Elliptic curve data - 432.b2

Formats: - HTML - YAML - JSON - 2025-09-22T12:35:05.093122

• 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': '432f', 'Clabel': '432f2', 'Cnumber': 2, 'abc_quality': 1.0496550478531228, 'absD': 509607936, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 72, 'ainvs': [0, 0, 0, -219, -1654], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 432, 'degree': 144, 'elladic_images': ['9.36.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.37794275246003414239336243646', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3, 9], 'jinv': [-1167051, 512], 'lmfdb_iso': '432.b', 'lmfdb_label': '432.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -123, -667], 'min_quad_twist_disc': 12, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.36.0.d.1', '12.8.0-3.a.1.1', '24.16.0-24.d.1.3', '36.72.0-9.d.1.1', '72.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.69396426048046166417974295920', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 27], [3, 8, 8]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.77295954837829020510522186705', 'prec': 107}, 'szpiro_ratio': 4.670906625877731, '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, 1, 0, 0, 0, -3, 0, -4, 0, 0, 0, 0, 0, -2, 0], 'aplist': [0, 0, -3, 1, -3, -4, 0, -2, -6, -6, -5, 2, 6, 10, 6, -9, 12, 8, -14, 0, -7, -8, -3, 18, -1], 'class_deg': 9, 'class_size': 3, 'conductor': 432, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '432.b', 'trace_hash': 1507146505962271206}
• 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': '0.46959460223644852825867039009', 'prec': 103}, 'conductor': 432, 'gens': [[29, 128, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.69396426048046166417974295920', 'prec': 103}], 'lmfdb_label': '432.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.60758162138622298858746753073', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6865597222672403496253662103544195530', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [23, 29]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [5, 0], '17': [1, 3, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '432.b2'}
• ec_torsion_growth •

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

  
  
  • id: 18808
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '432.b2', 'torsion': [9]}
  • id: 18809
    {'degree': 3, 'field': [-2, 3, 0, 1], 'lmfdb_label': '432.b2', 'torsion': [2]}
  • id: 18811
    {'degree': 6, 'field': [-3, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '432.b2', 'torsion': [3]}
  • id: 18812
    {'degree': 6, 'field': [4, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '432.b2', 'torsion': [18]}
  • id: 18810
    {'degree': 6, 'field': [6, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '432.b2', 'torsion': [2, 2]}
  • id: 18815
    {'degree': 12, 'field': [1, 0, 0, 8, 15, -24, 32, 24, 15, -8, 0, 0, 1], 'lmfdb_label': '432.b2', 'torsion': [2, 18]}
  • id: 18814
    {'degree': 12, 'field': [4, 12, 66, -170, 135, -108, 135, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '432.b2', 'torsion': [3, 9]}
  • id: 18813
    {'degree': 12, 'field': [4, 18, 6, 14, -6, -6, 6, -6, 12, -7, 3, -3, 1], 'lmfdb_label': '432.b2', 'torsion': [4]}
  • id: 18816
    {'degree': 18, 'field': [16, 0, 0, 0, 0, 0, 729, 0, 1458, 0, 1215, 0, 540, 0, 135, 0, 18, 0, 1], 'lmfdb_label': '432.b2', 'torsion': [27]}
  • id: 18817
    {'degree': 18, 'field': [64, 0, 0, -480, 0, 0, -72, 0, 0, -16, 0, 0, 60, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '432.b2', '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: 4498
    {'conductor': 432, 'conductor_valuation': 4, 'discriminant_valuation': 21, 'j_denominator_valuation': 9, 'kodaira_symbol': -17, 'lmfdb_label': '432.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4499
    {'conductor': 432, 'conductor_valuation': 3, 'discriminant_valuation': 5, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '432.b2', 'prime': 3, 'reduction_type': 0, '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: 1667656
    {'adelic_gens': [[10, 9, 9, 1], [1, 18, 10, 37], [65, 54, 63, 19], [1, 18, 0, 1], [55, 18, 54, 19], [1, 0, 18, 1], [17, 54, 0, 71], [37, 18, 45, 19]], 'adelic_image': '72.144.3.?', 'conductor': 432, 'lmfdb_label': '432.b2', 'prime': 0}
  • id: 1842
    {'conductor': 432, 'elladic_image': '9.36.0.4', 'lmfdb_label': '432.b2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 6050
    {'lmfdb_iso': '432.b', 'p': 5, 'prec': 20, 'unit': 17285177590252, 'val': 1}
  • id: 6051
    {'lmfdb_iso': '432.b', 'p': 7, 'prec': 20, 'unit': 76627659722588840, 'val': -1}
  • id: 6049
    {'lmfdb_iso': '432.b', 'p': 11, 'prec': 20, 'unit': 44178345226837482961, 'val': 1}
  • id: 6056
    {'lmfdb_iso': '432.b', 'p': 13, 'prec': 20, 'unit': 33052716129327548197, 'val': 2}
  • id: 6059
    {'lmfdb_iso': '432.b', 'p': 19, 'prec': 20, 'unit': 1151066430850103714742617, 'val': 1}
  • id: 6062
    {'lmfdb_iso': '432.b', 'p': 23, 'prec': 20, 'unit': 57995452663530736126653762, 'val': 1}
  • id: 6055
    {'lmfdb_iso': '432.b', 'p': 29, 'prec': 20, 'unit': 731133260860857814177241611, 'val': 1}
  • id: 6052
    {'lmfdb_iso': '432.b', 'p': 31, 'prec': 20, 'unit': 2140483047272857528007355858, 'val': 1}
  • id: 6067
    {'lmfdb_iso': '432.b', 'p': 37, 'prec': 20, 'unit': 75467622647707204034165270765, 'val': 1}
  • id: 6053
    {'lmfdb_iso': '432.b', 'p': 41, 'prec': 20, 'unit': 4235461421079245023494056995682, 'val': 1}
  • id: 6054
    {'lmfdb_iso': '432.b', 'p': 43, 'prec': 20, 'unit': 9030602712069600527975498369465, 'val': 1}
  • id: 6064
    {'lmfdb_iso': '432.b', 'p': 47, 'prec': 20, 'unit': 15899378735535599013639580495163, 'val': 1}
  • id: 6060
    {'lmfdb_iso': '432.b', 'p': 53, 'prec': 20, 'unit': 223543129250796765997471541290477, 'val': 1}
  • id: 6058
    {'lmfdb_iso': '432.b', 'p': 59, 'prec': 20, 'unit': 1641820488202570543412269743846889, 'val': 1}
  • id: 6065
    {'lmfdb_iso': '432.b', 'p': 61, 'prec': 20, 'unit': 1855613442021185706097340050803800, 'val': 1}
  • id: 6048
    {'lmfdb_iso': '432.b', 'p': 67, 'prec': 20, 'unit': 42394414213934591265172403500619655, 'val': 1}
  • id: 6061
    {'lmfdb_iso': '432.b', 'p': 73, 'prec': 20, 'unit': 83648553102981891164884775715015214, 'val': 1}
  • id: 6057
    {'lmfdb_iso': '432.b', 'p': 79, 'prec': 20, 'unit': 1128694397468363426720318547226882121, 'val': 1}
  • id: 6066
    {'lmfdb_iso': '432.b', 'p': 83, 'prec': 20, 'unit': 621831993626637856218262271454852757, 'val': 1}
  • id: 6063
    {'lmfdb_iso': '432.b', 'p': 89, 'prec': 20, 'unit': 4741930132477158476808958896795362042, 'val': 1}
  • id: 6047
    {'lmfdb_iso': '432.b', 'p': 97, 'prec': 20, 'unit': 45870648315506985371288723989188390565, 'val': 1}