Elliptic curve data - 15870.u5

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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': '15870u', 'Clabel': '15870u5', 'Cnumber': 5, 'abc_quality': 1.0339287621454463, 'absD': 786723408860490, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 2760, 'ainvs': [1, 0, 1, -36248, 2284868], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 23], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 15870, 'degree': 101376, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5826069488468716799949961190', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 4, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [35578826569, 5314410], 'lmfdb_iso': '15870.u', 'lmfdb_label': '15870.u5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -69, -194], 'min_quad_twist_disc': -23, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.96.1.dj.4', '40.12.0.v.1', '60.48.0.c.4', '69.8.0-3.a.1.2', '120.192.5.?', '138.24.0.?', '184.12.0.?', '276.48.0.?', '460.12.0.?', '552.192.1.?', '920.24.0.?', '1380.96.0.?', '2760.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703096', 'prec': 107}, 'szpiro_ratio': 4.456901745403064, '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, 1, 1, 1, -1, 4, -1, 1, -1, 0, 1, 2, -4, 1, 1, -6, -1, 4, 1], 'aplist': [-1, 1, 1, 4, 0, 2, -6, 4, 0, -6, 8, -2, -6, 4, 0, 6, 0, 10, 4, 0, 2, -8, -12, -18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 15870, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '15870.u', 'trace_hash': 933821727705709608}
• 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': '0.042205113272155645554255436592', 'prec': 107}, 'conductor': 15870, 'gens': [], 'heights': [], 'lmfdb_label': '15870.u5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.48308290467798712164653529975', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8984974280679227298792117985273410428', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[567, -571, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [3, 0], '5': [1, 0], '23': 'a'}, 'iwp0': 5, 'lmfdb_label': '15870.u5'}
• ec_torsion_growth •

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

  
  
  • id: 814459
    {'degree': 2, 'field': [-115, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [4]}
  • id: 814458
    {'degree': 2, 'field': [-46, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [4]}
  • id: 814457
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [2, 2]}
  • id: 814460
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '15870.u5', 'torsion': [6]}
  • id: 814464
    {'degree': 4, 'field': [6, -22, 23, -2, 1], 'lmfdb_label': '15870.u5', 'torsion': [12]}
  • id: 814463
    {'degree': 4, 'field': [18, -16, 17, -2, 1], 'lmfdb_label': '15870.u5', 'torsion': [12]}
  • id: 814461
    {'degree': 4, 'field': [81, 0, -28, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [2, 4]}
  • id: 814462
    {'degree': 4, 'field': [246, 8, -7, -2, 1], 'lmfdb_label': '15870.u5', 'torsion': [2, 6]}
  • id: 814465
    {'degree': 6, 'field': [-15, -705, 400, -51, -2, -3, 1], 'lmfdb_label': '15870.u5', 'torsion': [6]}
  • id: 814467
    {'degree': 8, 'field': [-1620, 6480, -5784, -288, 1168, -24, -68, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [8]}
  • id: 814469
    {'degree': 8, 'field': [4374, -612, 810, -412, 247, -52, 22, -4, 1], 'lmfdb_label': '15870.u5', 'torsion': [2, 12]}
  • id: 814466
    {'degree': 8, 'field': [42736, 39040, 14576, 2240, 636, -80, 36, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [2, 4]}
  • id: 814468
    {'degree': 8, 'field': [672486, -88320, 6556, -5520, 201, -230, 51, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [8]}
  • id: 814471
    {'degree': 12, 'field': [-1449135, 1657350, 82995, -695130, 263170, -21330, -4009, -726, 720, -90, 5, -6, 1], 'lmfdb_label': '15870.u5', 'torsion': [2, 6]}
  • id: 814473
    {'degree': 12, 'field': [-242811, 504666, 405237, -306360, 29080, -14114, 5029, -922, 200, 80, -23, -2, 1], 'lmfdb_label': '15870.u5', 'torsion': [12]}
  • id: 814470
    {'degree': 12, 'field': [25281, 0, 45015, 0, 17758, 0, 3995, 0, 498, 0, 35, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [3, 6]}
  • id: 814472
    {'degree': 12, 'field': [1617984, 0, -1440480, 0, 284128, 0, -31960, 0, 1992, 0, -70, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [12]}
  • id: 814478
    {'degree': 16, 'field': [899532, 439488, -667968, 443760, -95534, -432800, 674024, -581616, 316975, -133792, 47104, -12304, 3082, -504, 92, -8, 1], 'lmfdb_label': '15870.u5', 'torsion': [24]}
  • id: 814479
    {'degree': 16, 'field': [2825286, -6207648, 6637990, -5089184, 3375313, -2017794, 1124484, -570306, 253750, -94772, 32428, -8574, 2292, -414, 82, -8, 1], 'lmfdb_label': '15870.u5', 'torsion': [24]}
  • id: 814474
    {'degree': 16, 'field': [7134241, -13034480, 11907200, -7395600, 2470306, -351240, 352000, -74080, -34969, 11560, 800, 1280, 6, -40, 0, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [4, 4]}
  • id: 814477
    {'degree': 16, 'field': [7134241, 0, -2174076, 0, 1436262, 0, 713952, 0, 118615, 0, 8568, 0, 642, 0, 36, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [2, 12]}
  • id: 814475
    {'degree': 16, 'field': [7217289, 14085432, -40934904, -9742752, 41771296, 618600, -15522672, 108096, 2489226, -19656, -195032, 1248, 7680, -24, -144, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [2, 8]}
  • id: 814476
    {'degree': 16, 'field': [717704100, 0, -313949400, 0, 70098280, 0, -10450380, 0, 1086381, 0, -75464, 0, 3306, 0, -84, 0, 1], 'lmfdb_label': '15870.u5', 'torsion': [2, 8]}
  • id: 814480
    {'degree': 18, 'field': [17202672, 25612848, 23957208, 7033620, 14738544, -2656836, 5767721, -1460049, 1266684, -269828, 165717, -29133, 15516, -2313, 1089, -130, 48, -3, 1], 'lmfdb_label': '15870.u5', '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: 351642
    {'conductor': 15870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15870.u5', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 351643
    {'conductor': 15870, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '15870.u5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 351644
    {'conductor': 15870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15870.u5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 351645
    {'conductor': 15870, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '15870.u5', 'prime': 23, 'reduction_type': 0, '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: 1769687
    {'adelic_gens': [[2737, 24, 2736, 25], [1312, 483, 2277, 2554], [2071, 1104, 2070, 1], [1, 12, 12, 145], [1381, 1104, 92, 2669], [15, 106, 1454, 1811], [162, 2599, 437, 1772], [1559, 0, 0, 2759], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '2760.384.5.?', 'conductor': 15870, 'lmfdb_label': '15870.u5', 'prime': 0}
  • id: 74698
    {'conductor': 15870, 'elladic_image': '4.6.0.1', 'lmfdb_label': '15870.u5', 'modell_image': '2B', 'prime': 2}
  • id: 74699
    {'conductor': 15870, 'elladic_image': '3.4.0.1', 'lmfdb_label': '15870.u5', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 15870.u does not appear in ec_padic