Elliptic curve data - 120.b4

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• 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': '120a2', 'Cnumber': 2, 'abc_quality': 1.0257583484881192, 'absD': 518400, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 120, 'ainvs': [0, 1, 0, -20, 0], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 120, 'degree': 16, 'elladic_images': ['8.48.0.26'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.21314831549003071802851605372', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [3631696, 2025], 'lmfdb_iso': '120.b', 'lmfdb_label': '120.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -20, 0], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '8.48.0-8.d.2.1', '20.48.0-20.c.1.1', '24.96.0-24.p.2.3', '40.96.0-40.j.1.2', '120.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.67524643586332759097333746803', 'prec': 107}, 'szpiro_ratio': 4.3134043605136725, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
• 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': '1.5315750203576398821675216394', 'prec': 100}, 'conductor': 120, 'gens': [], 'heights': [], 'lmfdb_label': '120.b4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.5389885559266659796928128541', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2694942779633329898464064270624422458', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[0, 0, 1], [-2, 6, 1]], 'xcoord_integral_points': [-5, -2, 0, 4, 10]}
• 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.b4'}
• ec_torsion_growth •

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

  
  
  • id: 4491
    {'degree': 4, 'field': [1, 0, -8, 0, 1], 'lmfdb_label': '120.b4', 'torsion': [2, 8]}
  • id: 4490
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '120.b4', 'torsion': [4, 4]}
  • id: 4492
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '120.b4', 'torsion': [2, 8]}
  • id: 4494
    {'degree': 8, 'field': [-3, 0, -28, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '120.b4', 'torsion': [2, 12]}
  • id: 4493
    {'degree': 8, 'field': [1, 2, 2, -10, 11, -10, 8, -4, 1], 'lmfdb_label': '120.b4', 'torsion': [4, 8]}
  • id: 4497
    {'degree': 16, 'field': [1, 0, -32, 0, -212, 0, 256, 0, 1270, 0, 256, 0, -212, 0, -32, 0, 1], 'lmfdb_label': '120.b4', 'torsion': [2, 16]}
  • id: 4496
    {'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 48, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '120.b4', 'torsion': [4, 8]}
  • id: 4498
    {'degree': 16, 'field': [1, 0, 16, 0, 124, 0, 208, 0, 598, 0, 208, 0, 124, 0, 16, 0, 1], 'lmfdb_label': '120.b4', 'torsion': [2, 16]}
  • id: 4495
    {'degree': 16, 'field': [841, 0, 1280, 0, -694, 0, -1140, 0, 311, 0, 540, 0, 146, 0, 20, 0, 1], 'lmfdb_label': '120.b4', '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: 802
    {'conductor': 120, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '120.b4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 803
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '120.b4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 804
    {'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '120.b4', '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: 1666251
    {'adelic_gens': [[3, 34, 8, 101], [113, 8, 112, 9], [79, 2, 54, 115], [1, 0, 8, 1], [5, 4, 116, 117], [41, 8, 44, 33], [65, 92, 92, 61], [1, 8, 0, 1]], 'adelic_image': '120.192.1.?', 'conductor': 120, 'lmfdb_label': '120.b4', 'prime': 0}
  • id: 439
    {'conductor': 120, 'elladic_image': '8.48.0.26', 'lmfdb_label': '120.b4', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 120.b does not appear in ec_padic