Elliptic curve data - 157170.x3

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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': '157170cq', 'Clabel': '157170cq5', 'Cnumber': 5, 'abc_quality': 1.0019471514445586, 'absD': 247004528132373346140, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 96720, 'ainvs': [1, 0, 1, -3197484, -2327248298], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13, 31], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 157170, 'degree': 7864320, 'elladic_images': ['8.24.0.90'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6643003209456114025223170331', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-749011598724977281, 51173462246460], 'lmfdb_iso': '157170.x', 'lmfdb_label': '157170.x3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -18920, -1060740], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '30.6.0.a.1', '52.12.0-4.c.1.1', '60.12.0.g.1', '104.48.0.?', '120.48.0.?', '496.48.0.?', '780.24.0.?', '1560.96.0.?', '6448.96.0.?', '7440.96.1.?', '96720.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '13.670868519935475685180367084', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3818256422148430344955733123', 'prec': 100}, 'szpiro_ratio': 4.735347004864738, '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, 0, -1, 1, 1, 4, 1, 0, 0, -1, 1, 2, -1, -4, -1], 'aplist': [-1, 1, -1, 0, 4, 0, 2, -4, -8, 6, 1, 2, -10, -4, 0, -10, 12, -2, 4, 0, -2, 0, -4, 14, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 157170, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '157170.x', 'trace_hash': 1754662832713169501}
• 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': '0.0048508533459496728495302804687', 'prec': 110}, 'conductor': 157170, 'gens': [[848653, 779653211, 4]], 'heights': [{'__RealLiteral__': 0, 'data': '13.670868519935475685180367084', 'prec': 100}], 'lmfdb_label': '157170.x3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.056228892508312505951151178197', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.1495823720218011613419171590324673323', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[8311, -8315, 2]], 'xcoord_integral_points': []}
• lmfdb_label 157170.x3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7041626
    {'degree': 2, 'field': [-195, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [4]}
  • id: 7041625
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '157170.x3', 'torsion': [2, 2]}
  • id: 7041627
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [4]}
  • id: 7041630
    {'degree': 4, 'field': [49, 0, 12, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [8]}
  • id: 7041628
    {'degree': 4, 'field': [94, -34, 35, -2, 1], 'lmfdb_label': '157170.x3', 'torsion': [2, 4]}
  • id: 7041629
    {'degree': 4, 'field': [289, 0, 86, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [8]}
  • id: 7041634
    {'degree': 8, 'field': [-1343280, 269904, 60324, -13808, -160, -212, 4, -4, 1], 'lmfdb_label': '157170.x3', 'torsion': [6]}
  • id: 7041632
    {'degree': 8, 'field': [-719, -90, 128, 30, 189, -30, -28, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [8]}
  • id: 7041633
    {'degree': 8, 'field': [334, -140, 586, -932, 567, -124, 46, -4, 1], 'lmfdb_label': '157170.x3', 'torsion': [2, 8]}
  • id: 7041631
    {'degree': 8, 'field': [5541, -2292, 2466, -336, 139, 32, -6, -4, 1], 'lmfdb_label': '157170.x3', 'torsion': [2, 4]}
  • id: 7041637
    {'degree': 16, 'field': [14641, 0, 6636, 0, 79090, 0, -37476, 0, 11379, 0, -1836, 0, 250, 0, -24, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [2, 8]}
  • id: 7041635
    {'degree': 16, 'field': [25281, 0, 283752, 0, 522330, 0, 29652, 0, 15979, 0, 2548, 0, 270, 0, 28, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [4, 4]}
  • id: 7041636
    {'degree': 16, 'field': [58101, -144264, 261636, -232176, 115458, -13944, 24864, -9528, -5717, 3016, 1456, -728, -182, 112, 4, -8, 1], 'lmfdb_label': '157170.x3', 'torsion': [2, 8]}
  • id: 7041642
    {'degree': 16, 'field': [788544, 0, -292419, 0, -138150, 0, 92227, 0, 28235, 0, 1447, 0, 295, 0, 26, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [12]}
  • id: 7041639
    {'degree': 16, 'field': [7778219588, 480591264, 4232323360, 511184544, 1013025848, 137176240, 127680768, 14725248, 7883144, 643808, 150192, 1488, -3420, -248, 16, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [16]}
  • id: 7041640
    {'degree': 16, 'field': [2343141257040, -1023763101840, 7438223844, 38665391472, -4013733456, -552670020, 333132156, -32329284, 1556433, 1845456, 140860, -31236, -1086, -428, 24, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [2, 6]}
  • id: 7041638
    {'degree': 16, 'field': [25855099513681, 0, 7078317452936, 0, 819665194312, 0, 41519359808, 0, 840079870, 0, 2546552, 0, 74632, 0, 224, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [16]}
  • id: 7041641
    {'degree': 16, 'field': [29383988490000, 0, -5414261227875, 0, 393690992850, 0, -15933709125, 0, 401505075, 0, -6505545, 0, 66375, 0, -390, 0, 1], 'lmfdb_label': '157170.x3', 'torsion': [12]}
• 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: 3887812
    {'conductor': 157170, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '157170.x3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3887813
    {'conductor': 157170, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '157170.x3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3887814
    {'conductor': 157170, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '157170.x3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3887815
    {'conductor': 157170, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '157170.x3', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3887816
    {'conductor': 157170, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '157170.x3', 'prime': 31, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2681496
    {'adelic_gens': [[86503, 66976, 29094, 2185], [22319, 0, 0, 96719], [91768, 22321, 86879, 7450], [1, 16, 0, 1], [87361, 66976, 6968, 52209], [15, 2, 96622, 96707], [74413, 66976, 16484, 31305], [1496, 22321, 41743, 7450], [1, 0, 16, 1], [5, 4, 96716, 96717], [96705, 16, 96704, 17]], 'adelic_image': '96720.192.1.?', 'conductor': 157170, 'lmfdb_label': '157170.x3', 'prime': 0}
  • id: 600121
    {'conductor': 157170, 'elladic_image': '8.24.0.90', 'lmfdb_label': '157170.x3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 157170.x does not appear in ec_padic