Elliptic curve data - 133584.j2

Formats: - HTML - YAML - JSON - 2024-04-27T11:19:50.804947

• 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': '133584bn', 'Clabel': '133584bn4', 'Cnumber': 4, 'abc_quality': 0.9727192509165055, 'absD': 2211338782971039744, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 6072, 'ainvs': [0, -1, 0, -11265624, -14550023376], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 133584, 'degree': 3932160, 'elladic_images': ['8.24.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6606288286607665249457172845', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4], 'jinv': [21790813729717297, 304746849], 'lmfdb_iso': '133584.j', 'lmfdb_label': '133584.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -5819, -171336], 'min_quad_twist_disc': 44, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0-4.b.1.8', '12.24.0-4.b.1.2', '24.48.0-24.h.1.31', '44.24.0-4.b.1.3', '88.48.0.?', '132.48.0.?', '184.48.0.?', '264.96.0.?', '552.96.0.?', '2024.96.0.?', '6072.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.76853401170163594349751337406', 'prec': 103}, 'szpiro_ratio': 5.111245533695861, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, -2, 0, -4, 0], 'aplist': [0, -1, -2, 0, 0, 2, -2, -4, 1, 2, 0, -10, 6, -12, 0, 14, 4, -6, 4, 8, 6, 8, 4, -14, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 133584, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '133584.j', 'trace_hash': 1877167513040986240}
• 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': '0.0048866041855118646253940157406', 'prec': 110}, 'conductor': 133584, 'gens': [], 'heights': [], 'lmfdb_label': '133584.j2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.082406430519871897625472446377', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.65925144415897518100377957101586977947', 'prec': 133}, 'tamagawa_product': 128, 'torsion_generators': [[-1932, 0, 1], [3876, 0, 1]], 'xcoord_integral_points': [-1943, -1932, 3876]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '11': 'a', '23': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '133584.j2'}
• ec_torsion_growth •

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

  
  
  • id: 6057553
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '133584.j2', 'torsion': [2, 4]}
  • id: 6057554
    {'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '133584.j2', 'torsion': [2, 4]}
  • id: 6057555
    {'degree': 4, 'field': [121, 0, 11, 0, 1], 'lmfdb_label': '133584.j2', 'torsion': [2, 4]}
  • id: 6057559
    {'degree': 8, 'field': [-43923, 0, -14696, 0, -726, 0, 0, 0, 1], 'lmfdb_label': '133584.j2', 'torsion': [2, 6]}
  • id: 6057556
    {'degree': 8, 'field': [81, 0, 45, 0, 16, 0, 5, 0, 1], 'lmfdb_label': '133584.j2', 'torsion': [4, 4]}
  • id: 6057557
    {'degree': 8, 'field': [2209, 0, -802, 0, 263, 0, 26, 0, 1], 'lmfdb_label': '133584.j2', 'torsion': [2, 8]}
  • id: 6057558
    {'degree': 8, 'field': [202321, 21784, -18194, -7076, 3279, 308, -98, -4, 1], 'lmfdb_label': '133584.j2', 'torsion': [2, 8]}
  • id: 6057562
    {'degree': 16, 'field': [59049, 0, -459621, 0, 1179423, 0, -423954, 0, 67011, 0, -4106, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '133584.j2', 'torsion': [2, 12]}
  • id: 6057560
    {'degree': 16, 'field': [116944, -1367616, 779948, 534616, 68801, 481062, -274426, -238806, 95086, 46356, -15854, -4810, 1494, 218, -62, -4, 1], 'lmfdb_label': '133584.j2', 'torsion': [2, 8]}
  • id: 6057561
    {'degree': 16, 'field': [1336336, 0, 453152, 0, 70432, 0, 37472, 0, 5596, 0, -1072, 0, -56, 0, -4, 0, 1], 'lmfdb_label': '133584.j2', 'torsion': [4, 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: 3295138
    {'conductor': 133584, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '133584.j2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3295139
    {'conductor': 133584, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '133584.j2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3295140
    {'conductor': 133584, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '133584.j2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3295141
    {'conductor': 133584, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '133584.j2', 'prime': 23, '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: 2533388
    {'adelic_gens': [[3961, 4, 0, 1], [6065, 8, 6064, 9], [1097, 6070, 4986, 5], [1, 0, 8, 1], [1, 8, 0, 1], [4055, 6, 6066, 6067], [5, 4, 6068, 6069], [3041, 4556, 4576, 3045], [6065, 1512, 6, 4559]], 'adelic_image': '6072.192.1.?', 'conductor': 133584, 'lmfdb_label': '133584.j2', 'prime': 0}
  • id: 518520
    {'conductor': 133584, 'elladic_image': '8.24.0.11', 'lmfdb_label': '133584.j2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 133584.j does not appear in ec_padic