Elliptic curve data - 20160.cz8

Formats: - HTML - YAML - JSON - 2024-06-03T09:45:36.053591

• 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': '20160ce', 'Clabel': '20160ce6', 'Cnumber': 6, 'abc_quality': 1.1083142308531486, 'absD': 51438240000000000000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [0, 0, 0, 731508, 10909262576], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 20160, 'degree': 1572864, 'elladic_images': ['16.96.0.191'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0368827417895632020678929873', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 77, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [226523624554079, 269165039062500], 'lmfdb_iso': '20160.cz', 'lmfdb_label': '20160.cz8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1270, -789048], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0-8.q.1.4', '16.96.0-16.j.1.6', '24.96.0-24.be.1.3', '48.192.1-48.bf.2.5', '56.96.0-56.bd.1.9', '84.24.0.?', '112.192.1.?', '160.192.2.?', '168.192.1.?', '336.384.5.?', '480.384.5.?', '1120.384.5.?', '3360.768.13.?'], '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': '0.89494940331649729518440028616', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4478558266155903922444221867', 'prec': 100}, 'szpiro_ratio': 6.028267017300838, '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, -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': [[-1858, 56000, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.89494940331649729518440028616', 'prec': 103}], 'lmfdb_label': '20160.cz8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.087957680906410141337720124459', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.0379311388348558694982160760296695746', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[-2108, 0, 1]], 'xcoord_integral_points': [-2108, -1858, -1208, 13517, 54142]}
• 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.cz8'}
• ec_torsion_growth •

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

  
  
  • id: 1028494
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [4]}
  • id: 1028493
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [2, 2]}
  • id: 1028495
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [8]}
  • id: 1028497
    {'degree': 4, 'field': [4, 0, -10, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [8]}
  • id: 1028496
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [2, 8]}
  • id: 1028499
    {'degree': 4, 'field': [24, 0, 0, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [16]}
  • id: 1028498
    {'degree': 4, 'field': [25, 0, 4, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [8]}
  • id: 1028503
    {'degree': 8, 'field': [-3888, 0, 2022, 0, -216, 0, 0, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [6]}
  • id: 1028500
    {'degree': 8, 'field': [1, 0, 0, 0, 23, 0, 0, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [4, 8]}
  • id: 1028501
    {'degree': 8, 'field': [25, 0, 76, 0, -6, 0, 4, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [2, 16]}
  • id: 1028502
    {'degree': 8, 'field': [87025, 0, -3524, 0, 594, 0, 4, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [2, 16]}
  • id: 1028505
    {'degree': 16, 'field': [2401, 0, 0, 0, -74088, 0, 0, 0, 7154, 0, 0, 0, -168, 0, 0, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [16]}
  • id: 1028506
    {'degree': 16, 'field': [2401, 0, 0, 0, 74088, 0, 0, 0, 7154, 0, 0, 0, 168, 0, 0, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [16]}
  • id: 1028504
    {'degree': 16, 'field': [30625, 0, 0, 8400, -12974, -2952, 1152, -1248, 2391, 1416, 288, 288, 22, -24, 0, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [4, 16]}
  • id: 1028509
    {'degree': 16, 'field': [263169, 0, -1737936, 0, -397548, 0, -102492, 0, -2430, 0, 1152, 0, 208, 0, -4, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [12]}
  • id: 1028510
    {'degree': 16, 'field': [291600, 0, 1312200, 0, -140940, 0, 96984, 0, 4644, 0, 684, 0, 328, 0, 20, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [24]}
  • id: 1028508
    {'degree': 16, 'field': [455625, 0, 0, 0, -121500, 0, 0, 0, 6750, 0, 0, 0, 196, 0, 0, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [2, 6]}
  • id: 1028507
    {'degree': 16, 'field': [1382976, 0, 0, 0, -2145024, 0, 0, 0, 1698096, 0, 0, 0, -1824, 0, 0, 0, 1], 'lmfdb_label': '20160.cz8', 'torsion': [32]}
• 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: 456951
    {'conductor': 20160, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '20160.cz8', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 456952
    {'conductor': 20160, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '20160.cz8', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 456953
    {'conductor': 20160, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '20160.cz8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 456954
    {'conductor': 20160, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '20160.cz8', '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: 1798691
    {'adelic_gens': [[2017, 16, 0, 1], [3359, 3352, 0, 2939], [1, 0, 32, 1], [25, 16, 1624, 2249], [1, 32, 0, 1], [7, 16, 2775, 793], [985, 16, 1974, 2473], [1091, 3336, 3234, 475], [3329, 32, 3328, 33], [1, 32, 4, 129]], 'adelic_image': '3360.768.13.?', 'conductor': 20160, 'lmfdb_label': '20160.cz8', 'prime': 0}
  • id: 93884
    {'conductor': 20160, 'elladic_image': '16.96.0.191', 'lmfdb_label': '20160.cz8', 'modell_image': '2B', '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}