Elliptic curve data - 3192.h1

Formats: - HTML - YAML - JSON - 2023-06-01T19:14:29.978615

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '3192j', 'Clabel': '3192j3', 'Cnumber': 3, 'absD': 672959809536, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, -1, 0, -3232, -57620], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3192, 'degree': 5120, 'elladic_images': ['8.24.0.102'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.98859859310155967628396181411', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2, 4], 'jinv': [1823652903746, 328593657], 'lmfdb_iso': '3192.h', 'lmfdb_label': '3192.h1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -3232, -57620], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.m.1.5', '228.12.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.35321367758827647598483236944', 'prec': 103}, '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, 2, 0, -1, 0], 'aplist': [0, -1, 2, -1, -4, -6, 2, -1, -4, 6, 4, 2, 10, 12, 4, 14, -4, 6, 4, -8, -6, -12, 12, -6, 2], '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.h', 'trace_hash': 1046751436216970068}
• 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': '0.13845676250093500566093180712', 'prec': 103}, 'conductor': 3192, 'gens': [], 'heights': [], 'lmfdb_label': '3192.h1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.64101354140234452973819251734', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2820270828046890594763850346809869962', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[-43, 0, 1]], 'xcoord_integral_points': [-43]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '7': [0, 0], '19': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '3192.h1'}
• ec_torsion_growth •

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

  
  
  • id: 166590
    {'degree': 2, 'field': [-114, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [2, 2]}
  • id: 166591
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [4]}
  • id: 166592
    {'degree': 2, 'field': [57, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [4]}
  • id: 166594
    {'degree': 4, 'field': [114, 0, -8, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [8]}
  • id: 166593
    {'degree': 4, 'field': [841, 0, -56, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [2, 4]}
  • id: 166598
    {'degree': 8, 'field': [-48, 0, -848, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [6]}
  • id: 166597
    {'degree': 8, 'field': [1089, 0, -1356, 0, 472, 0, -28, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [2, 8]}
  • id: 166595
    {'degree': 8, 'field': [12100, 0, -2768, 0, -204, 0, -8, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [2, 4]}
  • id: 166596
    {'degree': 8, 'field': [32041, -43318, 29282, -10522, 2122, -158, 2, -2, 1], 'lmfdb_label': '3192.h1', 'torsion': [8]}
  • id: 166603
    {'degree': 16, 'field': [49729, 0, 97348, 0, 36712, 0, -8040, 0, -3546, 0, 708, 0, 100, 0, 16, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [12]}
  • id: 166599
    {'degree': 16, 'field': [10556001, 0, 0, 0, 0, 0, 0, 0, 110466, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [4, 4]}
  • id: 166601
    {'degree': 16, 'field': [168896016, 0, -47409408, 0, 31294368, 0, -13099968, 0, 2183328, 0, -114912, 0, 2408, 0, -32, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [16]}
  • id: 166602
    {'degree': 16, 'field': [194769936, 0, -183124800, 0, -570677600, 0, -237720432, 0, 4396776, 0, -164032, 0, 14316, 0, -228, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [2, 6]}
  • id: 166600
    {'degree': 16, 'field': [799814961, 0, -546696864, 0, 161212578, 0, -26244420, 0, 2574019, 0, -156020, 0, 5718, 0, -116, 0, 1], 'lmfdb_label': '3192.h1', 'torsion': [2, 8]}
  • id: 166604
    {'degree': 16, 'field': [3711733776, 0, -2780991456, 0, 721618192, 0, -74148672, 0, 4004616, 0, 584, 0, 2688, 0, 0, 0, 1], 'lmfdb_label': '3192.h1', '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: 57707
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '3192.h1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 57708
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.h1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 57709
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '3192.h1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57710
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.h1', '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: 1684735
    {'adelic_gens': [[449, 8, 448, 9], [388, 1, 407, 6], [1, 0, 8, 1], [1, 8, 0, 1], [403, 400, 194, 405], [1, 4, 4, 17], [7, 6, 450, 451], [308, 1, 175, 6], [400, 179, 289, 318]], 'adelic_image': '456.48.0.?', 'conductor': 3192, 'lmfdb_label': '3192.h1', 'prime': 0}
  • id: 16006
    {'conductor': 3192, 'elladic_image': '8.24.0.102', 'lmfdb_label': '3192.h1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3192.h does not appear in ec_padic