Elliptic curve data - 6840.d6

Formats: - HTML - YAML - JSON - 2025-09-28T13:35:12.837684

• 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': '6840e', 'Clabel': '6840e1', 'Cnumber': 1, 'abc_quality': 1.120296945835437, 'absD': 7012068750000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 4560, 'ainvs': [0, 0, 0, 2742, 114793], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 19], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 6840, 'degree': 8192, 'elladic_images': ['8.24.0.92'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1481776538279356536064456047', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [195469297664, 601171875], 'lmfdb_iso': '6840.d', 'lmfdb_label': '6840.d6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 305, -4150], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.ba.1', '12.12.0-4.c.1.2', '24.48.0-8.ba.1.1', '38.6.0.b.1', '76.12.0.?', '80.48.0.?', '152.48.0.?', '228.24.0.?', '240.96.0.?', '456.96.0.?', '1520.96.1.?', '4560.192.1.?'], '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, 171], [3, 8, 760], [5, 6, 1368], [19, 20, 360]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.36782244930723237143641227909', 'prec': 103}, 'szpiro_ratio': 4.170175839031932, '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, -1, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, -1, 0], 'aplist': [0, 0, -1, 0, -4, -2, -2, -1, 0, -6, 0, 6, 6, 4, -8, -6, 12, -2, 4, -8, -6, 16, 4, 6, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 6840, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '6840.d', 'trace_hash': 379124748565284470}
• 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': '0.10062492308102544061219648148', 'prec': 103}, 'conductor': 6840, 'gens': [], 'heights': [], 'lmfdb_label': '6840.d6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.52667026358742219489321323762', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0533405271748443897864264752298837585', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-31, 0, 1]], 'xcoord_integral_points': [-31]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '19': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '6840.d6'}
• ec_torsion_growth •

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

  
  
  • id: 359373
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '6840.d6', 'torsion': [4]}
  • id: 359374
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '6840.d6', 'torsion': [4]}
  • id: 359372
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '6840.d6', 'torsion': [2, 2]}
  • id: 359376
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '6840.d6', 'torsion': [8]}
  • id: 359375
    {'degree': 4, 'field': [25, -5, -4, -1, 1], 'lmfdb_label': '6840.d6', 'torsion': [2, 4]}
  • id: 359377
    {'degree': 4, 'field': [361, 0, 19, 0, 1], 'lmfdb_label': '6840.d6', 'torsion': [8]}
  • id: 359381
    {'degree': 8, 'field': [-33708, 0, 10236, 0, 396, 0, 20, 0, 1], 'lmfdb_label': '6840.d6', 'torsion': [6]}
  • id: 359379
    {'degree': 8, 'field': [6, 48, -56, 18, -13, 2, 4, -4, 1], 'lmfdb_label': '6840.d6', 'torsion': [8]}
  • id: 359378
    {'degree': 8, 'field': [25, 10, 58, 94, 63, 2, 4, -4, 1], 'lmfdb_label': '6840.d6', 'torsion': [2, 4]}
  • id: 359380
    {'degree': 8, 'field': [625, 0, 225, 0, 56, 0, 9, 0, 1], 'lmfdb_label': '6840.d6', 'torsion': [2, 8]}
  • id: 359387
    {'degree': 16, 'field': [9, 0, 17304, 0, 33269806, 0, 34608, 0, 39, 0, 11536, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '6840.d6', 'torsion': [12]}
  • id: 359382
    {'degree': 16, 'field': [625, -250, 50, -720, 169, -242, 498, -154, 180, -232, 168, -74, 25, -12, 8, -4, 1], 'lmfdb_label': '6840.d6', 'torsion': [4, 8]}
  • id: 359383
    {'degree': 16, 'field': [2910436, -1078192, -1497648, 907680, 429852, -277848, -61088, 3848, 25146, -1296, -2232, -216, 182, 40, -12, -4, 1], 'lmfdb_label': '6840.d6', 'torsion': [16]}
  • id: 359386
    {'degree': 16, 'field': [900720144, 0, -332576016, 0, -128815784, 0, -12777312, 0, -443931, 0, -7864, 0, -534, 0, 0, 0, 1], 'lmfdb_label': '6840.d6', 'torsion': [12]}
  • id: 359385
    {'degree': 16, 'field': [5791056725, -661982528, 722513820, -124134064, 69165342, -6951456, -115068, 1718248, 49611, -352808, 105084, -20328, 4662, -616, 108, -8, 1], 'lmfdb_label': '6840.d6', 'torsion': [2, 6]}
  • id: 359384
    {'degree': 16, 'field': [9542554596, -13214962080, 16793188048, -2384606400, 674897300, -579567640, 95699328, -19112480, 4490574, -1119480, 241512, 12160, 3150, -760, -28, 0, 1], 'lmfdb_label': '6840.d6', 'torsion': [16]}
• 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: 139494
    {'conductor': 6840, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '6840.d6', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 139495
    {'conductor': 6840, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '6840.d6', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 139496
    {'conductor': 6840, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '6840.d6', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 139497
    {'conductor': 6840, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6840.d6', '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: 1709188
    {'adelic_gens': [[15, 2, 4462, 4547], [5, 4, 4556, 4557], [1, 16, 0, 1], [2737, 1536, 2136, 3169], [1, 0, 16, 1], [205, 1536, 3714, 2011], [1519, 0, 0, 4559], [4545, 16, 4544, 17], [3376, 3045, 195, 4546], [1, 1536, 1140, 1141]], 'adelic_image': '4560.192.1.?', 'conductor': 6840, 'lmfdb_label': '6840.d6', 'prime': 0}
  • id: 33789
    {'conductor': 6840, 'elladic_image': '8.24.0.92', 'lmfdb_label': '6840.d6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6840.d does not appear in ec_padic