Elliptic curve data - 221760.kb2

Formats: - HTML - YAML - JSON - 2025-11-05T09:41:59.451264

• 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': '221760jo', 'Clabel': '221760jo3', 'Cnumber': 3, 'abc_quality': 0.9616858385970404, 'absD': 1971570585600000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [0, 0, 0, -401292, -70780176], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 221760, 'degree': 4194304, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2179355609218647267662809765', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 261, 'isogeny_degrees': [1, 2, 4], 'jinv': [37397086385121, 10316796875], 'lmfdb_iso': '221760.kb', 'lmfdb_label': '221760.kb2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -697, 5294], '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', '44.12.0.h.1', '56.12.0.z.1', '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': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 99], [3, 6, 24640], [5, 6, 44352], [7, 8, 31680], [11, 12, 20160]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.62890864574789191694281017585', 'prec': 103}, 'szpiro_ratio': 4.088025186361794, '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, 6, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, 1, -1, 1, 6, -6, 4, 8, -10, -4, -6, 10, -4, 4, 6, 0, 6, -4, 0, 6, -8, 12, -10, 10], '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.kb', 'trace_hash': 226028760458770649}
• 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': '0.011844743197588927500775021748', 'prec': 107}, 'conductor': 221760, 'gens': [], 'heights': [], 'lmfdb_label': '221760.kb2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.19362719039448371172068079353', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0980350463117393875308926965109465149', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[708, 0, 1]], 'xcoord_integral_points': [708]}
• lmfdb_label 221760.kb2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9650288
    {'degree': 2, 'field': [-66, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [4]}
  • id: 9650287
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [2, 2]}
  • id: 9650289
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [4]}
  • id: 9650290
    {'degree': 4, 'field': [25, 0, -34, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [2, 4]}
  • id: 9650294
    {'degree': 8, 'field': [-1200, 0, 0, 0, 120, 0, -18, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [6]}
  • id: 9650293
    {'degree': 8, 'field': [4, 0, 22, 0, 29, 0, -10, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [8]}
  • id: 9650291
    {'degree': 8, 'field': [625, 0, 1656, 0, 194, 0, 24, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [2, 4]}
  • id: 9650292
    {'degree': 8, 'field': [29241, 0, -10530, 0, 1251, 0, -60, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [8]}
  • id: 9650295
    {'degree': 16, 'field': [5625, 0, 1200, 0, 4714, 0, 1820, 0, 1623, 0, 460, 0, 162, 0, 20, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [4, 4]}
  • id: 9650300
    {'degree': 16, 'field': [278784, 0, -2426112, 0, -1406016, 0, -1166976, 0, 247440, 0, -36864, 0, 2652, 0, -84, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [12]}
  • id: 9650296
    {'degree': 16, 'field': [1693297, -833420, 739866, 232252, -209008, 58972, 57842, -47636, -9039, 10196, 1406, -1484, -56, 112, 4, -8, 1], 'lmfdb_label': '221760.kb2', 'torsion': [2, 8]}
  • id: 9650298
    {'degree': 16, 'field': [16024009, 0, 10243508, 0, -5690276, 0, -8439076, 0, 1513390, 0, -134164, 0, 5932, 0, -124, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [2, 6]}
  • id: 9650297
    {'degree': 16, 'field': [17631601, 0, -32055392, 0, 20464236, 0, -6335680, 0, 1067222, 0, -100960, 0, 5196, 0, -128, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [2, 8]}
  • id: 9650299
    {'degree': 16, 'field': [140067225, 0, 907038, 0, -17130771, 0, -1471104, 0, 372030, 0, 35610, 0, -1152, 0, -36, 0, 1], 'lmfdb_label': '221760.kb2', 'torsion': [12]}
• 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: 5499595
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '221760.kb2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5499596
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '221760.kb2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5499597
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '221760.kb2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 5499598
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '221760.kb2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5499599
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.kb2', '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: 3080033
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [7, 6, 1842, 1843], [232, 1779, 1467, 880], [1613, 1614, 1758, 221], [1231, 0, 0, 1847], [844, 1233, 1311, 622], [1585, 624, 180, 649]], 'adelic_image': '1848.48.0.?', 'conductor': 221760, 'lmfdb_label': '221760.kb2', 'prime': 0}
  • id: 812950
    {'conductor': 221760, 'elladic_image': '4.6.0.1', 'lmfdb_label': '221760.kb2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 221760.kb does not appear in ec_padic