Elliptic curve data - 1872.n4

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• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1872h', 'Clabel': '1872h4', 'Cnumber': 4, 'abc_quality': 0.9668256784127743, 'absD': 191886050304, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 624, 'ainvs': [0, 0, 0, 1221, 13210], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1872, 'degree': 2048, 'elladic_images': ['4.24.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.85213960958991333309672524638', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 4], 'jinv': [269676572, 257049], 'lmfdb_iso': '1872.n', 'lmfdb_label': '1872.n4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 136, 444], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.2', '12.48.0-12.e.1.1', '104.48.0.?', '208.96.0.?', '312.96.1.?', '624.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.1412251437019084452292642281', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 208], [13, 14, 144]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27478918521076260378192413996', 'prec': 107}, 'szpiro_ratio': 4.371190036662054, '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, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, -8, 0], 'aplist': [0, 0, 2, -4, 0, 1, -2, -8, 8, 2, -4, -10, -2, 4, -12, -6, 0, -2, -8, -12, 10, 8, 0, 14, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 1872, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1872.n', 'trace_hash': 1484104219353125141}
• 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': '0.18190345145395505146631621501', 'prec': 103}, 'conductor': 1872, 'gens': [[3, 130, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.1412251437019084452292642281', 'prec': 100}], 'lmfdb_label': '1872.n4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.66106618420139652531380159423', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0177014042468441117895638985423089711', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-10, 0, 1]], 'xcoord_integral_points': [-10, 3, 107]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [3, 0], '11': [1, 3, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [3, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1872.n4'}
• ec_torsion_growth •

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

  
  
  • id: 94849
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1872.n4', 'torsion': [4]}
  • id: 94850
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '1872.n4', 'torsion': [4]}
  • id: 94848
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1872.n4', 'torsion': [2, 2]}
  • id: 94851
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '1872.n4', 'torsion': [4, 4]}
  • id: 94854
    {'degree': 8, 'field': [-243, 0, 408, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '1872.n4', 'torsion': [6]}
  • id: 94852
    {'degree': 8, 'field': [1, 0, 12, 0, -5, 0, -12, 0, 1], 'lmfdb_label': '1872.n4', 'torsion': [8]}
  • id: 94853
    {'degree': 8, 'field': [16, 0, 24, 0, 40, 0, -6, 0, 1], 'lmfdb_label': '1872.n4', 'torsion': [8]}
  • id: 94856
    {'degree': 16, 'field': [1, 0, 0, 0, -11, 0, 0, 0, 120, 0, 0, 0, -11, 0, 0, 0, 1], 'lmfdb_label': '1872.n4', 'torsion': [4, 8]}
  • id: 94859
    {'degree': 16, 'field': [9, 0, 132, 0, 1918, 0, 264, 0, 39, 0, 88, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '1872.n4', 'torsion': [12]}
  • id: 94857
    {'degree': 16, 'field': [49, -532, 2888, -1344, 140, 1060, -1328, 1560, -362, -636, 712, -400, 188, -84, 32, -8, 1], 'lmfdb_label': '1872.n4', 'torsion': [2, 6]}
  • id: 94855
    {'degree': 16, 'field': [81, 0, 0, 0, -324, 0, 0, 0, 666, 0, 0, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '1872.n4', 'torsion': [4, 8]}
  • id: 94858
    {'degree': 16, 'field': [11664, 0, -139872, 0, 68752, 0, -12000, 0, 4104, 0, -1672, 0, 240, 0, -24, 0, 1], 'lmfdb_label': '1872.n4', '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: 30297
    {'conductor': 1872, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '1872.n4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 30298
    {'conductor': 1872, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '1872.n4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 30299
    {'conductor': 1872, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1872.n4', 'prime': 13, 'reduction_type': 1, '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: 1676229
    {'adelic_gens': [[145, 12, 0, 1], [338, 259, 79, 166], [5, 16, 64, 205], [1, 16, 0, 1], [169, 552, 28, 205], [609, 622, 514, 13], [1, 12, 4, 49], [1, 0, 16, 1], [609, 16, 608, 17]], 'adelic_image': '624.192.3.?', 'conductor': 1872, 'lmfdb_label': '1872.n4', 'prime': 0}
  • id: 9170
    {'conductor': 1872, 'elladic_image': '4.24.0.9', 'lmfdb_label': '1872.n4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 53313
    {'lmfdb_iso': '1872.n', 'p': 5, 'prec': 20, 'unit': 3650776478743, 'val': 1}
  • id: 53314
    {'lmfdb_iso': '1872.n', 'p': 7, 'prec': 20, 'unit': 139062270914004, 'val': 3}
  • id: 53320
    {'lmfdb_iso': '1872.n', 'p': 17, 'prec': 20, 'unit': 155812628226689558006042, 'val': 1}
  • id: 53321
    {'lmfdb_iso': '1872.n', 'p': 19, 'prec': 20, 'unit': 1047680149138975910139237, 'val': 1}
  • id: 53324
    {'lmfdb_iso': '1872.n', 'p': 23, 'prec': 20, 'unit': 3025906265280954210507844, 'val': 1}
  • id: 53318
    {'lmfdb_iso': '1872.n', 'p': 29, 'prec': 20, 'unit': 185291081273922618455570097, 'val': 2}
  • id: 53315
    {'lmfdb_iso': '1872.n', 'p': 31, 'prec': 20, 'unit': 11179674622663005950999132260, 'val': 1}
  • id: 53329
    {'lmfdb_iso': '1872.n', 'p': 37, 'prec': 20, 'unit': 354663162700279799986042457121, 'val': 1}
  • id: 53316
    {'lmfdb_iso': '1872.n', 'p': 41, 'prec': 20, 'unit': 1216516435311004919122063429671, 'val': 1}
  • id: 53317
    {'lmfdb_iso': '1872.n', 'p': 43, 'prec': 20, 'unit': 6516026400173000009124381032296, 'val': 1}
  • id: 53319
    {'lmfdb_iso': '1872.n', 'p': 47, 'prec': 20, 'unit': 52746670774015621141299740803340, 'val': 1}
  • id: 53322
    {'lmfdb_iso': '1872.n', 'p': 53, 'prec': 20, 'unit': 453607859679799502030893837824657, 'val': 1}
  • id: 53328
    {'lmfdb_iso': '1872.n', 'p': 61, 'prec': 20, 'unit': 3422914468273964847553342573839788, 'val': 1}
  • id: 53312
    {'lmfdb_iso': '1872.n', 'p': 67, 'prec': 20, 'unit': 623550553518132397408935639491409, 'val': 1}
  • id: 53326
    {'lmfdb_iso': '1872.n', 'p': 71, 'prec': 20, 'unit': 48167185773014168081433099426352458, 'val': 1}
  • id: 53323
    {'lmfdb_iso': '1872.n', 'p': 73, 'prec': 20, 'unit': 192806204826697270661681183143054283, 'val': 1}
  • id: 53327
    {'lmfdb_iso': '1872.n', 'p': 79, 'prec': 20, 'unit': 803209947805722674314660271678472742, 'val': 1}
  • id: 53325
    {'lmfdb_iso': '1872.n', 'p': 89, 'prec': 20, 'unit': 6191705785392893476609231325041039078, 'val': 1}
  • id: 53311
    {'lmfdb_iso': '1872.n', 'p': 97, 'prec': 20, 'unit': 49656818452674188414028073866164288853, 'val': 1}