Elliptic curve data - 221760.it2

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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': '221760br', 'Clabel': '221760br4', 'Cnumber': 4, 'abc_quality': 1.0084342270778677, 'absD': 132202602233856000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, 0, 0, -145153452, 673114841296], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 221760, 'degree': 14155776, 'elladic_images': ['4.12.0.7', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0710016691324341700905911236', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 227, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [1769857772964702379561, 691787250], 'lmfdb_iso': '221760.it', 'lmfdb_label': '221760.it2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -252003, 48670756], 'min_quad_twist_disc': 24, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.12.0-4.c.1.1', '6.12.0.a.1', '12.48.0-12.g.1.1', '24.96.0-24.bu.2.31', '264.192.1.?', '420.96.0.?', '840.192.1.?', '3080.24.0.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8221695098308895049784500223', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4819747539584613602671203230', 'prec': 100}, 'szpiro_ratio': 5.523728192637563, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 4, -2, -6, -4, 0, 6, 0, -2, -4, 0, 2, -8, -12, -6, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 221760, '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': '221760.it', 'trace_hash': 119153468946423857}
• 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': '0.0021506108987156683703355002754', 'prec': 110}, 'conductor': 221760, 'gens': [[6992, 5220, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.8221695098308895049784500223', 'prec': 100}], 'lmfdb_label': '221760.it2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19777851929414919420026546348', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.6979740822173778475271433769796605829', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[6890, 9504, 1]], 'xcoord_integral_points': [-12118, 6890, 6956, 6992, 7077]}
• lmfdb_label 221760.it2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9643340
    {'degree': 2, 'field': [-210, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [2, 4]}
  • id: 9643341
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [12]}
  • id: 9643343
    {'degree': 4, 'field': [841, 0, -82, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [2, 12]}
  • id: 9643342
    {'degree': 4, 'field': [10290, 0, 168, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [8]}
  • id: 9643344
    {'degree': 6, 'field': [23724, 1848, 12, -308, 6, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [12]}
  • id: 9643347
    {'degree': 8, 'field': [-3440, 13360, -10870, -4880, 2191, 296, -94, -4, 1], 'lmfdb_label': '221760.it2', 'torsion': [2, 8]}
  • id: 9643348
    {'degree': 8, 'field': [396900, 0, -75600, 0, 4134, 0, 144, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [24]}
  • id: 9643346
    {'degree': 8, 'field': [1640961, 0, -327348, 0, 16104, 0, 108, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [2, 8]}
  • id: 9643345
    {'degree': 8, 'field': [27573001, 0, -62996, 0, 10506, 0, 4, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [4, 4]}
  • id: 9643349
    {'degree': 12, 'field': [954675, 580500, 304404, 29520, 31195, 2328, 2768, -1200, 225, -12, -4, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [3, 12]}
  • id: 9643350
    {'degree': 12, 'field': [16834427289, 11212479432, 306254016, -747885600, 137016051, 10770144, -2735384, 0, 40875, -616, -312, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [2, 12]}
  • id: 9643354
    {'degree': 16, 'field': [754660, 19212480, 25887320, -69191200, -14333464, 48935328, -836020, -11649600, 963901, 1190400, -131864, -54920, 6666, 1120, -140, -8, 1], 'lmfdb_label': '221760.it2', 'torsion': [2, 24]}
  • id: 9643353
    {'degree': 16, 'field': [11128795920225, 0, 761273748540, 0, 28686637944, 0, 983331576, 0, 31564359, 0, 751752, 0, 12936, 0, 156, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [2, 24]}
  • id: 9643352
    {'degree': 16, 'field': [12734413497961, 0, 152879720288, 0, -24928109192, 0, -148858024, 0, 20010550, 0, 14336, 0, -7112, 0, 8, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [4, 12]}
  • id: 9643351
    {'degree': 16, 'field': [2260032584040000, 0, 147593964672000, 0, 9431135683200, 0, 167503089600, 0, 1726684050, 0, -43500240, 0, 443352, 0, 336, 0, 1], 'lmfdb_label': '221760.it2', 'torsion': [16]}
  • id: 9643355
    {'degree': 18, 'field': [95394270790800, 23964799579200, 5240516616000, -462666651408, -547697758968, -56899270368, -21808653156, 641732976, 428433624, 46327740, 2151720, 286380, -197075, 2748, 6558, 238, -129, -6, 1], 'lmfdb_label': '221760.it2', 'torsion': [36]}
• 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: 5496560
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '221760.it2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5496561
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '221760.it2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5496562
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '221760.it2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 5496563
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.it2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5496564
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '221760.it2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 3079914
    {'adelic_gens': [[4998, 6521, 2203, 2548], [1, 12, 12, 145], [15, 106, 7934, 11], [1336, 3, 6141, 9154], [2521, 24, 2532, 289], [6929, 9216, 6930, 9239], [3712, 3, 3237, 9154], [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.it2', 'prime': 0}
  • id: 812819
    {'conductor': 221760, 'elladic_image': '4.12.0.7', 'lmfdb_label': '221760.it2', 'modell_image': '2B', 'prime': 2}
  • id: 812820
    {'conductor': 221760, 'elladic_image': '3.4.0.1', 'lmfdb_label': '221760.it2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 221760.it does not appear in ec_padic