Elliptic curve data - 14157.f5

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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
  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': '14157l', 'Clabel': '14157l1', 'Cnumber': 1, 'abc_quality': 0.8840474094399083, 'absD': 1211684952279087, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 6864, 'ainvs': [1, -1, 1, -26159, 2342486], 'analytic_rank': 1, 'bad_primes': [3, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 14157, 'degree': 61440, 'elladic_images': ['16.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5962022390802096296811199012', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-1532808577, 938223], 'lmfdb_iso': '14157.f', 'lmfdb_label': '14157.f5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -24, 63], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.5', '24.24.0-8.n.1.8', '48.48.0-48.g.1.1', '88.24.0.?', '104.24.0.?', '132.12.0.?', '156.12.0.?', '176.48.0.?', '208.48.0.?', '264.48.0.?', '286.6.0.?', '312.48.0.?', '528.96.0.?', '572.12.0.?', '624.96.0.?', '1144.48.0.?', '1716.24.0.?', '2288.96.0.?', '3432.96.0.?', '6864.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.8843044388552370076330474552', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 8, 1573], [11, 72, 117], [13, 14, 1089]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15205154165303048804747450624', 'prec': 107}, 'szpiro_ratio': 4.483276867821984, '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, -1, 0, -1, 2, 0, 0, 3, 0, -2, 0, 0, -1, 0, 0, -1, -6, 0, 4, -2], 'aplist': [-1, 0, 2, 0, 0, -1, -6, 4, 8, -10, 0, 6, 10, -4, -8, 10, 12, -14, -12, 0, 6, -8, 12, -2, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 14157, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '14157.f', 'trace_hash': 2124057353352221080}
• 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': '0.041072992997135797359120267837', 'prec': 107}, 'conductor': 14157, 'gens': [[48, 1069, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8843044388552370076330474552', 'prec': 100}], 'lmfdb_label': '14157.f5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.44984035645657530292334222503', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3905447217893876717926120355033380605', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-195, 97, 1]], 'xcoord_integral_points': [-195, 48, 168]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 0], '7': [3, 3, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '14157.f5'}
• ec_torsion_growth •

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

  
  
  • id: 727872
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '14157.f5', 'torsion': [4]}
  • id: 727873
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '14157.f5', 'torsion': [4]}
  • id: 727871
    {'degree': 2, 'field': [36, -1, 1], 'lmfdb_label': '14157.f5', 'torsion': [2, 2]}
  • id: 727876
    {'degree': 4, 'field': [9, -3, -2, -1, 1], 'lmfdb_label': '14157.f5', 'torsion': [8]}
  • id: 727875
    {'degree': 4, 'field': [25, 0, -23, 0, 1], 'lmfdb_label': '14157.f5', 'torsion': [8]}
  • id: 727874
    {'degree': 4, 'field': [108, -63, 19, -1, 1], 'lmfdb_label': '14157.f5', 'torsion': [2, 4]}
  • id: 727881
    {'degree': 8, 'field': [27, 195, -87, 1071, 279, 108, 36, -1, 1], 'lmfdb_label': '14157.f5', 'torsion': [6]}
  • id: 727880
    {'degree': 8, 'field': [643, 437, -344, -137, 131, 19, -20, -1, 1], 'lmfdb_label': '14157.f5', 'torsion': [16]}
  • id: 727879
    {'degree': 8, 'field': [1296, 0, 36, 0, -35, 0, 1, 0, 1], 'lmfdb_label': '14157.f5', 'torsion': [2, 8]}
  • id: 727877
    {'degree': 8, 'field': [4104, -10800, 9694, -902, 441, -88, 36, -2, 1], 'lmfdb_label': '14157.f5', 'torsion': [2, 4]}
  • id: 727878
    {'degree': 8, 'field': [72868, -33988, 33778, 386, -107, -106, 40, -4, 1], 'lmfdb_label': '14157.f5', 'torsion': [8]}
  • id: 727884
    {'degree': 16, 'field': [-10859, -588626, -2426653, -349648, 484141, -295290, 43556, 11750, 13249, 5416, -1750, -1386, 280, 130, -34, -4, 1], 'lmfdb_label': '14157.f5', 'torsion': [16]}
  • id: 727885
    {'degree': 16, 'field': [42849, 57753, 15741, 55134, 57294, -16605, -8376, 10626, 205, -2002, -86, 139, 74, -2, -11, -1, 1], 'lmfdb_label': '14157.f5', 'torsion': [2, 16]}
  • id: 727887
    {'degree': 16, 'field': [62001, -372753, 60102, 783807, -4233, 64242, 105628, -211733, 65973, -33537, 10128, -4503, 897, -108, 3, -2, 1], 'lmfdb_label': '14157.f5', 'torsion': [12]}
  • id: 727883
    {'degree': 16, 'field': [274576, -419200, 320000, 1699568, 2895320, 984184, 383112, 423292, 127449, 96158, 48794, 3724, 855, 416, 18, -6, 1], 'lmfdb_label': '14157.f5', 'torsion': [2, 8]}
  • id: 727882
    {'degree': 16, 'field': [14776336, 0, 0, 0, 3667304, 0, 0, 0, 193377, 0, 0, 0, 38, 0, 0, 0, 1], 'lmfdb_label': '14157.f5', 'torsion': [4, 4]}
  • id: 727888
    {'degree': 16, 'field': [71545419, 207862974, 215330940, 89538141, 9147534, -1010592, 600667, 449657, 278640, -9449, -19384, -2970, 830, 154, -27, -4, 1], 'lmfdb_label': '14157.f5', 'torsion': [12]}
  • id: 727886
    {'degree': 16, 'field': [124022583, 163307664, 184365801, -22953537, -583686, -7269102, -513621, -368343, 79801, -58018, 45469, -7357, 2890, -259, 79, -4, 1], 'lmfdb_label': '14157.f5', '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: 310365
    {'conductor': 14157, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '14157.f5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 310366
    {'conductor': 14157, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '14157.f5', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 310367
    {'conductor': 14157, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '14157.f5', '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: 1758108
    {'adelic_gens': [[1, 16, 1724, 1845], [6017, 16, 4490, 5439], [6849, 16, 6848, 17], [1, 16, 0, 1], [15, 2, 6766, 6851], [1072, 5, 4707, 6850], [5, 4, 6860, 6861], [2287, 6848, 4568, 6735], [1, 0, 16, 1], [6232, 6863, 4913, 6854]], 'adelic_image': '6864.192.1.?', 'conductor': 14157, 'lmfdb_label': '14157.f5', 'prime': 0}
  • id: 66988
    {'conductor': 14157, 'elladic_image': '16.24.0.3', 'lmfdb_label': '14157.f5', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 631094
    {'lmfdb_iso': '14157.f', 'p': 5, 'prec': 20, 'unit': 11514931422968, 'val': 1}
  • id: 631085
    {'lmfdb_iso': '14157.f', 'p': 17, 'prec': 20, 'unit': 219681782003920711361801, 'val': 1}
  • id: 631077
    {'lmfdb_iso': '14157.f', 'p': 19, 'prec': 20, 'unit': 1726719152801131434424475, 'val': 1}
  • id: 631090
    {'lmfdb_iso': '14157.f', 'p': 23, 'prec': 20, 'unit': 52701965330095192605508903, 'val': 1}
  • id: 631083
    {'lmfdb_iso': '14157.f', 'p': 29, 'prec': 20, 'unit': 3279265076572823363513335761, 'val': 1}
  • id: 631080
    {'lmfdb_iso': '14157.f', 'p': 37, 'prec': 20, 'unit': 20494756213756464417145152820, 'val': 1}
  • id: 631081
    {'lmfdb_iso': '14157.f', 'p': 41, 'prec': 20, 'unit': 1312784203837786623181750049018, 'val': 1}
  • id: 631082
    {'lmfdb_iso': '14157.f', 'p': 43, 'prec': 20, 'unit': 3820247131679554997801993343790, 'val': 1}
  • id: 631092
    {'lmfdb_iso': '14157.f', 'p': 47, 'prec': 20, 'unit': 53390606917819744352701558661263, 'val': 1}
  • id: 631087
    {'lmfdb_iso': '14157.f', 'p': 53, 'prec': 20, 'unit': 295335203649084434031423832358672, 'val': 1}
  • id: 631088
    {'lmfdb_iso': '14157.f', 'p': 59, 'prec': 20, 'unit': 1766277486110866590498473672071963, 'val': 1}
  • id: 631093
    {'lmfdb_iso': '14157.f', 'p': 61, 'prec': 20, 'unit': 6560709275685646494059276203137638, 'val': 1}
  • id: 631079
    {'lmfdb_iso': '14157.f', 'p': 67, 'prec': 20, 'unit': 5218564117498896253870919054917516, 'val': 1}
  • id: 631089
    {'lmfdb_iso': '14157.f', 'p': 73, 'prec': 20, 'unit': 90810289860033203942123455073667995, 'val': 1}
  • id: 631084
    {'lmfdb_iso': '14157.f', 'p': 79, 'prec': 20, 'unit': 690071570787247852408970457519239528, 'val': 1}
  • id: 631086
    {'lmfdb_iso': '14157.f', 'p': 83, 'prec': 20, 'unit': 1093258262511741070274640072925617795, 'val': 1}
  • id: 631091
    {'lmfdb_iso': '14157.f', 'p': 89, 'prec': 20, 'unit': 9233265925012852046966053150126390650, 'val': 1}
  • id: 631078
    {'lmfdb_iso': '14157.f', 'p': 97, 'prec': 20, 'unit': 53189224909884470366734409738099552352, 'val': 1}