Elliptic curve data - 42432.b1

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• 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': '42432h', 'Clabel': '42432h1', 'Cnumber': 1, 'abc_quality': 0.7898620484243712, 'absD': 105910272, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1768, 'ainvs': [0, -1, 0, -169, 745], 'analytic_rank': 2, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 42432, 'degree': 10240, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.25634232928761864222264248714', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [131096512, 25857], 'lmfdb_iso': '42432.b', 'lmfdb_label': '42432.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -42, -72], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '34.6.0.a.1', '104.6.0.?', '1768.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 17, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.0377301807506358359689422853', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.43680485127232666719458963432', 'prec': 107}, 'szpiro_ratio': 2.5347294670152474, '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, 0, 0, 1, 0, 2, 0, 1, 0, 2, 0, -1, 0, -4, 0], 'aplist': [0, -1, -2, 0, 2, 1, -1, -4, -6, -8, -4, 6, -12, -4, 0, -6, -4, -4, -12, -12, -4, 2, 0, -6, -12], 'class_deg': 2, 'class_size': 2, 'conductor': 42432, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '42432.b', 'trace_hash': 1971636156672239999}
• 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': '0.59888561527539275807398762970', 'prec': 103}, 'conductor': 42432, 'gens': [[1, 24, 1], [-8, 39, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.97855834685976201974600709121', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.0831041887834446658968081052', 'prec': 100}], 'lmfdb_label': '42432.b1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '1.7854701514630251843465874935', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.4113450520103610705502373272202058153', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[5, 0, 1]], 'xcoord_integral_points': [-13, -8, 1, 3, 5, 13, 31, 57, 397]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': [2, 2, 0], '11': [2, 0], '13': [5, 0], '17': [4, 0], '19': [2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 2, 0]}, 'iwp0': 0, 'lmfdb_label': '42432.b1'}
• ec_torsion_growth •

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

  
  
  • id: 2081669
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '42432.b1', 'torsion': [2, 2]}
  • id: 2081670
    {'degree': 4, 'field': [126, -52, 6, 0, 1], 'lmfdb_label': '42432.b1', 'torsion': [4]}
  • id: 2081673
    {'degree': 8, 'field': [-774192, 0, 74368, 0, -3048, 0, 0, 0, 1], 'lmfdb_label': '42432.b1', 'torsion': [6]}
  • id: 2081672
    {'degree': 8, 'field': [22334, -15964, 12718, -2448, 591, -96, 2, -4, 1], 'lmfdb_label': '42432.b1', 'torsion': [2, 4]}
  • id: 2081671
    {'degree': 8, 'field': [214816, 103264, 13976, 2472, -1717, -222, -1, -2, 1], 'lmfdb_label': '42432.b1', 'torsion': [2, 4]}
  • id: 2081674
    {'degree': 16, 'field': [15824484, 0, 0, 0, 5696496, 0, 668304, 0, 11428, 0, -28448, 0, 2216, 0, -56, 0, 1], 'lmfdb_label': '42432.b1', 'torsion': [8]}
  • id: 2081675
    {'degree': 16, 'field': [1052872704, 0, 2249035776, 0, -877026176, 0, 28035072, 0, 313005, 0, -24432, 0, -1302, 0, 0, 0, 1], 'lmfdb_label': '42432.b1', 'torsion': [2, 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: 1006899
    {'conductor': 42432, 'conductor_valuation': 6, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '42432.b1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1006900
    {'conductor': 42432, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42432.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1006901
    {'conductor': 42432, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42432.b1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1006902
    {'conductor': 42432, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42432.b1', 'prime': 17, 'reduction_type': -1, '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: 1947017
    {'adelic_gens': [[210, 1, 1663, 0], [1, 2, 2, 5], [1, 4, 0, 1], [1765, 4, 1764, 5], [225, 1548, 1104, 663], [1, 0, 4, 1], [1497, 4, 1226, 9], [3, 4, 8, 11], [885, 4, 2, 9]], 'adelic_image': '1768.12.0.?', 'conductor': 42432, 'lmfdb_label': '42432.b1', 'prime': 0}
  • id: 185306
    {'conductor': 42432, 'elladic_image': '2.3.0.1', 'lmfdb_label': '42432.b1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2111627
    {'lmfdb_iso': '42432.b', 'p': 5, 'prec': 20, 'unit': 7867267781674, 'val': 2}
  • id: 2111634
    {'lmfdb_iso': '42432.b', 'p': 11, 'prec': 20, 'unit': 4721447053137762243, 'val': 2}
  • id: 2111635
    {'lmfdb_iso': '42432.b', 'p': 19, 'prec': 20, 'unit': 1665914429935253303635652, 'val': 2}
  • id: 2111638
    {'lmfdb_iso': '42432.b', 'p': 23, 'prec': 20, 'unit': 138319251509581152549634, 'val': 2}
  • id: 2111632
    {'lmfdb_iso': '42432.b', 'p': 29, 'prec': 20, 'unit': 3527205366266702160028931854, 'val': 2}
  • id: 2111629
    {'lmfdb_iso': '42432.b', 'p': 31, 'prec': 20, 'unit': 8434057037384953124066820464, 'val': 2}
  • id: 2111642
    {'lmfdb_iso': '42432.b', 'p': 37, 'prec': 20, 'unit': 490885622599202985404144812889, 'val': 2}
  • id: 2111630
    {'lmfdb_iso': '42432.b', 'p': 41, 'prec': 20, 'unit': 610736876993630670686463868361, 'val': 2}
  • id: 2111631
    {'lmfdb_iso': '42432.b', 'p': 43, 'prec': 20, 'unit': 4792193681828874888464215662113, 'val': 2}
  • id: 2111636
    {'lmfdb_iso': '42432.b', 'p': 53, 'prec': 20, 'unit': 572292960774192943127837204409991, 'val': 2}
  • id: 2111640
    {'lmfdb_iso': '42432.b', 'p': 59, 'prec': 20, 'unit': 3995369350878924350254631839405469, 'val': 2}
  • id: 2111641
    {'lmfdb_iso': '42432.b', 'p': 61, 'prec': 20, 'unit': 4186619116636029035811847933159511, 'val': 2}
  • id: 2111626
    {'lmfdb_iso': '42432.b', 'p': 67, 'prec': 20, 'unit': 15216917706977351927987604515945837, 'val': 2}
  • id: 2111628
    {'lmfdb_iso': '42432.b', 'p': 71, 'prec': 20, 'unit': 139457070297157397078110022469865370, 'val': 2}
  • id: 2111637
    {'lmfdb_iso': '42432.b', 'p': 73, 'prec': 20, 'unit': 193920918059287231341335245898725546, 'val': 2}
  • id: 2111633
    {'lmfdb_iso': '42432.b', 'p': 79, 'prec': 20, 'unit': 356138426727932225845564845099654849, 'val': 2}
  • id: 2111639
    {'lmfdb_iso': '42432.b', 'p': 89, 'prec': 20, 'unit': 3713388238792795836302344418880507716, 'val': 2}
  • id: 2111625
    {'lmfdb_iso': '42432.b', 'p': 97, 'prec': 20, 'unit': 15607551463580495294617481967802144978, 'val': 2}