Elliptic curve data - 3136.p4

Formats: - HTML - YAML - JSON - 2023-03-20T19:47:58.264053

• 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': '3136s', 'Clabel': '3136s1', 'Cnumber': 1, 'absD': 13492928512, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 56, 'ainvs': [0, 0, 0, 196, 5488], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3136, 'degree': 1536, 'elladic_images': ['8.24.0.107'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.62434865744909650949751677400', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [432, 7], 'lmfdb_iso': '3136.p', 'lmfdb_label': '3136.p4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 1, 2], 'min_quad_twist_disc': 56, 'modell_images': ['2B'], 'modm_images': ['1.1.0.1', '2.3.0.1', '4.6.0.1', '8.24.0.107', '14.6.0.2', '28.12.0.9', '56.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9330572333397874665166854078', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1572781277318296707085970728', '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, 0, 0, 2, 0, 0, 0, -3, 0, -4, 0, 2, 0, 0, 0, 6, 0, -8, 0], 'aplist': [0, 0, 2, 0, -4, 2, 6, -8, 0, -6, 8, 2, -2, -4, -8, -6, 0, -6, -4, 8, -10, -16, -8, 6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 3136, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3136.p', 'trace_hash': 293581156173131875}
• 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': '0.28687826559391947223068749184', 'prec': 103}, 'conductor': 3136, 'gens': [[-6, 64, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9330572333397874665166854078', 'prec': 100}], 'lmfdb_label': '3136.p4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.93493147424956756866377454482', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6145520979503156654594075894304716037', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-14, 0, 1]], 'xcoord_integral_points': [-14, -6, 84]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [7, 3, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 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': '3136.p4'}
• ec_torsion_growth •

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

  
  
  • id: 162632
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '3136.p4', 'torsion': [4]}
  • id: 162631
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '3136.p4', 'torsion': [2, 2]}
  • id: 162633
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '3136.p4', 'torsion': [4]}
  • id: 162634
    {'degree': 4, 'field': [2, -8, 9, -2, 1], 'lmfdb_label': '3136.p4', 'torsion': [2, 4]}
  • id: 162638
    {'degree': 8, 'field': [-2352, 0, -1344, 0, 168, 0, 0, 0, 1], 'lmfdb_label': '3136.p4', 'torsion': [6]}
  • id: 162636
    {'degree': 8, 'field': [-7, 0, 18, 4, -14, 0, 6, -4, 1], 'lmfdb_label': '3136.p4', 'torsion': [8]}
  • id: 162637
    {'degree': 8, 'field': [1, 0, -10, 0, 34, 0, -10, 0, 1], 'lmfdb_label': '3136.p4', 'torsion': [2, 8]}
  • id: 162635
    {'degree': 8, 'field': [4, 0, 10, 0, 5, 0, -2, 0, 1], 'lmfdb_label': '3136.p4', 'torsion': [2, 4]}
  • id: 162640
    {'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 16, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '3136.p4', 'torsion': [2, 8]}
  • id: 162639
    {'degree': 16, 'field': [16, 0, 0, 0, -24, 0, 0, 0, 73, 0, 0, 0, 15, 0, 0, 0, 1], 'lmfdb_label': '3136.p4', 'torsion': [4, 4]}
  • id: 162643
    {'degree': 16, 'field': [16, 0, 1600, 0, -224, 0, 112, 0, 280, 0, -56, 0, 28, 0, 4, 0, 1], 'lmfdb_label': '3136.p4', 'torsion': [12]}
  • id: 162641
    {'degree': 16, 'field': [2304, 0, -3456, 0, 2592, 0, -1728, 0, 669, 0, -54, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '3136.p4', 'torsion': [2, 6]}
  • id: 162642
    {'degree': 16, 'field': [9604, 0, -30184, 0, 29596, 0, -6664, 0, -2744, 0, -196, 0, 112, 0, 14, 0, 1], 'lmfdb_label': '3136.p4', '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: 56312
    {'conductor': 3136, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '3136.p4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 56313
    {'conductor': 3136, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '3136.p4', 'prime': 7, 'reduction_type': 0, '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: 1684311
    {'adelic_gens': [[32, 53, 27, 54], [31, 32, 50, 25], [49, 8, 48, 9], [1, 0, 8, 1], [13, 18, 30, 5], [1, 4, 4, 17], [7, 6, 50, 51], [1, 8, 0, 1]], 'adelic_image': '56.48.0.?', 'conductor': 3136, 'lmfdb_label': '3136.p4', 'prime': 0}
  • id: 15624
    {'conductor': 3136, 'elladic_image': '8.24.0.107', 'lmfdb_label': '3136.p4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 102456
    {'lmfdb_iso': '3136.p', 'p': 5, 'prec': 20, 'unit': 11908445812099, 'val': 1}
  • id: 102455
    {'lmfdb_iso': '3136.p', 'p': 11, 'prec': 20, 'unit': 56509935621477794331, 'val': 1}
  • id: 102462
    {'lmfdb_iso': '3136.p', 'p': 13, 'prec': 20, 'unit': 16104047731919954308, 'val': 1}
  • id: 102464
    {'lmfdb_iso': '3136.p', 'p': 17, 'prec': 20, 'unit': 57844946017799588034175, 'val': 1}
  • id: 102465
    {'lmfdb_iso': '3136.p', 'p': 19, 'prec': 20, 'unit': 1081995942294233562178779, 'val': 1}
  • id: 102461
    {'lmfdb_iso': '3136.p', 'p': 29, 'prec': 20, 'unit': 2569307246109567854834814645, 'val': 1}
  • id: 102458
    {'lmfdb_iso': '3136.p', 'p': 31, 'prec': 20, 'unit': 11447014503679891305516881794, 'val': 1}
  • id: 102472
    {'lmfdb_iso': '3136.p', 'p': 37, 'prec': 20, 'unit': 492924840973815069754642299794, 'val': 1}
  • id: 102459
    {'lmfdb_iso': '3136.p', 'p': 41, 'prec': 20, 'unit': 3302481781618581880330482997125, 'val': 1}
  • id: 102460
    {'lmfdb_iso': '3136.p', 'p': 43, 'prec': 20, 'unit': 2286699166486456939440918588157, 'val': 1}
  • id: 102463
    {'lmfdb_iso': '3136.p', 'p': 47, 'prec': 20, 'unit': 18560823433028635590932421945215, 'val': 1}
  • id: 102466
    {'lmfdb_iso': '3136.p', 'p': 53, 'prec': 20, 'unit': 392208261939859451993206856343503, 'val': 1}
  • id: 102471
    {'lmfdb_iso': '3136.p', 'p': 61, 'prec': 20, 'unit': 371874796237062174367656146456793, 'val': 1}
  • id: 102454
    {'lmfdb_iso': '3136.p', 'p': 67, 'prec': 20, 'unit': 47278108839631897985987079865831548, 'val': 1}
  • id: 102457
    {'lmfdb_iso': '3136.p', 'p': 71, 'prec': 20, 'unit': 68685682754680478461766937908669246, 'val': 1}
  • id: 102467
    {'lmfdb_iso': '3136.p', 'p': 73, 'prec': 20, 'unit': 5670106855039894473714378739937513, 'val': 1}
  • id: 102470
    {'lmfdb_iso': '3136.p', 'p': 79, 'prec': 20, 'unit': 129359007591201333855586180204198178, 'val': 1}
  • id: 102468
    {'lmfdb_iso': '3136.p', 'p': 83, 'prec': 20, 'unit': 450433517631086730658345644013184906, 'val': 1}
  • id: 102469
    {'lmfdb_iso': '3136.p', 'p': 89, 'prec': 20, 'unit': 4798056593822965475506305562139447850, 'val': 1}
  • id: 102453
    {'lmfdb_iso': '3136.p', 'p': 97, 'prec': 20, 'unit': 18846459181408657203064101989328933017, 'val': 1}