Elliptic curve data - 122034.d4

Formats: - HTML - YAML - JSON - 2024-06-09T04:01:54.707739

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '122034d', 'Clabel': '122034d2', 'Cnumber': 2, 'abc_quality': 1.1002106061618209, 'absD': 1445302085386512672, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 56760, 'ainvs': [1, 1, 0, 212597, -43752995], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 43], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 122034, 'degree': 3225600, 'elladic_images': ['8.6.0.5', '5.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1703079583062513372599333049', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [168105213359, 228637728], 'lmfdb_iso': '122034.d', 'lmfdb_label': '122034.d4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 115, 561], 'min_quad_twist_disc': -43, 'modell_images': ['2B', '5B.4.1'], 'modm_images': ['2.3.0.a.1', '5.12.0.a.1', '8.6.0.a.1', '10.36.0.a.2', '40.72.1.c.1', '132.6.0.?', '215.24.0.?', '264.12.0.?', '430.72.0.?', '660.72.1.?', '1320.144.5.?', '1720.144.1.?', '28380.144.1.?', '56760.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.989010124184200395084744061', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.28970790045947012552351204823', 'prec': 103}, 'szpiro_ratio': 4.159417966252607, '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, -1, -1, 1, 4, 1, 2, -1, 1, -4, 1, -1, 4, -2, -4, 1, -2, -1, 0, 4], 'aplist': [-1, -1, 4, 2, 1, 4, -2, 0, -6, -10, -8, 2, 2, 0, -2, 4, 0, 8, -12, -2, 6, 10, 4, -10, -2], 'class_deg': 10, 'class_size': 4, 'conductor': 122034, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '122034.d', 'trace_hash': 1735906457646151590}
• 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': '0.013028501261365115843601155365', 'prec': 107}, 'conductor': 122034, 'gens': [[7440015, 5481030115, 203]], 'heights': [{'__RealLiteral__': 0, 'data': '11.989010124184200395084744061', 'prec': 100}], 'lmfdb_label': '122034.d4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14339129551906468239436050545', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.8764787747918201820926306624289855925', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[715, -715, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': [1, 0], '5': [1, 0], '7': [3, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 3, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': 'a', '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '122034.d4'}
• ec_torsion_growth •

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

  
  
  • id: 5575098
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '122034.d4', 'torsion': [2, 2]}
  • id: 5575099
    {'degree': 2, 'field': [11, -1, 1], 'lmfdb_label': '122034.d4', 'torsion': [10]}
  • id: 5575100
    {'degree': 4, 'field': [-14792, 0, -43, 0, 1], 'lmfdb_label': '122034.d4', 'torsion': [4]}
  • id: 5575101
    {'degree': 4, 'field': [83, -26, 27, -2, 1], 'lmfdb_label': '122034.d4', 'torsion': [2, 10]}
  • id: 5575104
    {'degree': 8, 'field': [-2692576, 1017980, 38807, -22822, 6767, -328, 1, -2, 1], 'lmfdb_label': '122034.d4', 'torsion': [6]}
  • id: 5575105
    {'degree': 8, 'field': [10861, -6134, 6868, -1514, 873, -142, 52, -4, 1], 'lmfdb_label': '122034.d4', 'torsion': [20]}
  • id: 5575103
    {'degree': 8, 'field': [60516, 0, 5600, 0, 422, 0, -8, 0, 1], 'lmfdb_label': '122034.d4', 'torsion': [2, 4]}
  • id: 5575102
    {'degree': 8, 'field': [12931216, 0, 22632, 0, -7711, 0, 60, 0, 1], 'lmfdb_label': '122034.d4', 'torsion': [2, 4]}
  • id: 5575108
    {'degree': 16, 'field': [26575417, -115466692, 155452324, -88670692, 67346306, -31251568, 16797012, -6114652, 2369747, -613376, 176892, -31580, 6962, -812, 136, -8, 1], 'lmfdb_label': '122034.d4', 'torsion': [2, 20]}
  • id: 5575110
    {'degree': 16, 'field': [114875524, 0, 162745619, 0, 52889566, 0, 9201633, 0, 994695, 0, 70449, 0, 3199, 0, 86, 0, 1], 'lmfdb_label': '122034.d4', 'torsion': [30]}
  • id: 5575109
    {'degree': 16, 'field': [790175907, -335570928, 407546324, -153719368, 102193796, -33015704, 15543664, -4259336, 1545297, -350280, 101076, -18272, 4198, -560, 100, -8, 1], 'lmfdb_label': '122034.d4', 'torsion': [2, 20]}
  • id: 5575106
    {'degree': 16, 'field': [7502077176064, 0, -4694049379200, 0, 88050107344, 0, -520183632, 0, -59677044, 0, 1056552, 0, 39406, 0, 348, 0, 1], 'lmfdb_label': '122034.d4', 'torsion': [8]}
  • id: 5575107
    {'degree': 16, 'field': [9781755976164, -6201139979136, 1289795795804, 102976319944, -70793881675, 11506653868, 1205987726, -431249900, 49083723, -2013984, 247248, -76376, 15035, -716, 22, -4, 1], 'lmfdb_label': '122034.d4', 'torsion': [2, 6]}
  • id: 5575111
    {'degree': 20, 'field': [123383957781095, -26786220666095, -44043225834135, 6655749443805, 7605216482776, -685670501757, -800445038130, 34896117060, 55331849955, -716574936, -2625754718, -18050515, 86433755, 1601620, -1942293, -44359, 28560, 580, -250, -3, 1], 'lmfdb_label': '122034.d4', 'torsion': [10]}
• 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: 3005347
    {'conductor': 122034, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '122034.d4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3005348
    {'conductor': 122034, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '122034.d4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3005349
    {'conductor': 122034, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '122034.d4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3005350
    {'conductor': 122034, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '122034.d4', 'prime': 43, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2460502
    {'adelic_gens': [[5161, 36980, 13330, 29241], [37841, 36980, 56330, 29241], [56741, 20, 56740, 21], [1, 10, 10, 101], [1, 0, 20, 1], [27736, 9245, 1935, 29026], [11, 16, 56520, 56411], [15051, 36980, 19780, 47387], [1, 20, 0, 1], [37626, 9245, 30745, 26446], [26399, 0, 0, 56759]], 'adelic_image': '56760.288.5.?', 'conductor': 122034, 'lmfdb_label': '122034.d4', 'prime': 0}
  • id: 478902
    {'conductor': 122034, 'elladic_image': '8.6.0.5', 'lmfdb_label': '122034.d4', 'modell_image': '2B', 'prime': 2}
  • id: 478903
    {'conductor': 122034, 'elladic_image': '5.12.0.1', 'lmfdb_label': '122034.d4', 'modell_image': '5B.4.1', 'prime': 5}
• ec_padic •

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

  
  
  • id: 6383568
    {'lmfdb_iso': '122034.d', 'p': 5, 'prec': 20, 'unit': 1709859326098, 'val': 1}
  • id: 6383569
    {'lmfdb_iso': '122034.d', 'p': 7, 'prec': 20, 'unit': 1058021760466252, 'val': 2}
  • id: 6383574
    {'lmfdb_iso': '122034.d', 'p': 13, 'prec': 20, 'unit': 5259369611561644935, 'val': 1}
  • id: 6383576
    {'lmfdb_iso': '122034.d', 'p': 17, 'prec': 20, 'unit': 182836792519561122251849, 'val': 1}
  • id: 6383580
    {'lmfdb_iso': '122034.d', 'p': 23, 'prec': 20, 'unit': 21521102442136241263035965, 'val': 1}
  • id: 6383573
    {'lmfdb_iso': '122034.d', 'p': 29, 'prec': 20, 'unit': 5056064449107495075607935357, 'val': 1}
  • id: 6383570
    {'lmfdb_iso': '122034.d', 'p': 31, 'prec': 20, 'unit': 537111259161467887157057808, 'val': 1}
  • id: 6383584
    {'lmfdb_iso': '122034.d', 'p': 37, 'prec': 20, 'unit': 187497395686105675709213626240, 'val': 1}
  • id: 6383571
    {'lmfdb_iso': '122034.d', 'p': 41, 'prec': 20, 'unit': 3453206202516317201596910479589, 'val': 1}
  • id: 6383575
    {'lmfdb_iso': '122034.d', 'p': 47, 'prec': 20, 'unit': 21530333838126212277145133033314, 'val': 1}
  • id: 6383578
    {'lmfdb_iso': '122034.d', 'p': 53, 'prec': 20, 'unit': 470541607203159155295022509034097, 'val': 1}
  • id: 6383583
    {'lmfdb_iso': '122034.d', 'p': 61, 'prec': 20, 'unit': 8041195102178181844462143788298675, 'val': 1}
  • id: 6383567
    {'lmfdb_iso': '122034.d', 'p': 67, 'prec': 20, 'unit': 42670793333143546710340232003729078, 'val': 1}
  • id: 6383572
    {'lmfdb_iso': '122034.d', 'p': 71, 'prec': 20, 'unit': 109489045395585184210126496560013223, 'val': 1}
  • id: 6383579
    {'lmfdb_iso': '122034.d', 'p': 73, 'prec': 20, 'unit': 52336879910193974821709797229027674, 'val': 1}
  • id: 6383582
    {'lmfdb_iso': '122034.d', 'p': 79, 'prec': 20, 'unit': 342544563877156356756412652603277321, 'val': 1}
  • id: 6383577
    {'lmfdb_iso': '122034.d', 'p': 83, 'prec': 20, 'unit': 2254535073494435134136577898559151394, 'val': 1}
  • id: 6383581
    {'lmfdb_iso': '122034.d', 'p': 89, 'prec': 20, 'unit': 9588715104146710728722699515471297759, 'val': 1}
  • id: 6383566
    {'lmfdb_iso': '122034.d', 'p': 97, 'prec': 20, 'unit': 5399262145054920169408238162719205994, 'val': 1}