Elliptic curve data - 32856.g4

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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': '32856c', 'Clabel': '32856c2', 'Cnumber': 2, 'abc_quality': 0.972547111469975, 'absD': 5911433646336, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 888, 'ainvs': [0, -1, 0, -5932, 133300], 'analytic_rank': 1, 'bad_primes': [2, 3, 37], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 32856, 'degree': 50688, 'elladic_images': ['8.48.0.138'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1601066702422549495250371587', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 4], 'jinv': [35152, 9], 'lmfdb_iso': '32856.g', 'lmfdb_label': '32856.g4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -4, 4], 'min_quad_twist_disc': 37, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.h.1', '12.24.0.c.1', '24.96.1.bu.1', '148.24.0.?', '296.96.0.?', '444.48.0.?', '888.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.8020958651816916324731044493', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1369], [3, 4, 10952], [37, 686, 24]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1074504064531541456038320911', 'prec': 103}, 'szpiro_ratio': 3.622934758211498, '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, -1, 0, 2, 0, 0, 0, 1, 0, 4, 0, 2, 0, -2, 0, -2, 0, 4, 0], 'aplist': [0, -1, 2, 0, 4, 2, -2, 4, 8, -6, -8, 0, -6, -4, 0, -2, -4, 2, -4, 8, 10, 8, -4, 6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 32856, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '32856.g', 'trace_hash': 1966660673645980500}
• 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': '0.098252622106255104880067387412', 'prec': 107}, 'conductor': 32856, 'gens': [[3253, 353430, 13]], 'heights': [{'__RealLiteral__': 0, 'data': '8.8020958651816916324731044493', 'prec': 100}], 'lmfdb_label': '32856.g4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.70905797711419640468187225398', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.2411962885309627078281298861691228621', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[25, 0, 1], [62, 0, 1]], 'xcoord_integral_points': [-86, 25, 62]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': 'a', '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '32856.g4'}
• ec_torsion_growth •

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

  
  
  • id: 1636337
    {'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '32856.g4', 'torsion': [2, 4]}
  • id: 1636339
    {'degree': 4, 'field': [100, 0, 17, 0, 1], 'lmfdb_label': '32856.g4', 'torsion': [2, 4]}
  • id: 1636338
    {'degree': 4, 'field': [1369, 0, -37, 0, 1], 'lmfdb_label': '32856.g4', 'torsion': [2, 4]}
  • id: 1636341
    {'degree': 8, 'field': [1825, 2380, -1808, -1100, 441, 128, -38, -4, 1], 'lmfdb_label': '32856.g4', 'torsion': [2, 8]}
  • id: 1636340
    {'degree': 8, 'field': [6561, 0, -1539, 0, 280, 0, -19, 0, 1], 'lmfdb_label': '32856.g4', 'torsion': [4, 4]}
  • id: 1636342
    {'degree': 8, 'field': [6561, 0, 0, 0, 199, 0, 0, 0, 1], 'lmfdb_label': '32856.g4', 'torsion': [2, 8]}
  • id: 1636343
    {'degree': 8, 'field': [8038, -3512, 4052, -1118, 655, -118, 44, -4, 1], 'lmfdb_label': '32856.g4', 'torsion': [2, 8]}
  • id: 1636344
    {'degree': 8, 'field': [19658, -106604, 34898, -6494, 1250, -56, 4, -4, 1], 'lmfdb_label': '32856.g4', 'torsion': [2, 6]}
  • id: 1636348
    {'degree': 16, 'field': [28087949, 13105854, -28046836, -6537602, 13429724, 1252486, -3501684, -104960, 534627, 2272, -49266, 172, 2692, -8, -80, 0, 1], 'lmfdb_label': '32856.g4', 'torsion': [2, 12]}
  • id: 1636347
    {'degree': 16, 'field': [43046721, 0, 0, 0, -1305639, 0, 0, 0, 33040, 0, 0, 0, -199, 0, 0, 0, 1], 'lmfdb_label': '32856.g4', 'torsion': [4, 8]}
  • id: 1636346
    {'degree': 16, 'field': [64609444, 0, -52805808, 0, 19095652, 0, -3936708, 0, 509733, 0, -42876, 0, 2302, 0, -72, 0, 1], 'lmfdb_label': '32856.g4', 'torsion': [4, 8]}
  • id: 1636345
    {'degree': 16, 'field': [8903243449, 0, -4455843636, 0, 964233130, 0, -116068368, 0, 8450499, 0, -380496, 0, 10354, 0, -156, 0, 1], 'lmfdb_label': '32856.g4', 'torsion': [2, 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: 769608
    {'conductor': 32856, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '32856.g4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 769609
    {'conductor': 32856, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '32856.g4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 769610
    {'conductor': 32856, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '32856.g4', 'prime': 37, '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: 1883762
    {'adelic_gens': [[881, 8, 880, 9], [479, 0, 0, 887], [1, 0, 8, 1], [593, 0, 592, 149], [5, 4, 884, 885], [815, 74, 222, 667], [149, 296, 814, 75], [1, 8, 0, 1]], 'adelic_image': '888.192.1.?', 'conductor': 32856, 'lmfdb_label': '32856.g4', 'prime': 0}
  • id: 146905
    {'conductor': 32856, 'elladic_image': '8.48.0.138', 'lmfdb_label': '32856.g4', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1603076
    {'lmfdb_iso': '32856.g', 'p': 5, 'prec': 20, 'unit': 1377393964757, 'val': 1}
  • id: 1603083
    {'lmfdb_iso': '32856.g', 'p': 11, 'prec': 20, 'unit': 41878043982310073063, 'val': 1}
  • id: 1603081
    {'lmfdb_iso': '32856.g', 'p': 13, 'prec': 20, 'unit': 27040281743182634399, 'val': 1}
  • id: 1603084
    {'lmfdb_iso': '32856.g', 'p': 17, 'prec': 20, 'unit': 2227170654919786811306, 'val': 1}
  • id: 1603085
    {'lmfdb_iso': '32856.g', 'p': 19, 'prec': 20, 'unit': 536705377187828183731546, 'val': 1}
  • id: 1603088
    {'lmfdb_iso': '32856.g', 'p': 23, 'prec': 20, 'unit': 54871502179092704994212560, 'val': 1}
  • id: 1603080
    {'lmfdb_iso': '32856.g', 'p': 29, 'prec': 20, 'unit': 6010365095740580043150513394, 'val': 1}
  • id: 1603092
    {'lmfdb_iso': '32856.g', 'p': 31, 'prec': 20, 'unit': 17892490476494558229193374739, 'val': 1}
  • id: 1603078
    {'lmfdb_iso': '32856.g', 'p': 41, 'prec': 20, 'unit': 4252186032349501391967594829923, 'val': 1}
  • id: 1603079
    {'lmfdb_iso': '32856.g', 'p': 43, 'prec': 20, 'unit': 5682750366147771935452086247171, 'val': 1}
  • id: 1603086
    {'lmfdb_iso': '32856.g', 'p': 53, 'prec': 20, 'unit': 956504284691340077600686070855, 'val': 1}
  • id: 1603090
    {'lmfdb_iso': '32856.g', 'p': 59, 'prec': 20, 'unit': 434454626265418026545531226500565, 'val': 1}
  • id: 1603091
    {'lmfdb_iso': '32856.g', 'p': 61, 'prec': 20, 'unit': 5846062293545583126107500634313325, 'val': 1}
  • id: 1603075
    {'lmfdb_iso': '32856.g', 'p': 67, 'prec': 20, 'unit': 8092341033200468766059905732583306, 'val': 1}
  • id: 1603077
    {'lmfdb_iso': '32856.g', 'p': 71, 'prec': 20, 'unit': 8891038707124616596416644479711626, 'val': 1}
  • id: 1603087
    {'lmfdb_iso': '32856.g', 'p': 73, 'prec': 20, 'unit': 18475039283101518235309336893580116, 'val': 1}
  • id: 1603082
    {'lmfdb_iso': '32856.g', 'p': 79, 'prec': 20, 'unit': 202696677559591092389635763751339353, 'val': 1}
  • id: 1603074
    {'lmfdb_iso': '32856.g', 'p': 83, 'prec': 20, 'unit': 2618731020600025468408910979876719394, 'val': 1}
  • id: 1603089
    {'lmfdb_iso': '32856.g', 'p': 89, 'prec': 20, 'unit': 10111138401581860902907847171183502015, 'val': 1}
  • id: 1603073
    {'lmfdb_iso': '32856.g', 'p': 97, 'prec': 20, 'unit': 6647570911633343059954248277565680314, 'val': 1}