Elliptic curve data - 182070.l8

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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': '182070dj', 'Clabel': '182070dj7', 'Cnumber': 7, 'abc_quality': 1.0876511700840974, 'absD': 238709796862882324218750, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 14280, 'ainvs': [1, -1, 0, 1896075, 23484821611], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 182070, 'degree': 21233664, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1649388293980876446483325281', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [42841933504271, 13565917968750], 'lmfdb_iso': '182070.l', 'lmfdb_label': '182070.l8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 729, -176985], 'min_quad_twist_disc': -51, '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', '24.48.0.bu.2', '51.8.0-3.a.1.2', '56.12.0.v.1', '84.48.0.?', '102.24.0.?', '120.96.1.?', '168.96.1.?', '204.48.0.?', '408.96.0.?', '680.12.0.?', '840.192.5.?', '1428.96.0.?', '2040.192.1.?', '2856.192.1.?', '4760.24.0.?', '14280.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1990260130359247588259426007', 'prec': 100}, 'szpiro_ratio': 5.059584293205953, '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, -1, 0, -1, -1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, -4, -1], 'aplist': [-1, 0, -1, -1, 0, 2, 0, -4, 0, -6, 4, -2, 6, 8, 12, -6, 12, -2, 8, 0, -14, 16, -12, -6, -14], 'class_deg': 12, 'class_size': 8, 'conductor': 182070, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '182070.l', 'trace_hash': 211469774780778115}
• 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': '0.0017822517985947833842981115771', 'prec': 110}, 'conductor': 182070, 'gens': [], 'heights': [], 'lmfdb_label': '182070.l8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.076734312848360494893796021633', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2277490055737679183007363461294180100', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-10573, 10573, 2]], 'xcoord_integral_points': []}
• lmfdb_label 182070.l8 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8046570
    {'degree': 2, 'field': [-102, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [4]}
  • id: 8046572
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '182070.l8', 'torsion': [6]}
  • id: 8046569
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [2, 2]}
  • id: 8046571
    {'degree': 2, 'field': [357, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [4]}
  • id: 8046575
    {'degree': 4, 'field': [-2, 20, -19, -2, 1], 'lmfdb_label': '182070.l8', 'torsion': [12]}
  • id: 8046574
    {'degree': 4, 'field': [338, -20, 21, -2, 1], 'lmfdb_label': '182070.l8', 'torsion': [2, 6]}
  • id: 8046576
    {'degree': 4, 'field': [646, -34, 35, -2, 1], 'lmfdb_label': '182070.l8', 'torsion': [12]}
  • id: 8046573
    {'degree': 4, 'field': [841, 0, -44, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [2, 4]}
  • id: 8046577
    {'degree': 6, 'field': [2461, -957, 528, -67, 42, -3, 1], 'lmfdb_label': '182070.l8', 'torsion': [6]}
  • id: 8046581
    {'degree': 8, 'field': [3838, -956, 1090, -260, 111, 20, -2, -4, 1], 'lmfdb_label': '182070.l8', 'torsion': [2, 12]}
  • id: 8046579
    {'degree': 8, 'field': [15876, 0, -11088, 0, -866, 0, 88, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [8]}
  • id: 8046578
    {'degree': 8, 'field': [267996, 97776, 52840, 2464, 4360, -56, 116, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [2, 4]}
  • id: 8046580
    {'degree': 8, 'field': [2598894, -1026018, 405171, -62832, 12283, -714, 191, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [8]}
  • id: 8046582
    {'degree': 12, 'field': [2500, -10500, 41400, -12440, 5676, -3336, 77, 15, 60, 5, 18, -3, 1], 'lmfdb_label': '182070.l8', 'torsion': [3, 6]}
  • id: 8046584
    {'degree': 12, 'field': [562500, 0, 0, 0, 0, 0, 1092, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [12]}
  • id: 8046583
    {'degree': 12, 'field': [5468535, 833058, -2414475, 1690914, 354564, -420174, 215857, -36582, 10320, -806, 177, -6, 1], 'lmfdb_label': '182070.l8', 'torsion': [2, 6]}
  • id: 8046585
    {'degree': 12, 'field': [55919061, 2585088, 7698159, -2185098, 990738, -204588, 39835, -6594, 1878, -176, 51, -6, 1], 'lmfdb_label': '182070.l8', 'torsion': [12]}
  • id: 8046590
    {'degree': 16, 'field': [1058841, 0, -14713788, 0, 5295550, 0, -128688, 0, -57921, 0, -4072, 0, 210, 0, -12, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [24]}
  • id: 8046589
    {'degree': 16, 'field': [27279729, 0, -3477228, 0, 4112710, 0, -697984, 0, 204855, 0, -26600, 0, 2226, 0, -76, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [2, 12]}
  • id: 8046586
    {'degree': 16, 'field': [41615401, -164010224, 323189888, 212478448, 61557290, 15779624, 2182656, 310688, 120207, 105112, 1568, -4480, 1254, -56, 0, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [4, 4]}
  • id: 8046591
    {'degree': 16, 'field': [174785536, 11366144, -13517984, 3754496, -261784, -2618992, 2012088, -988852, 268397, -23084, 14112, -5876, 1586, -308, 64, -8, 1], 'lmfdb_label': '182070.l8', 'torsion': [24]}
  • id: 8046587
    {'degree': 16, 'field': [141469925625, 26035695000, -24754977000, -2524455000, 1176611400, 84053400, 1769680, -22859120, 2459481, 2037752, -277372, -68136, 8990, 1064, -132, -8, 1], 'lmfdb_label': '182070.l8', 'torsion': [2, 8]}
  • id: 8046588
    {'degree': 16, 'field': [1613037162916, 0, -180767022296, 0, 15253282216, 0, -727900796, 0, 26177149, 0, -643664, 0, 11818, 0, -140, 0, 1], 'lmfdb_label': '182070.l8', 'torsion': [2, 8]}
  • id: 8046592
    {'degree': 18, 'field': [38351356, 169695840, 75323640, -253373578, -64320306, 67391316, 142017231, 37176957, -28879860, -8202066, 3133269, 791241, -186318, -39471, 6081, 946, -114, -9, 1], 'lmfdb_label': '182070.l8', '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: 4504825
    {'conductor': 182070, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '182070.l8', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4504826
    {'conductor': 182070, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '182070.l8', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4504827
    {'conductor': 182070, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '182070.l8', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4504828
    {'conductor': 182070, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '182070.l8', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4504829
    {'conductor': 182070, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '182070.l8', 'prime': 17, '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: 2834996
    {'adelic_gens': [[2379, 7276, 5032, 12987], [6376, 11781, 9435, 3826], [1, 12, 12, 145], [5879, 0, 0, 14279], [10711, 13464, 3162, 4489], [13686, 10489, 10115, 7736], [2857, 13464, 12444, 4489], [14257, 24, 14256, 25], [1, 24, 0, 1], [15, 106, 12974, 5051], [1, 0, 24, 1]], 'adelic_image': '14280.384.5.?', 'conductor': 182070, 'lmfdb_label': '182070.l8', 'prime': 0}
  • id: 682109
    {'conductor': 182070, 'elladic_image': '4.6.0.1', 'lmfdb_label': '182070.l8', 'modell_image': '2B', 'prime': 2}
  • id: 682110
    {'conductor': 182070, 'elladic_image': '3.4.0.1', 'lmfdb_label': '182070.l8', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 182070.l does not appear in ec_padic