Elliptic curve data - 3192.i3

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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': '3192a', 'Clabel': '3192a1', 'Cnumber': 1, 'abc_quality': 0.8528219859240784, 'absD': 172368, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3192, 'ainvs': [0, -1, 0, -47, -108], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3192, 'degree': 512, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.19195445960494039801835823489', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2, 4], 'jinv': [733001728, 10773], 'lmfdb_iso': '3192.i', 'lmfdb_label': '3192.i3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -47, -108], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.3', '28.12.0-4.c.1.2', '76.12.0.?', '168.24.0.?', '266.6.0.?', '456.24.0.?', '532.24.0.?', '3192.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 133], [3, 4, 1064], [7, 8, 456], [19, 20, 168]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.42300351979158883449076894204', 'prec': 107}, 'szpiro_ratio': 2.873585697017941, '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, 2, 0, -1, 0, 1, 0, 4, 0, -6, 0, -2, 0, 6, 0, 1, 0], 'aplist': [0, -1, 2, -1, 4, -6, 6, 1, 8, -6, 0, -2, 6, -4, 4, 2, 12, -10, 8, 0, 10, -12, 16, 6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 3192, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '3192.i', 'trace_hash': 944336970067489027}
• 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': '1.4680117279246208492848207132', 'prec': 100}, 'conductor': 3192, 'gens': [], 'heights': [], 'lmfdb_label': '3192.i3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.8217734478845659963623206492', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8217734478845659963623206491955261482', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-4, 0, 1]], 'xcoord_integral_points': [-4]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '7': [0, 0], '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '3192.i3'}
• ec_torsion_growth •

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

  
  
  • id: 166312
    {'degree': 2, 'field': [-33, -1, 1], 'lmfdb_label': '3192.i3', 'torsion': [2, 2]}
  • id: 166313
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '3192.i3', 'torsion': [4]}
  • id: 166314
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '3192.i3', 'torsion': [4]}
  • id: 166315
    {'degree': 4, 'field': [9, 0, 13, 0, 1], 'lmfdb_label': '3192.i3', 'torsion': [2, 4]}
  • id: 166319
    {'degree': 8, 'field': [-243, 0, 468, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '3192.i3', 'torsion': [6]}
  • id: 166316
    {'degree': 8, 'field': [81, 0, -7150, 0, -877, 0, -26, 0, 1], 'lmfdb_label': '3192.i3', 'torsion': [2, 4]}
  • id: 166317
    {'degree': 8, 'field': [1369, 592, 1352, 580, 490, -40, 32, -4, 1], 'lmfdb_label': '3192.i3', 'torsion': [8]}
  • id: 166318
    {'degree': 8, 'field': [17689, 0, -5054, 0, 1311, 0, -38, 0, 1], 'lmfdb_label': '3192.i3', 'torsion': [8]}
  • id: 166323
    {'degree': 16, 'field': [59049, 0, -6949800, 0, -1112130, 0, -50544, 0, -65001, 0, -12896, 0, -906, 0, 0, 0, 1], 'lmfdb_label': '3192.i3', 'torsion': [2, 6]}
  • id: 166324
    {'degree': 16, 'field': [1663132, -762856, 930860, -295104, 34712, 163432, -96380, 26280, 5593, -8424, 2248, -640, 410, -168, 44, -8, 1], 'lmfdb_label': '3192.i3', 'torsion': [12]}
  • id: 166320
    {'degree': 16, 'field': [2229049, 0, -1867304, 0, 603778, 0, -96936, 0, 5523, 0, -168, 0, 238, 0, 16, 0, 1], 'lmfdb_label': '3192.i3', 'torsion': [4, 4]}
  • id: 166321
    {'degree': 16, 'field': [10645573, -9567116, 12045480, -5130804, 3062682, -768096, 534352, -224636, 40251, 8112, 1176, -1932, 686, -196, 48, -8, 1], 'lmfdb_label': '3192.i3', 'torsion': [2, 8]}
  • id: 166325
    {'degree': 16, 'field': [13256449, -13299016, 15776420, -5214984, 3290090, -917960, 497716, -220224, 129319, -56688, 19108, -5008, 1502, -336, 68, -8, 1], 'lmfdb_label': '3192.i3', 'torsion': [12]}
  • id: 166322
    {'degree': 16, 'field': [31916836, 10262756, 13226598, -1141938, 8775957, -2507346, 2693308, -722386, 461172, -96618, 45510, -7086, 2600, -266, 78, -4, 1], 'lmfdb_label': '3192.i3', '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: 57595
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '3192.i3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57596
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '3192.i3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57597
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.i3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 57598
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.i3', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1684741
    {'adelic_gens': [[3185, 8, 3184, 9], [2801, 2796, 2798, 1199], [1, 0, 8, 1], [403, 402, 1210, 2803], [1, 8, 0, 1], [1, 4, 4, 17], [460, 1, 1847, 6], [7, 6, 3186, 3187], [1688, 3, 1853, 2], [2129, 8, 2132, 33]], 'adelic_image': '3192.48.0.?', 'conductor': 3192, 'lmfdb_label': '3192.i3', 'prime': 0}
  • id: 16012
    {'conductor': 3192, 'elladic_image': '4.6.0.1', 'lmfdb_label': '3192.i3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3192.i does not appear in ec_padic