Elliptic curve data - 120.b1

Formats: - HTML - YAML - JSON - 2024-04-20T05:14:21.454800

• 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': '120a', 'Clabel': '120a5', 'Cnumber': 5, 'abc_quality': 1.1283678564956034, 'absD': 153600, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 240, 'ainvs': [0, 1, 0, -3200, -70752], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 120, 'degree': 64, 'elladic_images': ['16.48.0.45'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.47999886506991459138871606774', 'prec': 103}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [1770025017602, 75], 'lmfdb_iso': '120.b', 'lmfdb_label': '120.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -3200, -70752], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.n.1.6', '16.48.0-16.f.1.3', '24.48.0-24.bj.1.7', '40.48.0-40.cb.2.3', '48.96.0-48.x.1.7', '80.96.0.?', '120.96.0.?', '240.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15538605044336860891041337693', 'prec': 107}, 'szpiro_ratio': 7.483382887673264, '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, 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': '0.38289375508940997054188040984', 'prec': 103}, 'conductor': 120, 'gens': [], 'heights': [], 'lmfdb_label': '120.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.63474713898166649492320321353', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2694942779633329898464064270624422458', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[-33, 0, 1]], 'xcoord_integral_points': [-33]}
• 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.b1'}
• ec_torsion_growth •

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

  
  
  • id: 4530
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [2, 2]}
  • id: 4532
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [4]}
  • id: 4531
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [4]}
  • id: 4533
    {'degree': 4, 'field': [-600, 0, 0, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [2, 4]}
  • id: 4536
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [8]}
  • id: 4535
    {'degree': 4, 'field': [6, 0, 0, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [8]}
  • id: 4534
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [2, 4]}
  • id: 4537
    {'degree': 4, 'field': [225, 0, 0, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [8]}
  • id: 4542
    {'degree': 8, 'field': [-3, 0, -28, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [6]}
  • id: 4540
    {'degree': 8, 'field': [49, 0, -68, 0, 18, 0, 4, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [2, 8]}
  • id: 4539
    {'degree': 8, 'field': [145, -140, 164, -44, 13, 8, 2, -4, 1], 'lmfdb_label': '120.b1', 'torsion': [2, 8]}
  • id: 4541
    {'degree': 8, 'field': [900, 0, 300, 0, -10, 0, -10, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [16]}
  • id: 4538
    {'degree': 8, 'field': [22801, 0, -1796, 0, 306, 0, 4, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [4, 4]}
  • id: 4550
    {'degree': 16, 'field': [576, -2304, 4608, -4416, 1536, 1824, -2656, 2368, -1040, -48, 328, -256, 164, -84, 32, -8, 1], 'lmfdb_label': '120.b1', 'torsion': [12]}
  • id: 4548
    {'degree': 16, 'field': [1296, 0, -1728, 0, 576, 0, -5616, 0, 1656, 0, -264, 0, 36, 0, -12, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [2, 6]}
  • id: 4549
    {'degree': 16, 'field': [1296, 0, 1728, 0, 576, 0, 5616, 0, 1656, 0, 264, 0, 36, 0, 12, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [12]}
  • id: 4547
    {'degree': 16, 'field': [2545, 21220, 121440, -177420, 106066, 30396, -17580, -22020, 10066, 3780, -1696, -700, 286, 60, -20, -4, 1], 'lmfdb_label': '120.b1', 'torsion': [2, 16]}
  • id: 4544
    {'degree': 16, 'field': [6241, 0, -8916, 0, 7318, 0, -2304, 0, 423, 0, 72, 0, 82, 0, 12, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [4, 8]}
  • id: 4543
    {'degree': 16, 'field': [318096, 0, -950400, 0, 531936, 0, -63360, 0, -984, 0, -2400, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [2, 8]}
  • id: 4545
    {'degree': 16, 'field': [360000, 0, 0, 0, -115200, 0, 0, 0, 10704, 0, 0, 0, -192, 0, 0, 0, 1], 'lmfdb_label': '120.b1', 'torsion': [16]}
  • id: 4546
    {'degree': 16, 'field': [4100625, 0, 0, 0, -364500, 0, 0, 0, 17775, 0, 0, 0, -180, 0, 0, 0, 1], 'lmfdb_label': '120.b1', '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: 811
    {'conductor': 120, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '120.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 812
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '120.b1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 813
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '120.b1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1666248
    {'adelic_gens': [[5, 4, 236, 237], [46, 185, 165, 106], [61, 16, 128, 165], [225, 16, 224, 17], [1, 0, 16, 1], [15, 2, 142, 227], [196, 181, 39, 130], [1, 16, 0, 1], [88, 1, 239, 10]], 'adelic_image': '240.192.1.?', 'conductor': 120, 'lmfdb_label': '120.b1', 'prime': 0}
  • id: 436
    {'conductor': 120, 'elladic_image': '16.48.0.45', 'lmfdb_label': '120.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 120.b does not appear in ec_padic