion': [8, 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: 456947
    {'conductor': 20160, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '20160.cz2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 456948
    {'conductor': 20160, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '20160.cz2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 456949
    {'conductor': 20160, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '20160.cz2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 456950
    {'conductor': 20160, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '20160.cz2', 'prime': 7, '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: 1798685
    {'adelic_gens': [[1671, 1664, 926, 1335], [489, 8, 1156, 1641], [1, 16, 0, 1], [1353, 16, 1076, 121], [1, 0, 16, 1], [1679, 1664, 1674, 1163], [1, 16, 6, 1567], [1, 16, 4, 65], [1665, 16, 1664, 17]], 'adelic_image': '1680.768.13.?', 'conductor': 20160, 'lmfdb_label': '20160.cz2', 'prime': 0}
  • id: 93878
    {'conductor': 20160, 'elladic_image': '8.96.0.30', 'lmfdb_label': '20160.cz2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 936898
    {'lmfdb_iso': '20160.cz', 'p': 11, 'prec': 20, 'unit': 30838997333419817013, 'val': 1}
  • id: 936896
    {'lmfdb_iso': '20160.cz', 'p': 13, 'prec': 20, 'unit': 698724450840601508904, 'val': 1}
  • id: 936899
    {'lmfdb_iso': '20160.cz', 'p': 17, 'prec': 20, 'unit': 203159811650930029075692, 'val': 1}
  • id: 936900
    {'lmfdb_iso': '20160.cz', 'p': 19, 'prec': 20, 'unit': 1391111612523225643461252, 'val': 1}
  • id: 936903
    {'lmfdb_iso': '20160.cz', 'p': 23, 'prec': 20, 'unit': 50356405141448092344469898, 'val': 1}
  • id: 936895
    {'lmfdb_iso': '20160.cz', 'p': 29, 'prec': 20, 'unit': 1156837698864905078369345911, 'val': 1}
  • id: 936891
    {'lmfdb_iso': '20160.cz', 'p': 37, 'prec': 20, 'unit': 365829890954981043618339756851, 'val': 1}
  • id: 936893
    {'lmfdb_iso': '20160.cz', 'p': 41, 'prec': 20, 'unit': 2109442960294498159123608553201, 'val': 1}
  • id: 936894
    {'lmfdb_iso': '20160.cz', 'p': 43, 'prec': 20, 'unit': 7779617090689689044577411774708, 'val': 1}
  • id: 936901
    {'lmfdb_iso': '20160.cz', 'p': 53, 'prec': 20, 'unit': 299244648049623172508854600040925, 'val': 1}
  • id: 936905
    {'lmfdb_iso': '20160.cz', 'p': 59, 'prec': 20, 'unit': 275307569242714969172263944706262, 'val': 1}
  • id: 936906
    {'lmfdb_iso': '20160.cz', 'p': 61, 'prec': 20, 'unit': 4575967700636244071393806599304172, 'val': 1}
  • id: 936890
    {'lmfdb_iso': '20160.cz', 'p': 67, 'prec': 20, 'unit': 2591727742433612076759927066334701, 'val': 1}
  • id: 936892
    {'lmfdb_iso': '20160.cz', 'p': 71, 'prec': 20, 'unit': 99309684580780867848019216012492659, 'val': 1}
  • id: 936902
    {'lmfdb_iso': '20160.cz', 'p': 73, 'prec': 20, 'unit': 250030924723283137322372965999609462, 'val': 1}
  • id: 936897
    {'lmfdb_iso': '20160.cz', 'p': 79, 'prec': 20, 'unit': 1116582320056957360281927999278924971, 'val': 1}
  • id: 936889
    {'lmfdb_iso': '20160.cz', 'p': 83, 'prec': 20, 'unit': 907416542303229547278224197279196126, 'val': 1}
  • id: 936904
    {'lmfdb_iso': '20160.cz', 'p': 89, 'prec': 20, 'unit': 5514432451192752819655378993338993746, 'val': 1}
  • id: 936888
    {'lmfdb_iso': '20160.cz', 'p': 97, 'prec': 20, 'unit': 31698432641202424765855701748721498207, 'val': 1}