Elliptic curve data - 221760.cp1

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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': '221760lp', 'Clabel': '221760lp3', 'Cnumber': 3, 'abc_quality': 1.0393554700052399, 'absD': 908499725844480000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [0, 0, 0, -6082560588, 182590332294512], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 221760, 'degree': 94371840, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8642309268989761770638602766', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 67, 'isogeny_degrees': [1, 2, 4], 'jinv': [130231365028993807856757649, 4753980000], 'lmfdb_iso': '221760.cp', 'lmfdb_label': '221760.cp1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -10560001, -13209092695], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.1', '56.12.0.z.1', '88.12.0.?', '132.12.0.?', '168.24.0.?', '264.24.0.?', '616.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.1480226945519155683740504926', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 99], [3, 8, 24640], [5, 6, 44352], [7, 8, 31680], [11, 12, 20160]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2752040117250033672403894760', 'prec': 100}, 'szpiro_ratio': 6.4341067084546975, '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, -8, 0], 'aplist': [0, 0, -1, -1, 1, 2, -6, -8, 0, -2, -4, 2, 2, -4, 4, 14, 4, -14, -12, 8, -2, -8, 16, -2, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 221760, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '221760.cp', 'trace_hash': 1808467665130648428}
• 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': '0.00044012056650725266995015370378', 'prec': 113}, 'conductor': 221760, 'gens': [[44302, 266112, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.1480226945519155683740504926', 'prec': 100}], 'lmfdb_label': '221760.cp1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10298019523438396454694667941', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1869438669956438798005645899023432779', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[45028, 0, 1]], 'xcoord_integral_points': [44302, 45028]}
• lmfdb_label 221760.cp1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9652342
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [2, 2]}
  • id: 9652343
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '221760.cp1', 'torsion': [4]}
  • id: 9652344
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [4]}
  • id: 9652345
    {'degree': 4, 'field': [16, 0, -14, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [2, 4]}
  • id: 9652349
    {'degree': 8, 'field': [-108, 0, 6, 0, 36, 0, 0, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [6]}
  • id: 9652348
    {'degree': 8, 'field': [49, 0, -126, 0, 74, 0, 18, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [8]}
  • id: 9652346
    {'degree': 8, 'field': [2704, 0, 7200, 0, 40, 0, 24, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [2, 4]}
  • id: 9652347
    {'degree': 8, 'field': [234256, 0, -85184, 0, 7326, 0, -176, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [8]}
  • id: 9652350
    {'degree': 16, 'field': [28561, 0, 0, 0, 806620, 0, 0, 0, -21162, 0, 0, 0, 124, 0, 0, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [4, 4]}
  • id: 9652352
    {'degree': 16, 'field': [627264, 0, 114048, 0, -1548, 0, 12636, 0, 7249, 0, 1758, 0, 230, 0, 18, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [2, 8]}
  • id: 9652355
    {'degree': 16, 'field': [6350400, 0, -3640896, 0, -590940, 0, -73008, 0, 48672, 0, -11220, 0, 1080, 0, -48, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [12]}
  • id: 9652354
    {'degree': 16, 'field': [44156524, 20224336, -18418878, -2724088, -647680, 1858464, 222292, -566864, -38781, 100876, -1616, -9000, 590, 392, -36, -8, 1], 'lmfdb_label': '221760.cp1', 'torsion': [12]}
  • id: 9652353
    {'degree': 16, 'field': [63354903616, 0, -19297032896, 0, 2882547364, 0, -267465008, 0, 15810016, 0, -593108, 0, 13624, 0, -176, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [2, 6]}
  • id: 9652351
    {'degree': 16, 'field': [277809109776, 0, -117858410208, 0, 19480728960, 0, -1665208776, 0, 80949121, 0, -2293676, 0, 36960, 0, -308, 0, 1], 'lmfdb_label': '221760.cp1', 'torsion': [2, 8]}
• 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: 5500440
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 23, 'j_denominator_valuation': 5, 'kodaira_symbol': -17, 'lmfdb_label': '221760.cp1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 5500441
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '221760.cp1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5500442
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '221760.cp1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5500443
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '221760.cp1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5500444
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.cp1', '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: 3079450
    {'adelic_gens': [[844, 1233, 1311, 622], [1841, 8, 1840, 9], [536, 1455, 1317, 98], [1, 0, 8, 1], [1585, 624, 180, 649], [232, 1779, 1467, 880], [7, 6, 1842, 1843], [1, 8, 0, 1], [1, 4, 4, 17], [1231, 0, 0, 1847]], 'adelic_image': '1848.48.0.?', 'conductor': 221760, 'lmfdb_label': '221760.cp1', 'prime': 0}
  • id: 812321
    {'conductor': 221760, 'elladic_image': '4.6.0.1', 'lmfdb_label': '221760.cp1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 221760.cp does not appear in ec_padic