Elliptic curve data - 816.d2

Formats: - HTML - YAML - JSON - 2025-01-23T08:30:57.984576

• 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': '816e', 'Clabel': '816e1', 'Cnumber': 1, 'abc_quality': 1.002934967692302, 'absD': 3248750592, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 408, 'ainvs': [0, -1, 0, -4088, -99216], 'analytic_rank': 0, 'bad_primes': [2, 3, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 816, 'degree': 576, 'elladic_images': ['8.6.0.4', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.78526735690731011826778736089', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [1845026709625, 793152], 'lmfdb_iso': '816.d', 'lmfdb_label': '816.d2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -256, 1550], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.d.1', '12.24.0-6.a.1.3', '24.48.0-24.bx.1.5', '34.6.0.a.1', '102.24.0.?', '136.12.0.?', '204.48.0.?', '408.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 17], [3, 4, 272], [17, 18, 48]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.092120176347364808850555239432', 'prec': 107}, 'szpiro_ratio': 5.453314652267319, '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, -2, 0, 1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 4, 0], 'aplist': [0, -1, 0, -2, 0, 2, -1, 4, 6, 0, 10, 8, 6, 4, -12, 6, 12, 8, 4, -6, 2, 10, -12, -18, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 816, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '816.d', 'trace_hash': 2201734356461484014}
• 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': '0.20793396746066958820161649006', 'prec': 103}, 'conductor': 816, 'gens': [], 'heights': [], 'lmfdb_label': '816.d2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.59706853537549561409827794335', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1941370707509912281965558866977719840', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-36, 0, 1]], 'xcoord_integral_points': [-36]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '17': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '816.d2'}
• ec_torsion_growth •

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

  
  
  • id: 38379
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '816.d2', 'torsion': [2, 2]}
  • id: 38380
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [6]}
  • id: 38381
    {'degree': 4, 'field': [6, -4, -2, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [4]}
  • id: 38382
    {'degree': 4, 'field': [16, 0, 9, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [2, 6]}
  • id: 38383
    {'degree': 6, 'field': [-12, 0, -11, 0, -1, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [6]}
  • id: 38386
    {'degree': 8, 'field': [1, -4, 8, -4, -7, 8, 2, -4, 1], 'lmfdb_label': '816.d2', 'torsion': [12]}
  • id: 38385
    {'degree': 8, 'field': [81, 0, 54, 0, 10, 0, 6, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [2, 4]}
  • id: 38384
    {'degree': 8, 'field': [361, 0, -411, 0, 182, 0, -27, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [2, 4]}
  • id: 38388
    {'degree': 12, 'field': [36, 0, -135, 0, 127, 0, -103, 0, 69, 0, -13, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [2, 6]}
  • id: 38387
    {'degree': 12, 'field': [144, 0, -132, 0, 109, 0, -35, 0, 12, 0, 1, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [3, 6]}
  • id: 38391
    {'degree': 16, 'field': [4, -40, 172, -400, 498, -136, -510, 472, 333, -124, -2, 56, 8, -4, -4, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [2, 12]}
  • id: 38389
    {'degree': 16, 'field': [8208, 13248, 8064, 8160, 13680, 4784, -9648, -8904, 569, 3064, 424, -544, -66, 72, 8, -8, 1], 'lmfdb_label': '816.d2', 'torsion': [8]}
  • id: 38390
    {'degree': 16, 'field': [11241, 12438, -2484, -14094, -5270, 8808, 6274, -6314, -597, 1740, -590, 54, 82, -70, 30, -8, 1], 'lmfdb_label': '816.d2', 'torsion': [2, 12]}
  • id: 38392
    {'degree': 18, 'field': [576, 0, 4320, 0, 12708, 0, 17329, 0, 6846, 0, -183, 0, -49, 0, -12, 0, -3, 0, 1], 'lmfdb_label': '816.d2', 'torsion': [18]}
• 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: 10556
    {'conductor': 816, 'conductor_valuation': 4, 'discriminant_valuation': 18, 'j_denominator_valuation': 6, 'kodaira_symbol': -14, 'lmfdb_label': '816.d2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 10557
    {'conductor': 816, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '816.d2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 10558
    {'conductor': 816, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '816.d2', 'prime': 17, '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: 1669764
    {'adelic_gens': [[370, 3, 21, 400], [397, 12, 396, 13], [1, 0, 12, 1], [11, 2, 358, 399], [1, 6, 6, 37], [281, 2, 126, 13], [1, 12, 0, 1], [205, 12, 6, 73], [81, 14, 370, 307]], 'adelic_image': '408.96.1.?', 'conductor': 816, 'lmfdb_label': '816.d2', 'prime': 0}
  • id: 3763
    {'conductor': 816, 'elladic_image': '8.6.0.4', 'lmfdb_label': '816.d2', 'modell_image': '2B', 'prime': 2}
  • id: 3764
    {'conductor': 816, 'elladic_image': '3.4.0.1', 'lmfdb_label': '816.d2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 816.d does not appear in ec_padic