Elliptic curve data - 120.b2

Formats: - HTML - YAML - JSON - 2023-03-31T22:13:19.292789

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '120a', 'Clabel': '120a3', 'Cnumber': 3, 'absD': 5760000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 120, 'ainvs': [0, 1, 0, -200, -1152], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 120, 'degree': 32, 'elladic_images': ['8.48.0.31'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.13342527478994193668010000701', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [868327204, 5625], 'lmfdb_iso': '120.b', 'lmfdb_label': '120.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -200, -1152], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['1.1.0.1', '2.6.0.1', '4.24.0.6', '8.48.0.31', '24.96.0.154', '40.96.0.153', '120.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, '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': '-0.44419737567667915450092676087', 'prec': 107}, '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, 1, 0, 0, 0, 1, 0, -4, 0, 6, 0, 1, 0, -6, 0, -4, 0], 'aplist': [0, 1, 1, 0, -4, 6, -6, -4, 0, -2, -8, -2, -6, 12, 8, 6, 12, 14, 4, 8, -6, -8, -12, 10, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 120, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '120.b', 'trace_hash': 704992717552055982}
• 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': '0.76578751017881994108376081968', 'prec': 103}, 'conductor': 120, 'gens': [], 'heights': [], 'lmfdb_label': '120.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2694942779633329898464064271', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2694942779633329898464064270624422458', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-8, 0, 1], [16, 0, 1]], 'xcoord_integral_points': [-9, -8, 16]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '120.b2'}
• ec_torsion_growth •

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

  
  
  • id: 4499
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 4]}
  • id: 4501
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 4]}
  • id: 4500
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 4]}
  • id: 4503
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 8]}
  • id: 4502
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [4, 4]}
  • id: 4504
    {'degree': 8, 'field': [-335, 360, -16, -48, 54, -24, -16, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 8]}
  • id: 4507
    {'degree': 8, 'field': [-3, 0, -28, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 6]}
  • id: 4505
    {'degree': 8, 'field': [81, 0, -108, 0, 60, 0, -12, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 8]}
  • id: 4506
    {'degree': 8, 'field': [145, -140, 164, -44, 13, 8, 2, -4, 1], 'lmfdb_label': '120.b2', 'torsion': [4, 8]}
  • id: 4509
    {'degree': 16, 'field': [81, 0, -324, 0, 648, 0, -864, 0, 711, 0, -288, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [4, 8]}
  • id: 4508
    {'degree': 16, 'field': [100, 0, 0, -960, 29164, 16272, 4608, -2112, 1149, 696, 288, -144, -38, -24, 0, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [4, 8]}
  • id: 4513
    {'degree': 16, 'field': [576, -2304, 4608, -4416, 1536, 1824, -2656, 2368, -1040, -48, 328, -256, 164, -84, 32, -8, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 12]}
  • id: 4511
    {'degree': 16, 'field': [1296, 0, -1728, 0, 576, 0, -5616, 0, 1656, 0, -264, 0, 36, 0, -12, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 12]}
  • id: 4512
    {'degree': 16, 'field': [1296, 0, 1728, 0, 576, 0, 5616, 0, 1656, 0, 264, 0, 36, 0, 12, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 12]}
  • id: 4510
    {'degree': 16, 'field': [2025, 0, -4050, 0, 5940, 0, -4680, 0, 2251, 0, -456, 0, 36, 0, -6, 0, 1], 'lmfdb_label': '120.b2', 'torsion': [2, 16]}
• 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: 805
    {'conductor': 120, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '120.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 806
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '120.b2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 807
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '120.b2', 'prime': 5, '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: 1666249
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [3, 34, 26, 115], [113, 8, 112, 9], [7, 92, 74, 17], [47, 6, 114, 115], [97, 8, 28, 33], [5, 4, 116, 117]], 'adelic_image': '120.192.1.?', 'conductor': 120, 'lmfdb_label': '120.b2', 'prime': 0}
  • id: 437
    {'conductor': 120, 'elladic_image': '8.48.0.31', 'lmfdb_label': '120.b2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 120.b does not appear in ec_padic