Elliptic curve data - 221760.cb8

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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': '221760ek', 'Clabel': '221760ek1', 'Cnumber': 1, 'abc_quality': 0.9990919448660593, 'absD': 49837699246325760000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, 0, 0, 915252, 42198928], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 221760, 'degree': 5308416, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4689952214814024196335697177', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 53, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [443688652450511, 260789760000], 'lmfdb_iso': '221760.cb', 'lmfdb_label': '221760.cb8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1589, 3185], 'min_quad_twist_disc': 24, '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', '24.48.0-12.g.1.21', '84.48.0.?', '88.12.0.?', '120.96.0.?', '132.48.0.?', '168.96.0.?', '264.96.0.?', '280.12.0.?', '462.24.0.?', '840.192.1.?', '924.96.1.?', '1320.192.1.?', '1848.192.1.?', '3080.24.0.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 693], [3, 2, 3520], [5, 6, 44352], [7, 8, 31680], [11, 12, 20160]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.87996830630742960981009891705', 'prec': 103}, 'szpiro_ratio': 4.288972440770008, '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, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, -1, -1, 1, -2, -6, -4, 0, 6, -8, 10, 6, 8, 0, 6, -12, -2, -4, 12, -10, 4, 12, -6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 221760, 'isogeny_matrix': [[1, 4, 2, 12, 3, 4, 6, 12], [4, 1, 2, 3, 12, 4, 6, 12], [2, 2, 1, 6, 6, 2, 3, 6], [12, 3, 6, 1, 4, 12, 2, 4], [3, 12, 6, 4, 1, 12, 2, 4], [4, 4, 2, 12, 12, 1, 6, 3], [6, 6, 3, 2, 2, 6, 1, 2], [12, 12, 6, 4, 4, 3, 2, 1]], 'lmfdb_iso': '221760.cb', 'trace_hash': 1853644609987354153}
• 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': '0.0071689904017807174175597736703', 'prec': 110}, 'conductor': 221760, 'gens': [], 'heights': [], 'lmfdb_label': '221760.cb8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.12172664483844056328006392528', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.97381315870752450624051140225147790914', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-46, 0, 1]], 'xcoord_integral_points': [-46]}
• lmfdb_label 221760.cb8 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9645885
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [4]}
  • id: 9645887
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [6]}
  • id: 9645886
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [4]}
  • id: 9645884
    {'degree': 2, 'field': [58, -1, 1], 'lmfdb_label': '221760.cb8', 'torsion': [2, 2]}
  • id: 9645890
    {'degree': 4, 'field': [16, 0, -14, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [12]}
  • id: 9645891
    {'degree': 4, 'field': [58, 8, -7, -2, 1], 'lmfdb_label': '221760.cb8', 'torsion': [12]}
  • id: 9645888
    {'degree': 4, 'field': [256, 0, 10, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [2, 4]}
  • id: 9645889
    {'degree': 4, 'field': [1600, 0, 74, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [2, 6]}
  • id: 9645892
    {'degree': 6, 'field': [3033, 660, 12, -110, 6, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [6]}
  • id: 9645896
    {'degree': 8, 'field': [1912, -104, 286, -344, 123, 56, -14, -4, 1], 'lmfdb_label': '221760.cb8', 'torsion': [2, 12]}
  • id: 9645895
    {'degree': 8, 'field': [19504, -7872, 8470, -1232, 707, -112, 42, -4, 1], 'lmfdb_label': '221760.cb8', 'torsion': [8]}
  • id: 9645894
    {'degree': 8, 'field': [23716, 0, -22264, 0, 792, 0, 44, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [8]}
  • id: 9645893
    {'degree': 8, 'field': [8179600, 0, -186098, 0, 5841, 0, 22, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [2, 4]}
  • id: 9645897
    {'degree': 12, 'field': [22788, -38088, 22962, -12072, 4681, 1806, -1681, 522, -18, -6, 11, -6, 1], 'lmfdb_label': '221760.cb8', 'torsion': [3, 6]}
  • id: 9645899
    {'degree': 12, 'field': [163971, 139518, 166923, 80610, 59391, 6700, 7530, -860, 1141, -170, 67, -6, 1], 'lmfdb_label': '221760.cb8', 'torsion': [12]}
  • id: 9645900
    {'degree': 12, 'field': [177412, 246480, 160252, 47316, 87771, 17934, 8825, -402, -306, 150, 25, -6, 1], 'lmfdb_label': '221760.cb8', 'torsion': [12]}
  • id: 9645898
    {'degree': 12, 'field': [119024812, -71091832, 17051648, -3090920, 785471, -170866, 82829, -9290, 3386, -130, 89, -2, 1], 'lmfdb_label': '221760.cb8', 'torsion': [2, 6]}
  • id: 9645906
    {'degree': 16, 'field': [553536, 0, -607584, 0, 220948, 0, -41916, 0, 20433, 0, 728, 0, 42, 0, -12, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [24]}
  • id: 9645903
    {'degree': 16, 'field': [100000000, 0, 18200000, 0, -7603900, 0, -601020, 0, 211361, 0, -3192, 0, 554, 0, -28, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [2, 8]}
  • id: 9645905
    {'degree': 16, 'field': [185379624, -620149392, 1183160160, -1059364656, 363434646, 198311172, -63882978, -2390844, 1205185, -401756, 76114, 3580, -1628, 448, -44, -8, 1], 'lmfdb_label': '221760.cb8', 'torsion': [24]}
  • id: 9645904
    {'degree': 16, 'field': [304362916, 0, 97073944, 0, 12542992, 0, 696388, 0, 230965, 0, -21896, 0, 2086, 0, -68, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [2, 12]}
  • id: 9645901
    {'degree': 16, 'field': [3949871104, -1854267392, 435243008, 189532928, 48340880, -183669280, 85444128, -42847344, 10285348, 295488, -103488, 38840, -6412, -64, 32, -8, 1], 'lmfdb_label': '221760.cb8', 'torsion': [4, 4]}
  • id: 9645902
    {'degree': 16, 'field': [132828175936, 0, -19514439296, 0, 1334494624, 0, -32261504, 0, 845044, 0, -67496, 0, 3424, 0, -44, 0, 1], 'lmfdb_label': '221760.cb8', 'torsion': [2, 8]}
  • id: 9645907
    {'degree': 18, 'field': [-6567280628, 327991840632, -926479312884, 727189171356, 150361240734, -355577654988, 43591135185, 22421346336, -2965075200, 90773888, -20022165, -12300804, 1763094, -219564, 33687, -1080, 288, 0, 1], 'lmfdb_label': '221760.cb8', '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: 5497665
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 30, 'j_denominator_valuation': 12, 'kodaira_symbol': -24, 'lmfdb_label': '221760.cb8', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5497666
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '221760.cb8', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5497667
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '221760.cb8', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5497668
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '221760.cb8', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5497669
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.cb8', 'prime': 11, '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: 3079406
    {'adelic_gens': [[2303, 9216, 1818, 7553], [1, 12, 12, 145], [15, 106, 7934, 11], [3697, 24, 7404, 289], [1336, 3, 6141, 9154], [3376, 21, 2235, 8866], [7311, 8852, 340, 1891], [9217, 24, 9216, 25], [1, 24, 0, 1], [9224, 4599, 1825, 3454], [1, 0, 24, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 221760, 'lmfdb_label': '221760.cb8', 'prime': 0}
  • id: 812261
    {'conductor': 221760, 'elladic_image': '4.6.0.1', 'lmfdb_label': '221760.cb8', 'modell_image': '2B', 'prime': 2}
  • id: 812262
    {'conductor': 221760, 'elladic_image': '3.4.0.1', 'lmfdb_label': '221760.cb8', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 221760.cb does not appear in ec_padic