Elliptic curve data - 42432.cl2

Formats: - HTML - YAML - JSON - 2025-11-09T01:32:06.766349

• 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': '42432y', 'Clabel': '42432y2', 'Cnumber': 2, 'abc_quality': 0.9326517624097936, 'absD': 168589241892864, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 5304, 'ainvs': [0, 1, 0, 10543, 468975], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 42432, 'degree': 110592, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4157729274340398492917251588', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 63, 'isogeny_degrees': [1, 2], 'jinv': [7909612346288, 10289870721], 'lmfdb_iso': '42432.cl', 'lmfdb_label': '42432.cl2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 2636, 57304], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '12.12.0-4.a.1.1', '52.12.0.d.1', '156.24.0.?', '1768.24.0.?', '5304.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0208691399969065531091498073', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 14144], [13, 14, 3264], [17, 18, 2496]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.60710121678077032163828768376', 'prec': 103}, 'szpiro_ratio': 3.7186545713784662, '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, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, -1, 0, -2, 0], 'aplist': [0, 1, 2, 2, 2, 1, -1, -2, -4, -10, -2, -2, -2, -12, 2, 10, 6, -6, -2, -6, 2, 8, -6, -2, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 42432, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '42432.cl', 'trace_hash': 1833618073990541472}
• 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': '0.058921698836547223250646822562', 'prec': 107}, 'conductor': 42432, 'gens': [[13, 780, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0208691399969065531091498073', 'prec': 100}], 'lmfdb_label': '42432.cl2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.38531615656714071223480949127', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.3440823593850125799170396061899723477', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-39, 0, 1]], 'xcoord_integral_points': [-39, 13, 250]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [2, 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, 0]}, 'iwp0': 0, 'lmfdb_label': '42432.cl2'}
• ec_torsion_growth •

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

  
  
  • id: 2082100
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '42432.cl2', 'torsion': [2, 2]}
  • id: 2082101
    {'degree': 4, 'field': [-4, 0, -6, 0, 1], 'lmfdb_label': '42432.cl2', 'torsion': [4]}
  • id: 2082104
    {'degree': 8, 'field': [-3888, 0, -928, 0, 216, 0, 0, 0, 1], 'lmfdb_label': '42432.cl2', 'torsion': [6]}
  • id: 2082103
    {'degree': 8, 'field': [1, 0, 0, 0, 11, 0, 0, 0, 1], 'lmfdb_label': '42432.cl2', 'torsion': [2, 4]}
  • id: 2082102
    {'degree': 8, 'field': [169, 0, -52, 0, 3, 0, -4, 0, 1], 'lmfdb_label': '42432.cl2', 'torsion': [2, 4]}
  • id: 2082105
    {'degree': 16, 'field': [1, 0, 0, 0, -11, 0, 0, 0, 120, 0, 0, 0, -11, 0, 0, 0, 1], 'lmfdb_label': '42432.cl2', 'torsion': [4, 4]}
  • id: 2082107
    {'degree': 16, 'field': [59049, 0, 0, 0, 39700, 0, 0, 0, 2430, 0, 0, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '42432.cl2', 'torsion': [2, 6]}
  • id: 2082106
    {'degree': 16, 'field': [287404209, 0, 83932312, 0, -24946782, 0, 2333484, 0, 36419, 0, -33556, 0, 3078, 0, -108, 0, 1], 'lmfdb_label': '42432.cl2', 'torsion': [8]}
• 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: 1007079
    {'conductor': 42432, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '42432.cl2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1007080
    {'conductor': 42432, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '42432.cl2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 1007081
    {'conductor': 42432, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42432.cl2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1007082
    {'conductor': 42432, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '42432.cl2', 'prime': 17, 'reduction_type': -1, '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: 1947118
    {'adelic_gens': [[2651, 5296, 5302, 5287], [3979, 4, 4641, 1], [3, 8, 10, 27], [1, 0, 8, 1], [1873, 4, 0, 1], [1, 8, 0, 1], [1769, 8, 3538, 17], [5297, 8, 5296, 9], [5, 8, 48, 77], [3265, 6, 0, 1]], 'adelic_image': '5304.48.0.?', 'conductor': 42432, 'lmfdb_label': '42432.cl2', 'prime': 0}
  • id: 185411
    {'conductor': 42432, 'elladic_image': '4.6.0.5', 'lmfdb_label': '42432.cl2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2111903
    {'lmfdb_iso': '42432.cl', 'p': 5, 'prec': 20, 'unit': 15016772274682, 'val': 1}
  • id: 2111904
    {'lmfdb_iso': '42432.cl', 'p': 7, 'prec': 20, 'unit': 1907947411581431, 'val': 1}
  • id: 2111910
    {'lmfdb_iso': '42432.cl', 'p': 11, 'prec': 20, 'unit': 56108832693759249542, 'val': 1}
  • id: 2111912
    {'lmfdb_iso': '42432.cl', 'p': 19, 'prec': 20, 'unit': 242294916506962061820415, 'val': 1}
  • id: 2111915
    {'lmfdb_iso': '42432.cl', 'p': 23, 'prec': 20, 'unit': 51750288569554735811625665, 'val': 1}
  • id: 2111908
    {'lmfdb_iso': '42432.cl', 'p': 29, 'prec': 20, 'unit': 60216050987330477640338369, 'val': 1}
  • id: 2111905
    {'lmfdb_iso': '42432.cl', 'p': 31, 'prec': 20, 'unit': 13992940235863817194708164596, 'val': 1}
  • id: 2111920
    {'lmfdb_iso': '42432.cl', 'p': 37, 'prec': 20, 'unit': 64062872449850346410136155346, 'val': 1}
  • id: 2111906
    {'lmfdb_iso': '42432.cl', 'p': 41, 'prec': 20, 'unit': 643439479721627185383846391206, 'val': 1}
  • id: 2111907
    {'lmfdb_iso': '42432.cl', 'p': 43, 'prec': 20, 'unit': 2528161269970569080723066779889, 'val': 1}
  • id: 2111918
    {'lmfdb_iso': '42432.cl', 'p': 47, 'prec': 20, 'unit': 8321425429081189438203217625845, 'val': 1}
  • id: 2111913
    {'lmfdb_iso': '42432.cl', 'p': 53, 'prec': 20, 'unit': 350654164800159695486062398321398, 'val': 1}
  • id: 2111911
    {'lmfdb_iso': '42432.cl', 'p': 59, 'prec': 20, 'unit': 2752726242693303102704015513278693, 'val': 1}
  • id: 2111919
    {'lmfdb_iso': '42432.cl', 'p': 61, 'prec': 20, 'unit': 6419110569689736792951944675418181, 'val': 1}
  • id: 2111902
    {'lmfdb_iso': '42432.cl', 'p': 67, 'prec': 20, 'unit': 47195649058425337894124075745087240, 'val': 1}
  • id: 2111917
    {'lmfdb_iso': '42432.cl', 'p': 71, 'prec': 20, 'unit': 41980900451223611207635634726300270, 'val': 1}
  • id: 2111914
    {'lmfdb_iso': '42432.cl', 'p': 73, 'prec': 20, 'unit': 243991880004849264082754608142005750, 'val': 1}
  • id: 2111909
    {'lmfdb_iso': '42432.cl', 'p': 79, 'prec': 20, 'unit': 437116045068691136539713560966290291, 'val': 1}
  • id: 2111901
    {'lmfdb_iso': '42432.cl', 'p': 83, 'prec': 20, 'unit': 860129433601796713368335417770062160, 'val': 1}
  • id: 2111916
    {'lmfdb_iso': '42432.cl', 'p': 89, 'prec': 20, 'unit': 9038516009498590323136706031667694178, 'val': 1}
  • id: 2111900
    {'lmfdb_iso': '42432.cl', 'p': 97, 'prec': 20, 'unit': 45391509602941803507799923747828376333, 'val': 1}