Elliptic curve data - 116160.gb6

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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': '116160cu', 'Clabel': '116160cu5', 'Cnumber': 5, 'abc_quality': 1.0072755098036974, 'absD': 20158700925906138562560, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 880, 'ainvs': [0, 1, 0, 6001439, -3824307841], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 116160, 'degree': 7864320, 'elladic_images': ['16.48.0.135'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9674829477352548083738876591', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 157, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [102949393183198, 86815346805], 'lmfdb_iso': '116160.gb', 'lmfdb_label': '116160.gb6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 12400, 355212], 'min_quad_twist_disc': -88, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.ba.2', '16.48.0-8.ba.2.7', '40.48.0.bk.2', '80.96.0.?', '88.48.0.?', '176.96.0.?', '220.12.0.?', '440.96.0.?', '880.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.0748969816853438983605499968', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 605], [3, 4, 38720], [5, 6, 23232], [11, 72, 960]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.78657680554281368133517036472', 'prec': 103}, 'szpiro_ratio': 5.010504682516689, '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, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, 6, 0, -4, 0], 'aplist': [0, 1, -1, 0, 0, -2, 6, -4, 0, 6, -8, -6, -10, -4, -8, 10, 12, 6, 4, 0, 14, 0, 4, -6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 116160, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '116160.gb', 'trace_hash': 1643475553340459784}
• 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': '0.0026453129701572776479438279822', 'prec': 110}, 'conductor': 116160, 'gens': [[650, 18753, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '7.0748969816853438983605499968', 'prec': 100}], 'lmfdb_label': '116160.gb6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.067147376358663657715324719450', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.6009723252479892774863647784257403955', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[601, 0, 1]], 'xcoord_integral_points': [601, 650]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [7, 0], '7': [3, 1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '116160.gb6'}
• ec_torsion_growth •

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

  
  
  • id: 5325850
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [4]}
  • id: 5325849
    {'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [2, 2]}
  • id: 5325851
    {'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '116160.gb6', 'torsion': [4]}
  • id: 5325854
    {'degree': 4, 'field': [3, -10, 11, -2, 1], 'lmfdb_label': '116160.gb6', 'torsion': [8]}
  • id: 5325852
    {'degree': 4, 'field': [64, 0, -6, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [2, 4]}
  • id: 5325853
    {'degree': 4, 'field': [419, 46, -45, -2, 1], 'lmfdb_label': '116160.gb6', 'torsion': [8]}
  • id: 5325859
    {'degree': 8, 'field': [-363, 0, -9394, 0, 66, 0, 0, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [6]}
  • id: 5325857
    {'degree': 8, 'field': [59, -172, 312, -304, 213, -76, 30, -4, 1], 'lmfdb_label': '116160.gb6', 'torsion': [2, 8]}
  • id: 5325855
    {'degree': 8, 'field': [4225, 0, 3100, 0, 560, 0, -20, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [2, 4]}
  • id: 5325856
    {'degree': 8, 'field': [25600, 0, 0, 0, 230, 0, 0, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [8]}
  • id: 5325858
    {'degree': 8, 'field': [656100, 0, -92880, 0, 5148, 0, -120, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [16]}
  • id: 5325862
    {'degree': 16, 'field': [-40111199, -1474299132, 491225664, 169768688, -39214524, -5165204, -1849288, 1475684, 355887, -106148, -19032, -1028, 1316, 224, -64, -4, 1], 'lmfdb_label': '116160.gb6', 'torsion': [16]}
  • id: 5325860
    {'degree': 16, 'field': [15876, -90720, 259200, -388800, 218884, 193760, 80000, -4160, 9781, 3640, 800, -560, -86, -40, 0, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [4, 4]}
  • id: 5325861
    {'degree': 16, 'field': [343396, -890720, 1155200, -840000, 432364, -207840, 112000, -24640, -6499, 1240, 800, 560, -6, -40, 0, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [2, 8]}
  • id: 5325864
    {'degree': 16, 'field': [7360369, 0, -8398924, 0, 493060, 0, 1120668, 0, 98070, 0, 1788, 0, -188, 0, 20, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [2, 6]}
  • id: 5325865
    {'degree': 16, 'field': [96059601, 0, -34930764, 0, 3175524, 0, -2997412, 0, 213686, 0, -14212, 0, 484, 0, -44, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [12]}
  • id: 5325863
    {'degree': 16, 'field': [365421456, 0, -183148128, 0, 35755992, 0, -3650832, 0, 295488, 0, -25272, 0, 1062, 0, 12, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [2, 16]}
  • id: 5325866
    {'degree': 16, 'field': [4809145104, 0, -1865273184, 0, 307858120, 0, -20806992, 0, 730605, 0, 15558, 0, -1698, 0, 0, 0, 1], 'lmfdb_label': '116160.gb6', 'torsion': [12]}
• 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: 2857631
    {'conductor': 116160, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '116160.gb6', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2857632
    {'conductor': 116160, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '116160.gb6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2857633
    {'conductor': 116160, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '116160.gb6', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2857634
    {'conductor': 116160, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '116160.gb6', 'prime': 11, '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: 2423455
    {'adelic_gens': [[204, 219, 281, 430], [192, 5, 835, 866], [15, 2, 782, 867], [1, 16, 0, 1], [559, 864, 72, 751], [5, 4, 876, 877], [1, 0, 16, 1], [126, 665, 725, 426], [865, 16, 864, 17]], 'adelic_image': '880.192.1.?', 'conductor': 116160, 'lmfdb_label': '116160.gb6', 'prime': 0}
  • id: 458416
    {'conductor': 116160, 'elladic_image': '16.48.0.135', 'lmfdb_label': '116160.gb6', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 6065914
    {'lmfdb_iso': '116160.gb', 'p': 13, 'prec': 20, 'unit': 1300301379419739987655, 'val': 1}
  • id: 6065916
    {'lmfdb_iso': '116160.gb', 'p': 17, 'prec': 20, 'unit': 75032529212400074189245, 'val': 1}
  • id: 6065917
    {'lmfdb_iso': '116160.gb', 'p': 19, 'prec': 20, 'unit': 151187043477410778662162, 'val': 1}
  • id: 6065913
    {'lmfdb_iso': '116160.gb', 'p': 29, 'prec': 20, 'unit': 4391682759476856305648623577, 'val': 1}
  • id: 6065923
    {'lmfdb_iso': '116160.gb', 'p': 31, 'prec': 20, 'unit': 10717902520492662255334909886, 'val': 1}
  • id: 6065910
    {'lmfdb_iso': '116160.gb', 'p': 37, 'prec': 20, 'unit': 295773406245969803088387255770, 'val': 1}
  • id: 6065911
    {'lmfdb_iso': '116160.gb', 'p': 41, 'prec': 20, 'unit': 1619325287696181057914145175288, 'val': 1}
  • id: 6065912
    {'lmfdb_iso': '116160.gb', 'p': 43, 'prec': 20, 'unit': 9674485406249187462773745644564, 'val': 1}
  • id: 6065915
    {'lmfdb_iso': '116160.gb', 'p': 47, 'prec': 20, 'unit': 34433627329823932597715121687819, 'val': 1}
  • id: 6065918
    {'lmfdb_iso': '116160.gb', 'p': 53, 'prec': 20, 'unit': 14266414488985085607223470371919, 'val': 1}
  • id: 6065921
    {'lmfdb_iso': '116160.gb', 'p': 59, 'prec': 20, 'unit': 4361633230426705321247981320333922, 'val': 1}
  • id: 6065922
    {'lmfdb_iso': '116160.gb', 'p': 61, 'prec': 20, 'unit': 5419092253139080134448276670808828, 'val': 1}
  • id: 6065909
    {'lmfdb_iso': '116160.gb', 'p': 67, 'prec': 20, 'unit': 2428859929565075506318527951219813, 'val': 1}
  • id: 6065919
    {'lmfdb_iso': '116160.gb', 'p': 73, 'prec': 20, 'unit': 133454997215685076188259687004008795, 'val': 1}
  • id: 6065908
    {'lmfdb_iso': '116160.gb', 'p': 83, 'prec': 20, 'unit': 1112655587597288567421425801708551516, 'val': 1}
  • id: 6065920
    {'lmfdb_iso': '116160.gb', 'p': 89, 'prec': 20, 'unit': 6891142642498465236392054456660277336, 'val': 1}
  • id: 6065907
    {'lmfdb_iso': '116160.gb', 'p': 97, 'prec': 20, 'unit': 22988456187716075098876680960020945215, 'val': 1}