Elliptic curve data - 13872.bm6

Formats: - HTML - YAML - JSON - 2025-10-31T11:19:28.753151

• 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': '13872bi', 'Clabel': '13872bi4', 'Cnumber': 4, 'abc_quality': 1.0301007930420596, 'absD': 289402623953161961472, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 272, 'ainvs': [0, 1, 0, 1044928, 708081972], 'analytic_rank': 1, 'bad_primes': [2, 3, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 13872, 'degree': 442368, 'elladic_images': ['16.96.0.119'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6102585479495529490712104263', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 38, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [1276229915423, 2927177028], 'lmfdb_iso': '13872.bm', 'lmfdb_label': '13872.bm6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 226, -2232], 'min_quad_twist_disc': -68, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.48.0-8.ba.2.7', '16.96.0-16.y.2.7', '68.24.0-68.h.1.2', '136.96.0.?', '272.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.4925416020725004907466619393', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 289], [3, 4, 4624], [17, 162, 48]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.50050469536149959952921099591', 'prec': 103}, 'szpiro_ratio': 5.690964676657638, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 2, 0, 0, 0, 1, 0, -4, 0, -2, 0, 2, 0, 0, 0, -4, 0], 'aplist': [0, 1, 2, 0, -4, -2, 0, -4, 0, 10, 8, 2, -10, -12, 0, 6, -12, 10, 12, 0, -10, -8, -4, -6, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 13872, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '13872.bm', 'trace_hash': 1612944130425467075}
• 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': '0.0054045337415278848864759351949', 'prec': 110}, 'conductor': 13872, 'gens': [[-2391, 1499043, 4]], 'heights': [{'__RealLiteral__': 0, 'data': '6.4925416020725004907466619393', 'prec': 100}], 'lmfdb_label': '13872.bm6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12047737175750681963571328430', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.2576347859517404068789300553861224352', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[844, 46818, 1]], 'xcoord_integral_points': [-533, 844]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 3, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '13872.bm6'}
• ec_torsion_growth •

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

  
  
  • id: 714177
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [2, 4]}
  • id: 714178
    {'degree': 4, 'field': [-68, 0, 0, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [8]}
  • id: 714179
    {'degree': 4, 'field': [81, 0, -16, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [2, 8]}
  • id: 714183
    {'degree': 8, 'field': [-13872, 0, -3196, 0, 408, 0, 0, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [12]}
  • id: 714180
    {'degree': 8, 'field': [16, 8, 2, -22, 17, -10, 8, -4, 1], 'lmfdb_label': '13872.bm6', 'torsion': [4, 4]}
  • id: 714182
    {'degree': 8, 'field': [81, 0, -28, 0, 120, 0, -12, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [2, 16]}
  • id: 714181
    {'degree': 8, 'field': [324, 0, -200, 0, 40, 0, 4, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [2, 8]}
  • id: 714185
    {'degree': 16, 'field': [324, -2160, 7200, -8232, 4936, -936, 1128, -1892, 1669, -772, 296, -196, 130, -76, 32, -8, 1], 'lmfdb_label': '13872.bm6', 'torsion': [4, 8]}
  • id: 714184
    {'degree': 16, 'field': [4761, 0, -3800, 0, 9548, 0, -3752, 0, 206, 0, 56, 0, 28, 0, 8, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [4, 8]}
  • id: 714186
    {'degree': 16, 'field': [73984, 0, 0, 0, 166464, 0, 0, 0, 1156, 0, 0, 0, -612, 0, 0, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [16]}
  • id: 714187
    {'degree': 16, 'field': [1336336, 0, -2672672, 0, 2672672, 0, -1061208, 0, 240737, 0, -31212, 0, 2312, 0, -68, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [2, 16]}
  • id: 714188
    {'degree': 16, 'field': [27060804, 0, 12734496, 0, 1498176, 0, 535517, 0, 31790, 0, 7361, 0, 289, 0, 34, 0, 1], 'lmfdb_label': '13872.bm6', 'torsion': [2, 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: 303783
    {'conductor': 13872, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '13872.bm6', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 303784
    {'conductor': 13872, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '13872.bm6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 303785
    {'conductor': 13872, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '13872.bm6', 'prime': 17, '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: 1756183
    {'adelic_gens': [[257, 16, 256, 17], [1, 16, 0, 1], [94, 61, 145, 114], [1, 0, 16, 1], [13, 16, 60, 121], [5, 4, 268, 269], [15, 2, 174, 259], [248, 271, 1, 262]], 'adelic_image': '272.192.1.?', 'conductor': 13872, 'lmfdb_label': '13872.bm6', 'prime': 0}
  • id: 65749
    {'conductor': 13872, 'elladic_image': '16.96.0.119', 'lmfdb_label': '13872.bm6', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 615506
    {'lmfdb_iso': '13872.bm', 'p': 5, 'prec': 20, 'unit': 9835732037324, 'val': 1}
  • id: 615513
    {'lmfdb_iso': '13872.bm', 'p': 11, 'prec': 20, 'unit': 47642620533899894753, 'val': 1}
  • id: 615511
    {'lmfdb_iso': '13872.bm', 'p': 13, 'prec': 20, 'unit': 214347788077906647510, 'val': 1}
  • id: 615514
    {'lmfdb_iso': '13872.bm', 'p': 19, 'prec': 20, 'unit': 82297460914175304242717, 'val': 2}
  • id: 615510
    {'lmfdb_iso': '13872.bm', 'p': 29, 'prec': 20, 'unit': 1172310076473416749583509719, 'val': 1}
  • id: 615507
    {'lmfdb_iso': '13872.bm', 'p': 31, 'prec': 20, 'unit': 7371611020961556490024789843, 'val': 1}
  • id: 615520
    {'lmfdb_iso': '13872.bm', 'p': 37, 'prec': 20, 'unit': 450963638202489175600989477607, 'val': 1}
  • id: 615508
    {'lmfdb_iso': '13872.bm', 'p': 41, 'prec': 20, 'unit': 1656732753163376995807559655321, 'val': 1}
  • id: 615509
    {'lmfdb_iso': '13872.bm', 'p': 43, 'prec': 20, 'unit': 2817185835242423358744094721851, 'val': 1}
  • id: 615515
    {'lmfdb_iso': '13872.bm', 'p': 53, 'prec': 20, 'unit': 510631076951965568822894379971215, 'val': 1}
  • id: 615518
    {'lmfdb_iso': '13872.bm', 'p': 59, 'prec': 20, 'unit': 2344179789975050935497013852924497, 'val': 1}
  • id: 615519
    {'lmfdb_iso': '13872.bm', 'p': 61, 'prec': 20, 'unit': 35320885386162336440993972728527, 'val': 1}
  • id: 615505
    {'lmfdb_iso': '13872.bm', 'p': 67, 'prec': 20, 'unit': 6136483797054702574886830901398790, 'val': 1}
  • id: 615516
    {'lmfdb_iso': '13872.bm', 'p': 73, 'prec': 20, 'unit': 156323222675707599204571311108907754, 'val': 1}
  • id: 615512
    {'lmfdb_iso': '13872.bm', 'p': 79, 'prec': 20, 'unit': 1126696444905946946279242434488771001, 'val': 1}
  • id: 615504
    {'lmfdb_iso': '13872.bm', 'p': 83, 'prec': 20, 'unit': 557212504294723807613200570428072790, 'val': 1}
  • id: 615517
    {'lmfdb_iso': '13872.bm', 'p': 89, 'prec': 20, 'unit': 9500543667258640321780108674069901434, 'val': 1}
  • id: 615503
    {'lmfdb_iso': '13872.bm', 'p': 97, 'prec': 20, 'unit': 33096086519032558418177588240041100707, 'val': 1}