Elliptic curve data - 221760.ci1

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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': '221760ep', 'Clabel': '221760ep8', 'Cnumber': 8, 'abc_quality': 1.0452427382284861, 'absD': 1460237833764864000000000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, 0, 0, -14669561388, -683867929163312], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 221760, 'degree': 254803968, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.4212679352188665354459651131', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'iso_nlabel': 60, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [1826870018430810435423307849, 7641104625000000000], 'lmfdb_iso': '221760.ci', 'lmfdb_label': '221760.ci1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -25467989, -49471735264], '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', '12.48.0-12.g.1.5', '24.96.0-24.bu.2.29', '40.12.0.y.1', '120.192.1.?', '616.12.0.?', '924.96.0.?', '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': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 693], [3, 8, 448], [5, 6, 44352], [7, 8, 31680], [11, 12, 20160]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.8322410200448937256224943125', 'prec': 100}, 'szpiro_ratio': 6.648662846346082, '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, 4, -2, 6, -4, 0, -6, -12, -14, -16, 0, 2, 4, 0, 6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 221760, 'isogeny_matrix': [[1, 2, 3, 4, 6, 12, 12, 4], [2, 1, 6, 2, 3, 6, 6, 2], [3, 6, 1, 12, 2, 4, 4, 12], [4, 2, 12, 1, 6, 3, 12, 4], [6, 3, 2, 6, 1, 2, 2, 6], [12, 6, 4, 3, 2, 1, 4, 12], [12, 6, 4, 12, 2, 4, 1, 3], [4, 2, 12, 4, 6, 12, 3, 1]], 'lmfdb_iso': '221760.ci', 'trace_hash': 2064025439003230546}
• 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': '0.00014445596021869546653349239469', 'prec': 113}, 'conductor': 221760, 'gens': [], 'heights': [], 'lmfdb_label': '221760.ci1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.013718144761108162603310915748', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.65847094853319180495892395591251775423', 'prec': 133}, 'tamagawa_product': 48, 'torsion_generators': [[-70036, 0, 1]], 'xcoord_integral_points': [-70036]}
• lmfdb_label 221760.ci1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9646331
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [2, 2]}
  • id: 9646332
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '221760.ci1', 'torsion': [4]}
  • id: 9646334
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [6]}
  • id: 9646333
    {'degree': 2, 'field': [462, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [4]}
  • id: 9646337
    {'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [12]}
  • id: 9646336
    {'degree': 4, 'field': [1521, 0, -76, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [2, 6]}
  • id: 9646338
    {'degree': 4, 'field': [13225, 0, 232, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [12]}
  • id: 9646335
    {'degree': 4, 'field': [23716, 0, 154, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [2, 4]}
  • id: 9646339
    {'degree': 6, 'field': [-1176, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [6]}
  • id: 9646341
    {'degree': 8, 'field': [379456, 0, -29568, 0, 1688, 0, -48, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [8]}
  • id: 9646342
    {'degree': 8, 'field': [1601406, 1872, -399, -3024, 1708, -238, 84, -4, 1], 'lmfdb_label': '221760.ci1', 'torsion': [8]}
  • id: 9646343
    {'degree': 8, 'field': [2313441, 0, 115596, 0, 4255, 0, 76, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [2, 12]}
  • id: 9646340
    {'degree': 8, 'field': [56806369, 0, -271764, 0, -15038, 0, -12, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [2, 4]}
  • id: 9646344
    {'degree': 12, 'field': [19321, 35028, 22836, 3024, 4506, 504, 238, -504, 24, 0, -6, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [3, 12]}
  • id: 9646345
    {'degree': 12, 'field': [1572043201, 0, -627384048, 0, 37858515, 0, -1247072, 0, 22803, 0, -240, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [2, 6]}
  • id: 9646346
    {'degree': 12, 'field': [7067596761, 0, 90514584, 0, 15112980, 0, 163386, 0, 540, 0, -36, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [12]}
  • id: 9646349
    {'degree': 16, 'field': [531441, 10943748, 233972550, -168195528, 231767577, -11155728, 67795606, -11430484, 8868156, -338588, 383198, -21312, 10625, -248, 126, -4, 1], 'lmfdb_label': '221760.ci1', 'torsion': [2, 8]}
  • id: 9646348
    {'degree': 16, 'field': [506250000, 0, -257400000, 0, 94063600, 0, -14755840, 0, 1647276, 0, -121088, 0, 6108, 0, -88, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [2, 8]}
  • id: 9646351
    {'degree': 16, 'field': [926067771, 138266244, -457807590, -78232272, 103593493, 18679392, -13991874, -2523908, 1247810, 209716, -76438, -10712, 3177, 312, -82, -4, 1], 'lmfdb_label': '221760.ci1', 'torsion': [24]}
  • id: 9646352
    {'degree': 16, 'field': [2586984224400, 49445164800, -51299797440, 3621177840, -1583593151, -291665360, 130232984, -30116748, 9882664, -1689640, 461062, -70336, 14392, -1260, 200, -8, 1], 'lmfdb_label': '221760.ci1', 'torsion': [24]}
  • id: 9646350
    {'degree': 16, 'field': [3230384663079729, 0, 20631271936368, 0, -1702567306340, 0, -4556576336, 0, 340898550, 0, 121040, 0, -30084, 0, 16, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [2, 12]}
  • id: 9646347
    {'degree': 16, 'field': [3243264115813569, 0, -5154400098852, 0, -1711111114010, 0, 1138238624, 0, 342482775, 0, -30200, 0, -30174, 0, -4, 0, 1], 'lmfdb_label': '221760.ci1', 'torsion': [4, 4]}
  • id: 9646353
    {'degree': 18, 'field': [42036636353624, 14599335647952, -2947620406500, 2673133858272, 3130685591634, 634932216900, -120277448223, -55384038900, -1467944820, 1752953304, 174879099, -27556776, -4412910, 218772, 55143, -708, -360, 0, 1], 'lmfdb_label': '221760.ci1', '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: 5497800
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 27, 'j_denominator_valuation': 9, 'kodaira_symbol': -21, 'lmfdb_label': '221760.ci1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5497801
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '221760.ci1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5497802
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '221760.ci1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5497803
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.ci1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5497804
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '221760.ci1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 3079425
    {'adelic_gens': [[1, 12, 12, 145], [15, 106, 7934, 11], [3697, 24, 7404, 289], [3376, 21, 2235, 8866], [9217, 24, 9216, 25], [1539, 3076, 9220, 4539], [1, 24, 0, 1], [6929, 9216, 6918, 8951], [1336, 21, 1035, 8866], [7314, 8831, 5005, 6544], [1, 0, 24, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 221760, 'lmfdb_label': '221760.ci1', 'prime': 0}
  • id: 812281
    {'conductor': 221760, 'elladic_image': '4.6.0.1', 'lmfdb_label': '221760.ci1', 'modell_image': '2B', 'prime': 2}
  • id: 812282
    {'conductor': 221760, 'elladic_image': '3.4.0.1', 'lmfdb_label': '221760.ci1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 221760.ci does not appear in ec_padic