Elliptic curve data - 3192.f2

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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': '3192e', 'Clabel': '3192e1', 'Cnumber': 1, 'abc_quality': 0.8527708231252141, 'absD': 849072, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1596, 'ainvs': [0, -1, 0, -43, -104], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 3192, 'degree': 384, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.12043165117289994451131843658', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [-562432000, 53067], 'lmfdb_iso': '3192.f', 'lmfdb_label': '3192.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -43, -104], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '532.6.0.?', '1596.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5996686060265964694759331783', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 4, 1064], [7, 8, 456], [19, 20, 168]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.35148071135954838098372914373', 'prec': 107}, 'szpiro_ratio': 2.8594764319764523, '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, 0, 0, 1, 0, 1, 0, -4, 0, 2, 0, 0, 0, 0, 0, 1, 0], 'aplist': [0, -1, 0, 1, -4, 2, 0, 1, 0, 8, -8, -10, 2, 4, -2, 12, -4, -10, -8, 6, 6, -16, 6, -6, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 3192, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '3192.f', 'trace_hash': 613389108692964687}
• 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': '1.2723470965565626820697092734', 'prec': 100}, 'conductor': 3192, 'gens': [[15, 49, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5996686060265964694759331783', 'prec': 100}], 'lmfdb_label': '3192.f2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.92542310416606766708408506763', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9607405740522784896966931874589797662', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[8, 0, 1]], 'xcoord_integral_points': [8, 15, 27]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [2, 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': '3192.f2'}
• ec_torsion_growth •

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

  
  
  • id: 166470
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '3192.f2', 'torsion': [2, 2]}
  • id: 166471
    {'degree': 4, 'field': [-27, 0, 5, 0, 1], 'lmfdb_label': '3192.f2', 'torsion': [4]}
  • id: 166474
    {'degree': 8, 'field': [-50700, 0, -12788, 0, -780, 0, 0, 0, 1], 'lmfdb_label': '3192.f2', 'torsion': [6]}
  • id: 166472
    {'degree': 8, 'field': [729, 0, 135, 0, 52, 0, -5, 0, 1], 'lmfdb_label': '3192.f2', 'torsion': [2, 4]}
  • id: 166473
    {'degree': 8, 'field': [961, -434, 254, 166, 115, 26, -16, -4, 1], 'lmfdb_label': '3192.f2', 'torsion': [2, 4]}
  • id: 166476
    {'degree': 16, 'field': [729, 0, -14904, 0, 305190, 0, 9936, 0, 351, 0, -1104, 0, -18, 0, 0, 0, 1], 'lmfdb_label': '3192.f2', 'torsion': [2, 6]}
  • id: 166475
    {'degree': 16, 'field': [60417, 320754, -1069768, 1931090, -2144345, 1690276, -1042272, 448392, -157898, 27754, -2352, -2296, 868, -252, 56, -8, 1], 'lmfdb_label': '3192.f2', 'torsion': [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: 57651
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '3192.f2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57652
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.f2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 57653
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3192.f2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 57654
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3192.f2', 'prime': 19, '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: 1684732
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [913, 4, 230, 9], [1, 4, 0, 1], [1066, 1, 1063, 0], [1593, 4, 1592, 5], [401, 1198, 1196, 399], [1009, 4, 422, 9]], 'adelic_image': '1596.12.0.?', 'conductor': 3192, 'lmfdb_label': '3192.f2', 'prime': 0}
  • id: 16003
    {'conductor': 3192, 'elladic_image': '2.3.0.1', 'lmfdb_label': '3192.f2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 104734
    {'lmfdb_iso': '3192.f', 'p': 11, 'prec': 20, 'unit': 25524140087454261158, 'val': 1}
  • id: 104740
    {'lmfdb_iso': '3192.f', 'p': 13, 'prec': 20, 'unit': 1360872605794884782804, 'val': 1}
  • id: 104739
    {'lmfdb_iso': '3192.f', 'p': 29, 'prec': 20, 'unit': 3369411229400889271697438406, 'val': 1}
  • id: 104749
    {'lmfdb_iso': '3192.f', 'p': 31, 'prec': 20, 'unit': 1605550706710102192323844168, 'val': 1}
  • id: 104735
    {'lmfdb_iso': '3192.f', 'p': 37, 'prec': 20, 'unit': 191096431642029372597873087878, 'val': 1}
  • id: 104737
    {'lmfdb_iso': '3192.f', 'p': 41, 'prec': 20, 'unit': 1430399677421875279022863572125, 'val': 1}
  • id: 104738
    {'lmfdb_iso': '3192.f', 'p': 43, 'prec': 20, 'unit': 4453179543140906450435827928035, 'val': 1}
  • id: 104747
    {'lmfdb_iso': '3192.f', 'p': 47, 'prec': 20, 'unit': 43581578574392715062458441607713, 'val': 1}
  • id: 104744
    {'lmfdb_iso': '3192.f', 'p': 53, 'prec': 20, 'unit': 305720514849799882266291920921273, 'val': 1}
  • id: 104742
    {'lmfdb_iso': '3192.f', 'p': 59, 'prec': 20, 'unit': 4134278320014959207454777136334649, 'val': 1}
  • id: 104748
    {'lmfdb_iso': '3192.f', 'p': 61, 'prec': 20, 'unit': 7209009333028531110958096999299499, 'val': 1}
  • id: 104743
    {'lmfdb_iso': '3192.f', 'p': 67, 'prec': 20, 'unit': 33125744080460485969485241468587028, 'val': 1}
  • id: 104736
    {'lmfdb_iso': '3192.f', 'p': 71, 'prec': 20, 'unit': 110110098883746937561544537823695216, 'val': 1}
  • id: 104745
    {'lmfdb_iso': '3192.f', 'p': 73, 'prec': 20, 'unit': 71110003386660062631579046122895810, 'val': 1}
  • id: 104741
    {'lmfdb_iso': '3192.f', 'p': 79, 'prec': 20, 'unit': 983920067272543914328233027701574468, 'val': 1}
  • id: 104733
    {'lmfdb_iso': '3192.f', 'p': 83, 'prec': 20, 'unit': 905366770744561860316124905911364680, 'val': 1}
  • id: 104746
    {'lmfdb_iso': '3192.f', 'p': 89, 'prec': 20, 'unit': 7371075101610467979085416318540321408, 'val': 1}
  • id: 104732
    {'lmfdb_iso': '3192.f', 'p': 97, 'prec': 20, 'unit': 36663363308504893271339662821979312250, 'val': 1}