Elliptic curve data - 52272.k1

Formats: - HTML - YAML - JSON - 2026-07-03T09:52:18.141305

• 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': '52272co', 'Clabel': '52272co1', 'Cnumber': 1, 'abc_quality': 1.0251241218312794, 'absD': 2086161208344576, 'adelic_genus': 1, 'adelic_index': 24, 'adelic_level': 264, 'ainvs': [0, 0, 0, -11979, 2254714], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 52272, 'degree': 228096, 'elladic_images': ['3.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6215435496799279116776528786', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1], 'jinv': [-729, 8], 'lmfdb_iso': '52272.k', 'lmfdb_label': '52272.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -6, 28], 'min_quad_twist_disc': 44, 'modell_images': ['3Ns'], 'modm_images': ['3.6.0.b.1', '24.12.0.bx.1', '33.12.0.a.1', '264.24.1.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.2534643264484383353972080784', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 297], [3, 2, 1936], [11, 42, 432]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1446781576458227286348482356', 'prec': 103}, 'szpiro_ratio': 3.9377174015865375, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 6, 0], 'aplist': [0, 0, -3, 0, 0, 3, 3, 6, -3, 6, -4, -2, -3, 6, 0, 9, 12, -15, 5, -12, -6, -15, -9, 6, 17], 'class_deg': 1, 'class_size': 1, 'conductor': 52272, 'isogeny_matrix': [[1]], 'lmfdb_iso': '52272.k', 'trace_hash': 149028930755498170}
• 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': '0.039043178691140990468244414086', 'prec': 107}, 'conductor': 52272, 'gens': [[1815, 77198, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.2534643264484383353972080784', 'prec': 100}], 'lmfdb_label': '52272.k1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.39534547225193740688310982842', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1449695623783572126505064212049376460', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [1815]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [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': '52272.k1'}
• ec_torsion_growth •

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

  
  
  • id: 2531099
    {'degree': 3, 'field': [-14, -9, 0, 1], 'lmfdb_label': '52272.k1', 'torsion': [2]}
  • id: 2531101
    {'degree': 4, 'field': [-44, 0, -11, 0, 1], 'lmfdb_label': '52272.k1', 'torsion': [3]}
  • id: 2531100
    {'degree': 4, 'field': [33, 0, 11, 0, 1], 'lmfdb_label': '52272.k1', 'torsion': [3]}
  • id: 2531102
    {'degree': 6, 'field': [66, 0, 93, 0, 36, 0, 1], 'lmfdb_label': '52272.k1', 'torsion': [2, 2]}
  • id: 2531103
    {'degree': 8, 'field': [1089, 0, -363, 0, 88, 0, -11, 0, 1], 'lmfdb_label': '52272.k1', 'torsion': [3, 3]}
  • id: 2531104
    {'degree': 12, 'field': [-127776, 0, 143748, 0, -54087, 0, 7260, 0, -198, 0, 0, 0, 1], 'lmfdb_label': '52272.k1', 'torsion': [4]}
  • id: 2531106
    {'degree': 12, 'field': [-85184, 0, 63888, 0, -5808, 0, -968, 0, 132, 0, 33, 0, 1], 'lmfdb_label': '52272.k1', 'torsion': [6]}
  • id: 2531105
    {'degree': 12, 'field': [35937, 0, -35937, 0, 11979, 0, -726, 0, 363, 0, -33, 0, 1], 'lmfdb_label': '52272.k1', 'torsion': [6]}
• 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: 1252037
    {'conductor': 52272, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '52272.k1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1252038
    {'conductor': 52272, 'conductor_valuation': 3, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '52272.k1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1252039
    {'conductor': 52272, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '52272.k1', 'prime': 11, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 2011376
    {'adelic_gens': [[133, 6, 135, 239], [1, 0, 6, 1], [199, 6, 69, 19], [171, 2, 67, 261], [133, 6, 135, 19], [259, 6, 258, 7], [2, 3, 3, 5], [1, 6, 0, 1]], 'adelic_image': '264.24.1.?', 'conductor': 52272, 'lmfdb_label': '52272.k1', 'prime': 0}
  • id: 223575
    {'conductor': 52272, 'elladic_image': '3.6.0.1', 'lmfdb_label': '52272.k1', 'modell_image': '3Ns', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2633240
    {'lmfdb_iso': '52272.k', 'p': 5, 'prec': 20, 'unit': 15296453543623, 'val': 1}
  • id: 2633246
    {'lmfdb_iso': '52272.k', 'p': 13, 'prec': 20, 'unit': 1339547273227035245837, 'val': 1}
  • id: 2633248
    {'lmfdb_iso': '52272.k', 'p': 17, 'prec': 20, 'unit': 776720877006523392512, 'val': 1}
  • id: 2633237
    {'lmfdb_iso': '52272.k', 'p': 19, 'prec': 20, 'unit': 936428567750439855785301, 'val': 1}
  • id: 2633252
    {'lmfdb_iso': '52272.k', 'p': 23, 'prec': 20, 'unit': 19076251126749611451766717, 'val': 1}
  • id: 2633245
    {'lmfdb_iso': '52272.k', 'p': 29, 'prec': 20, 'unit': 1749574422242544911693172887, 'val': 1}
  • id: 2633242
    {'lmfdb_iso': '52272.k', 'p': 31, 'prec': 20, 'unit': 18591535994560765351477808123, 'val': 1}
  • id: 2633256
    {'lmfdb_iso': '52272.k', 'p': 37, 'prec': 20, 'unit': 604516750446951431710504139953, 'val': 1}
  • id: 2633243
    {'lmfdb_iso': '52272.k', 'p': 41, 'prec': 20, 'unit': 978859413178455491636938277460, 'val': 1}
  • id: 2633244
    {'lmfdb_iso': '52272.k', 'p': 43, 'prec': 20, 'unit': 3251896831358552365075872340655, 'val': 1}
  • id: 2633250
    {'lmfdb_iso': '52272.k', 'p': 53, 'prec': 20, 'unit': 548398565853859452350593275891390, 'val': 1}
  • id: 2633254
    {'lmfdb_iso': '52272.k', 'p': 59, 'prec': 20, 'unit': 817202539570428564787317312069290, 'val': 1}
  • id: 2633255
    {'lmfdb_iso': '52272.k', 'p': 61, 'prec': 20, 'unit': 996105901236787496470696425958520, 'val': 1}
  • id: 2633239
    {'lmfdb_iso': '52272.k', 'p': 67, 'prec': 20, 'unit': 7290329780600530641370334925734047, 'val': 1}
  • id: 2633241
    {'lmfdb_iso': '52272.k', 'p': 71, 'prec': 20, 'unit': 24644747283106613446686318208025175, 'val': 1}
  • id: 2633251
    {'lmfdb_iso': '52272.k', 'p': 73, 'prec': 20, 'unit': 73069969002151969620734112559300020, 'val': 1}
  • id: 2633247
    {'lmfdb_iso': '52272.k', 'p': 79, 'prec': 20, 'unit': 1126557768015579547136245989206466400, 'val': 1}
  • id: 2633249
    {'lmfdb_iso': '52272.k', 'p': 83, 'prec': 20, 'unit': 2408961263687494251186633283378714149, 'val': 1}
  • id: 2633253
    {'lmfdb_iso': '52272.k', 'p': 89, 'prec': 20, 'unit': 1658932260711252015897447309191042931, 'val': 1}
  • id: 2633238
    {'lmfdb_iso': '52272.k', 'p': 97, 'prec': 20, 'unit': 21612568676562234489385832516745188396, 'val': 1}