Elliptic curve data - 42042.b2

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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': '42042v', 'Clabel': '42042v2', 'Cnumber': 2, 'abc_quality': 1.0349530577780537, 'absD': 14067707264879019687936, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 24024, 'ainvs': [1, 1, 0, -3955354, -6461653484], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 42042, 'degree': 3538080, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9390508894695776423150722751', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [-58169016237585194137, 119573538788081664], 'lmfdb_iso': '42042.b', 'lmfdb_label': '42042.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -80722, 18827108], 'min_quad_twist_disc': -7, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '21.8.0-3.a.1.2', '1144.2.0.?', '3432.8.0.?', '24024.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '23.398975799801487319315608516', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.9660958149419209897623959034', 'prec': 100}, 'szpiro_ratio': 5.513676266583177, '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, -1, -1, 1, -3, 1, 0, -1, 1, 3, 1, -1, -1, 0, 3, 1, 0, -1, -2, -3], 'aplist': [-1, -1, -3, 0, 1, -1, 0, -2, 3, -3, -8, 2, 9, 5, 0, -6, 3, 1, 11, -6, 1, 2, -18, 0, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 42042, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '42042.b', 'trace_hash': 1620884719792670893}
• 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': '0.0028000954336394224115747130112', 'prec': 110}, 'conductor': 42042, 'gens': [[16287624709, 173876375316115, 2524]], 'heights': [{'__RealLiteral__': 0, 'data': '23.398975799801487319315608516', 'prec': 100}], 'lmfdb_label': '42042.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.050243080084284521741622882525', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3512732299993231920668715969759270633', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [1, 0], '5': [1, 0], '7': 'a', '11': [2, 0], '13': [1, 0], '17': [1, 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': '42042.b2'}
• ec_torsion_growth •

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

  
  
  • id: 2064490
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '42042.b2', 'torsion': [3]}
  • id: 2064491
    {'degree': 3, 'field': [2, 6, -1, 1], 'lmfdb_label': '42042.b2', 'torsion': [2]}
  • id: 2064494
    {'degree': 6, 'field': [-579, -207, 118, -5, -4, -1, 1], 'lmfdb_label': '42042.b2', 'torsion': [6]}
  • id: 2064492
    {'degree': 6, 'field': [1144, 0, 289, 0, 34, 0, 1], 'lmfdb_label': '42042.b2', 'torsion': [2, 2]}
  • id: 2064493
    {'degree': 6, 'field': [10304, -903, -279, 185, 9, -3, 1], 'lmfdb_label': '42042.b2', 'torsion': [3]}
  • id: 2064495
    {'degree': 12, 'field': [-7860743064, -1936557000, -2013032997, -36544596, -137680551, 306308, -3230931, 25440, -23171, -204, 83, -4, 1], 'lmfdb_label': '42042.b2', 'torsion': [4]}
  • id: 2064496
    {'degree': 12, 'field': [135100, -24150, 5877, 35660, -15555, -2910, 1307, -366, 195, -80, 27, -6, 1], 'lmfdb_label': '42042.b2', 'torsion': [3, 3]}
  • id: 2064497
    {'degree': 12, 'field': [14561017, -2278230, 2587889, -631074, 346050, -39798, 18685, -4878, 1518, -210, 53, -6, 1], 'lmfdb_label': '42042.b2', 'torsion': [2, 6]}
  • id: 2064498
    {'degree': 18, 'field': [-18558085631643, -6079635882369, 6842084741361, -2677667483904, 1521200804886, -641966441070, 122449441198, -2427081432, -1315286901, -237957503, 49771431, 11725560, -1879650, -180774, 26934, 2176, -267, -9, 1], 'lmfdb_label': '42042.b2', 'torsion': [9]}
  • id: 2064499
    {'degree': 18, 'field': [6134967416, -8231646186, 2905467822, -2046608031, 2166083091, -734691492, 228757908, 24471243, -13782627, 3440291, -109863, -193761, 31605, -63, 279, -162, 54, -9, 1], 'lmfdb_label': '42042.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: 997550
    {'conductor': 42042, 'conductor_valuation': 1, 'discriminant_valuation': 39, 'j_denominator_valuation': 39, 'kodaira_symbol': 43, 'lmfdb_label': '42042.b2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 997551
    {'conductor': 42042, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42042.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 997552
    {'conductor': 42042, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '42042.b2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 997553
    {'conductor': 42042, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42042.b2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 997554
    {'conductor': 42042, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '42042.b2', 'prime': 13, '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: 1944463
    {'adelic_gens': [[4369, 13734, 19971, 17179], [4, 3, 9, 7], [24019, 6, 24018, 7], [20591, 0, 0, 24023], [3578, 13587, 3871, 1723], [6007, 13734, 0, 1], [1, 6, 0, 1], [12937, 13734, 21651, 17179], [3, 4, 8, 11], [12013, 13734, 18879, 17179], [1, 0, 6, 1]], 'adelic_image': '24024.16.0.?', 'conductor': 42042, 'lmfdb_label': '42042.b2', 'prime': 0}
  • id: 183715
    {'conductor': 42042, 'elladic_image': '3.4.0.1', 'lmfdb_label': '42042.b2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2091080
    {'lmfdb_iso': '42042.b', 'p': 5, 'prec': 20, 'unit': 14058706401486, 'val': 1}
  • id: 2091064
    {'lmfdb_iso': '42042.b', 'p': 19, 'prec': 20, 'unit': 1023196597606132491728039, 'val': 1}
  • id: 2091077
    {'lmfdb_iso': '42042.b', 'p': 23, 'prec': 20, 'unit': 36432460925867237494497457, 'val': 1}
  • id: 2091072
    {'lmfdb_iso': '42042.b', 'p': 29, 'prec': 20, 'unit': 5336863972433734339154475397, 'val': 1}
  • id: 2091069
    {'lmfdb_iso': '42042.b', 'p': 31, 'prec': 20, 'unit': 12767161707390972669150828993, 'val': 1}
  • id: 2091067
    {'lmfdb_iso': '42042.b', 'p': 37, 'prec': 20, 'unit': 374941676976786865715896382665, 'val': 1}
  • id: 2091070
    {'lmfdb_iso': '42042.b', 'p': 41, 'prec': 20, 'unit': 1611804730059952819644576405996, 'val': 1}
  • id: 2091071
    {'lmfdb_iso': '42042.b', 'p': 43, 'prec': 20, 'unit': 8181994384096059234437760746838, 'val': 1}
  • id: 2091075
    {'lmfdb_iso': '42042.b', 'p': 53, 'prec': 20, 'unit': 473058485932574645908809504810002, 'val': 1}
  • id: 2091078
    {'lmfdb_iso': '42042.b', 'p': 59, 'prec': 20, 'unit': 2716652095094449870218115283099703, 'val': 1}
  • id: 2091079
    {'lmfdb_iso': '42042.b', 'p': 61, 'prec': 20, 'unit': 477519308054664528168587824876076880, 'val': -1}
  • id: 2091066
    {'lmfdb_iso': '42042.b', 'p': 67, 'prec': 20, 'unit': 45208435536008524983718839530586006, 'val': 1}
  • id: 2091068
    {'lmfdb_iso': '42042.b', 'p': 71, 'prec': 20, 'unit': 41652077868593003936829609937991674, 'val': 1}
  • id: 2091076
    {'lmfdb_iso': '42042.b', 'p': 73, 'prec': 20, 'unit': 12682384528751779756425845645664342611, 'val': -1}
  • id: 2091073
    {'lmfdb_iso': '42042.b', 'p': 79, 'prec': 20, 'unit': 260793464511587412500262180968448130, 'val': 1}
  • id: 2091074
    {'lmfdb_iso': '42042.b', 'p': 83, 'prec': 20, 'unit': 2677706694374883165818474683069981803, 'val': 1}
  • id: 2091065
    {'lmfdb_iso': '42042.b', 'p': 97, 'prec': 20, 'unit': 7714514219066334093323791128031733551, 'val': 1}