Elliptic curve data - 3192.g1

Formats: - HTML - YAML - JSON - 2025-04-29T14:42:48.171579

• 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': '3192d', 'Clabel': '3192d2', 'Cnumber': 2, 'abc_quality': 1.0063821965151891, 'absD': 366868062231552, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1596, 'ainvs': [0, -1, 0, -360088, 83283964], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 3192, 'degree': 19200, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8469218596698556622612442468', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2], 'jinv': [5042558062190438500, 358269592023], 'lmfdb_iso': '3192.g', 'lmfdb_label': '3192.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -360088, 83283964], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.a.1', '228.6.0.?', '1596.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.59081903903949793826091939207', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 7], [3, 4, 1064], [5, 2, 152], [7, 8, 456], [19, 20, 168]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2692992092032345710802174789', 'prec': 100}, 'szpiro_ratio': 6.196507194987615, '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, 2, 0, -4, 0, 0, 0, 0, 0, 1, 0], 'aplist': [0, -1, 0, 1, 2, -4, 0, 1, -6, 2, 4, 2, 2, -8, -8, -6, -4, 14, -2, 0, -6, -10, 0, 18, -16], 'class_deg': 2, 'class_size': 2, 'conductor': 3192, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '3192.g', 'trace_hash': 1822509694594648701}
• 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': '0.024876200909357186109283511803', 'prec': 107}, 'conductor': 3192, 'gens': [[330, 532, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.59081903903949793826091939207', 'prec': 103}], 'lmfdb_label': '3192.g1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.51055778597355126458036738183', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0164726048302721746562241941967806966', 'prec': 130}, 'tamagawa_product': 40, 'torsion_generators': [[349, 0, 1]], 'xcoord_integral_points': [106, 330, 349, 365]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [5, 5, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [2, 0], '23': [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.g1'}
• ec_torsion_growth •

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

  
  
  • id: 166463
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '3192.g1', 'torsion': [2, 2]}
  • id: 166464
    {'degree': 4, 'field': [4, -2, -10, -1, 1], 'lmfdb_label': '3192.g1', 'torsion': [4]}
  • id: 166467
    {'degree': 8, 'field': [-50700, 0, -12788, 0, -780, 0, 0, 0, 1], 'lmfdb_label': '3192.g1', 'torsion': [6]}
  • id: 166465
    {'degree': 8, 'field': [-1112, 1740, 505, -1474, 419, 112, -45, -2, 1], 'lmfdb_label': '3192.g1', 'torsion': [2, 4]}
  • id: 166466
    {'degree': 8, 'field': [84, -28, 42, -42, 57, -46, 20, -4, 1], 'lmfdb_label': '3192.g1', 'torsion': [2, 4]}
  • id: 166468
    {'degree': 16, 'field': [-1116416, -2903040, -1158016, 1169152, 603584, 161472, -695104, 52032, 264364, -4584, -42542, -1936, 2871, 176, -86, -4, 1], 'lmfdb_label': '3192.g1', 'torsion': [8]}
  • id: 166469
    {'degree': 16, 'field': [30988321225, 0, -1314309008, 0, 123832228, 0, -15338616, 0, -352866, 0, -66624, 0, -188, 0, -56, 0, 1], 'lmfdb_label': '3192.g1', 'torsion': [2, 6]}
• 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: 57647
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '3192.g1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57648
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '3192.g1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57649
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '3192.g1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 57650
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3192.g1', '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: 1684733
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [400, 1201, 1197, 400], [1, 4, 0, 1], [533, 4, 1066, 9], [1593, 4, 1592, 5], [230, 1, 683, 0], [1009, 4, 422, 9]], 'adelic_image': '1596.12.0.?', 'conductor': 3192, 'lmfdb_label': '3192.g1', 'prime': 0}
  • id: 16004
    {'conductor': 3192, 'elladic_image': '2.3.0.1', 'lmfdb_label': '3192.g1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 104716
    {'lmfdb_iso': '3192.g', 'p': 11, 'prec': 20, 'unit': 52612524155985635555, 'val': 1}
  • id: 104721
    {'lmfdb_iso': '3192.g', 'p': 13, 'prec': 20, 'unit': 376022675063070203705, 'val': 1}
  • id: 104727
    {'lmfdb_iso': '3192.g', 'p': 23, 'prec': 20, 'unit': 39175738961726627821490737, 'val': 1}
  • id: 104720
    {'lmfdb_iso': '3192.g', 'p': 29, 'prec': 20, 'unit': 2321700734714440716227512820, 'val': 1}
  • id: 104731
    {'lmfdb_iso': '3192.g', 'p': 31, 'prec': 20, 'unit': 8705306855017293638081612851, 'val': 1}
  • id: 104717
    {'lmfdb_iso': '3192.g', 'p': 37, 'prec': 20, 'unit': 339851482019927535470076347442, 'val': 1}
  • id: 104718
    {'lmfdb_iso': '3192.g', 'p': 41, 'prec': 20, 'unit': 4105462441190191553235905983359, 'val': 1}
  • id: 104719
    {'lmfdb_iso': '3192.g', 'p': 43, 'prec': 20, 'unit': 3783196482217949818380805448830, 'val': 1}
  • id: 104729
    {'lmfdb_iso': '3192.g', 'p': 47, 'prec': 20, 'unit': 32997511660805393224593527604043, 'val': 1}
  • id: 104725
    {'lmfdb_iso': '3192.g', 'p': 53, 'prec': 20, 'unit': 370705656654214386565880929005433, 'val': 1}
  • id: 104723
    {'lmfdb_iso': '3192.g', 'p': 59, 'prec': 20, 'unit': 1500670962550187430229734747388241, 'val': 1}
  • id: 104730
    {'lmfdb_iso': '3192.g', 'p': 61, 'prec': 20, 'unit': 2897467029060036850203804561805270, 'val': 1}
  • id: 104724
    {'lmfdb_iso': '3192.g', 'p': 67, 'prec': 20, 'unit': 9192092012675704531078602985467203, 'val': 1}
  • id: 104726
    {'lmfdb_iso': '3192.g', 'p': 73, 'prec': 20, 'unit': 96890789441488254544171745269698522, 'val': 1}
  • id: 104722
    {'lmfdb_iso': '3192.g', 'p': 79, 'prec': 20, 'unit': 508506734045163817063135183602277074, 'val': 1}
  • id: 104728
    {'lmfdb_iso': '3192.g', 'p': 89, 'prec': 20, 'unit': 5335247813216505302142618026867697665, 'val': 1}
  • id: 104715
    {'lmfdb_iso': '3192.g', 'p': 97, 'prec': 20, 'unit': 47205056839830990816090533661020187545, 'val': 1}