Elliptic curve data - 42432.g1

Formats: - HTML - YAML - JSON - 2024-06-09T16:00:25.273906

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '42432a', 'Clabel': '42432a3', 'Cnumber': 3, 'abc_quality': 1.0594629576132126, 'absD': 488726683481088, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 5304, 'ainvs': [0, -1, 0, -19813, -138299], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 42432, 'degree': 138240, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5084519752617179665791155878', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [840033089536000, 477272151837], 'lmfdb_iso': '42432.g', 'lmfdb_label': '42432.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -4953, -19764], 'min_quad_twist_disc': 8, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '24.24.0-6.a.1.3', '26.6.0.b.1', '68.6.0.b.1', '78.24.0.?', '204.24.0.?', '312.48.0.?', '408.48.0.?', '884.12.0.?', '2652.48.1.?', '5304.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.7474454098629776060642814476', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.93082932479509687539808881992', 'prec': 103}, 'szpiro_ratio': 3.8754935565564343, '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, 0, 0, -4, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, -2, 0], 'aplist': [0, -1, 0, -4, 0, -1, -1, -2, 0, -6, 8, -8, 0, -8, 6, 6, 6, 10, -2, 12, -4, 8, -18, 6, 8], 'class_deg': 6, 'class_size': 4, 'conductor': 42432, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '42432.g', 'trace_hash': 527982089522713022}
• 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': '0.048952543482731246269340961273', 'prec': 107}, 'conductor': 42432, 'gens': [[-23, 552, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.7474454098629776060642814476', 'prec': 100}], 'lmfdb_label': '42432.g1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.43465315608757104679611894252', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2576779493256489227723532251379910202', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-7, 0, 1]], 'xcoord_integral_points': [-23, -7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1], '5': [1, 1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [3, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '42432.g1'}
• ec_torsion_growth •

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

  
  
  • id: 2081553
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '42432.g1', 'torsion': [2, 2]}
  • id: 2081554
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '42432.g1', 'torsion': [6]}
  • id: 2081556
    {'degree': 4, 'field': [87, -6, 7, -2, 1], 'lmfdb_label': '42432.g1', 'torsion': [2, 6]}
  • id: 2081555
    {'degree': 4, 'field': [117, 0, 20, 0, 1], 'lmfdb_label': '42432.g1', 'torsion': [4]}
  • id: 2081557
    {'degree': 6, 'field': [-18, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '42432.g1', 'torsion': [6]}
  • id: 2081559
    {'degree': 8, 'field': [625, 0, -500, 0, -318, 0, -20, 0, 1], 'lmfdb_label': '42432.g1', 'torsion': [2, 4]}
  • id: 2081560
    {'degree': 8, 'field': [1764, 0, -744, 0, 100, 0, -8, 0, 1], 'lmfdb_label': '42432.g1', 'torsion': [12]}
  • id: 2081558
    {'degree': 8, 'field': [6561, 0, -1108, 0, 147, 0, -12, 0, 1], 'lmfdb_label': '42432.g1', 'torsion': [2, 4]}
  • id: 2081562
    {'degree': 12, 'field': [-1719, 8046, -8613, 1710, -2160, 1206, 145, -366, -30, 70, -3, -6, 1], 'lmfdb_label': '42432.g1', 'torsion': [2, 6]}
  • id: 2081561
    {'degree': 12, 'field': [289, 102, 291, -770, 360, -18, 105, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '42432.g1', 'torsion': [3, 6]}
  • id: 2081564
    {'degree': 16, 'field': [173313, -1102248, 3769092, -5784768, 3975678, -1170312, 158872, 226216, -86505, 12392, 4544, -3144, -22, 224, -12, -8, 1], 'lmfdb_label': '42432.g1', 'torsion': [2, 12]}
  • id: 2081565
    {'degree': 16, 'field': [37491129, 0, -22332336, 0, 6396754, 0, -1080820, 0, 148911, 0, -13748, 0, 762, 0, -28, 0, 1], 'lmfdb_label': '42432.g1', 'torsion': [2, 12]}
  • id: 2081563
    {'degree': 16, 'field': [138017724916, -112052425584, 46600289072, -9895583856, -67654776, 316728768, -53981216, -2187696, 3742864, -53448, 5080, 9384, 2700, -408, -40, 0, 1], 'lmfdb_label': '42432.g1', 'torsion': [8]}
  • id: 2081566
    {'degree': 18, 'field': [31462724376, 0, 516796848, 0, 1038959136, 0, 523280232, 0, 3841344, 0, 4211244, 0, -239586, 0, 30132, 0, 360, 0, 1], 'lmfdb_label': '42432.g1', 'torsion': [18]}
• 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: 1006843
    {'conductor': 42432, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '42432.g1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1006844
    {'conductor': 42432, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42432.g1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1006845
    {'conductor': 42432, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '42432.g1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1006846
    {'conductor': 42432, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '42432.g1', '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: 1947139
    {'adelic_gens': [[1, 6, 6, 37], [2663, 5292, 2664, 5291], [1, 12, 0, 1], [826, 3, 2013, 2644], [5293, 5302, 2702, 2661], [5293, 12, 5292, 13], [3753, 2870, 5062, 4183], [1769, 12, 1768, 1], [1873, 12, 630, 73], [2651, 0, 0, 5303], [1, 0, 12, 1], [11, 2, 5254, 5295]], 'adelic_image': '5304.96.1.?', 'conductor': 42432, 'lmfdb_label': '42432.g1', 'prime': 0}
  • id: 185432
    {'conductor': 42432, 'elladic_image': '2.3.0.1', 'lmfdb_label': '42432.g1', 'modell_image': '2B', 'prime': 2}
  • id: 185433
    {'conductor': 42432, 'elladic_image': '3.4.0.1', 'lmfdb_label': '42432.g1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2111595
    {'lmfdb_iso': '42432.g', 'p': 7, 'prec': 20, 'unit': 4542729106120645, 'val': 1}
  • id: 2111591
    {'lmfdb_iso': '42432.g', 'p': 19, 'prec': 20, 'unit': 1255270201088411661812109, 'val': 1}
  • id: 2111598
    {'lmfdb_iso': '42432.g', 'p': 29, 'prec': 20, 'unit': 1628424494774050747457396609, 'val': 1}
  • id: 2111607
    {'lmfdb_iso': '42432.g', 'p': 31, 'prec': 20, 'unit': 1195417997789713556233793257, 'val': 1}
  • id: 2111594
    {'lmfdb_iso': '42432.g', 'p': 37, 'prec': 20, 'unit': 484716778287000426078289682402, 'val': 1}
  • id: 2111597
    {'lmfdb_iso': '42432.g', 'p': 43, 'prec': 20, 'unit': 4752094581543786711604505434121, 'val': 1}
  • id: 2111605
    {'lmfdb_iso': '42432.g', 'p': 47, 'prec': 20, 'unit': 13409574545886995873725669003758, 'val': 1}
  • id: 2111602
    {'lmfdb_iso': '42432.g', 'p': 53, 'prec': 20, 'unit': 428802116203904330519570650278850, 'val': 1}
  • id: 2111600
    {'lmfdb_iso': '42432.g', 'p': 59, 'prec': 20, 'unit': 712074473364125172962365458669076, 'val': 1}
  • id: 2111606
    {'lmfdb_iso': '42432.g', 'p': 61, 'prec': 20, 'unit': 5343756163325179966701216674317361, 'val': 1}
  • id: 2111593
    {'lmfdb_iso': '42432.g', 'p': 67, 'prec': 20, 'unit': 6483964789750672054414779166966283, 'val': 1}
  • id: 2111604
    {'lmfdb_iso': '42432.g', 'p': 71, 'prec': 20, 'unit': 1377052009058292303755867646882205, 'val': 1}
  • id: 2111596
    {'lmfdb_iso': '42432.g', 'p': 73, 'prec': 20, 'unit': 188727821427057277678825182916232614, 'val': 1}
  • id: 2111599
    {'lmfdb_iso': '42432.g', 'p': 79, 'prec': 20, 'unit': 430420470865016635668456767852444661, 'val': 1}
  • id: 2111601
    {'lmfdb_iso': '42432.g', 'p': 83, 'prec': 20, 'unit': 2128110368339130860214845784596330089, 'val': 1}
  • id: 2111603
    {'lmfdb_iso': '42432.g', 'p': 89, 'prec': 20, 'unit': 5904186890178935005463301894746870297, 'val': 1}
  • id: 2111592
    {'lmfdb_iso': '42432.g', 'p': 97, 'prec': 20, 'unit': 248849491416319319230306719000903011, 'val': 1}