Elliptic curve data - 87120.ds1

Formats: - HTML - YAML - JSON - 2024-04-30T02:54:58.168511

• 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': '87120ck', 'Clabel': '87120ck2', 'Cnumber': 2, 'abc_quality': 0.8866917378259309, 'absD': 1800203031348480, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 220, 'ainvs': [0, 0, 0, -257367, -50213306], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 87120, 'degree': 491520, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8488297224427646295587158389', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 96, 'isogeny_degrees': [1, 2], 'jinv': [5702413264, 5445], 'lmfdb_iso': '87120.ds', 'lmfdb_label': '87120.ds1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -236, 1476], 'min_quad_twist_disc': -132, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '10.6.0.a.1', '44.6.0.c.1', '220.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.36152217866377236111469998285', 'prec': 107}, 'szpiro_ratio': 4.306654793803686, '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, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0], 'aplist': [0, 0, 1, -2, 0, -4, 0, -4, 4, -2, 8, -2, -6, -6, -4, -6, -4, 6, 0, -16, 4, -8, -6, -14, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 87120, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '87120.ds', 'trace_hash': 1767301581461112629}
• 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': '0.024781461019722151521609872687', 'prec': 107}, 'conductor': 87120, 'gens': [], 'heights': [], 'lmfdb_label': '87120.ds1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.21197577710781971353122862680', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.84790310843127885412491450721696996592', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-286, 0, 1]], 'xcoord_integral_points': [-286]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '87120.ds1'}
• ec_torsion_growth •

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

  
  
  • id: 4079268
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '87120.ds1', 'torsion': [2, 2]}
  • id: 4079269
    {'degree': 4, 'field': [3, -6, 4, -1, 1], 'lmfdb_label': '87120.ds1', 'torsion': [4]}
  • id: 4079270
    {'degree': 8, 'field': [-38099, 46642, -16358, 190, 471, 110, -32, -4, 1], 'lmfdb_label': '87120.ds1', 'torsion': [2, 4]}
  • id: 4079272
    {'degree': 8, 'field': [-29403, 0, 30888, 0, 594, 0, 0, 0, 1], 'lmfdb_label': '87120.ds1', 'torsion': [6]}
  • id: 4079271
    {'degree': 8, 'field': [55, -55, 36, -28, 29, -14, 4, -3, 1], 'lmfdb_label': '87120.ds1', 'torsion': [2, 4]}
  • id: 4079274
    {'degree': 16, 'field': [-973678859, 4084686152, -3192104896, -1818055800, 992609570, -104140136, 41317564, -6065808, 2031355, -356520, 84460, -7072, 1118, 0, 20, -8, 1], 'lmfdb_label': '87120.ds1', 'torsion': [2, 6]}
  • id: 4079273
    {'degree': 16, 'field': [6125625, 0, 816750, 0, 51975, 0, -57750, 0, 15865, 0, -1290, 0, 19, 0, 6, 0, 1], 'lmfdb_label': '87120.ds1', 'torsion': [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: 2126687
    {'conductor': 87120, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '87120.ds1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2126688
    {'conductor': 87120, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '87120.ds1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2126689
    {'conductor': 87120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '87120.ds1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2126690
    {'conductor': 87120, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '87120.ds1', 'prime': 11, 'reduction_type': 0, '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: 2237870
    {'adelic_gens': [[134, 1, 43, 0], [57, 166, 164, 55], [1, 2, 2, 5], [217, 4, 216, 5], [3, 4, 8, 11], [101, 4, 202, 9], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '220.12.0.?', 'conductor': 87120, 'lmfdb_label': '87120.ds1', 'prime': 0}
  • id: 354840
    {'conductor': 87120, 'elladic_image': '2.3.0.1', 'lmfdb_label': '87120.ds1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 87120.ds does not appear in ec_padic