Elliptic curve data - 90.b2

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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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '90b', 'Clabel': '90b2', 'Cnumber': 2, 'abc_quality': 1.0515389861488595, 'absD': 5400, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 120, 'ainvs': [1, -1, 1, -128, 587], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 90, 'degree': 16, 'elladic_images': ['2.3.0.1', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.17178813042935505157831109507', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [8527173507, 200], 'lmfdb_iso': '90.b', 'lmfdb_label': '90.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -1149, -14707], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '6.24.0-6.a.1.4', '24.48.0-24.ca.1.15', '40.6.0.e.1', '60.48.0-60.t.1.16', '120.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3], [3, 6, 5], [5, 6, 18]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.44644120259638247442712240430', 'prec': 107}, 'szpiro_ratio': 5.814103832648771, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
• 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, 1, 0, 1, -1, 0, 2, 1, 0, -1, -6, 0, -4, 2, 0, 1, 6, 0, -4, -1], 'aplist': [1, 0, -1, 2, -6, -4, 6, -4, 0, 6, -4, 8, 0, 8, 0, 6, -6, 2, -4, 12, -10, -4, -12, -12, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 90, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '90.b', 'trace_hash': 2284528933461194068}
• 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': '1.4099810447481858487409462636', 'prec': 100}, 'conductor': 90, 'gens': [], 'heights': [], 'lmfdb_label': '90.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.9710942585413486372981289183', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3236980861804495457660429727621209354', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[3, 13, 1]], 'xcoord_integral_points': [3, 7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': 'a', '5': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '90.b2'}
• ec_torsion_growth •

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

  
  
  • id: 3136
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '90.b2', 'torsion': [2, 6]}
  • id: 3137
    {'degree': 4, 'field': [24, 0, 9, 0, 1], 'lmfdb_label': '90.b2', 'torsion': [12]}
  • id: 3138
    {'degree': 6, 'field': [36, -18, -9, 3, 6, -3, 1], 'lmfdb_label': '90.b2', 'torsion': [3, 6]}
  • id: 3139
    {'degree': 8, 'field': [1, 0, -2, 0, 18, 0, -2, 0, 1], 'lmfdb_label': '90.b2', 'torsion': [2, 12]}
  • id: 3140
    {'degree': 8, 'field': [4, 0, -80, 0, 36, 0, -8, 0, 1], 'lmfdb_label': '90.b2', 'torsion': [2, 12]}
  • id: 3141
    {'degree': 9, 'field': [144, -216, 108, -90, 18, 0, -15, 9, -3, 1], 'lmfdb_label': '90.b2', 'torsion': [18]}
  • id: 3142
    {'degree': 12, 'field': [1089, -1980, 3204, -1380, 546, 840, 94, 0, 24, -20, -6, 0, 1], 'lmfdb_label': '90.b2', 'torsion': [6, 6]}
  • id: 3143
    {'degree': 16, 'field': [256, 0, 1024, 0, 1520, 0, 1216, 0, 814, 0, 356, 0, 95, 0, 14, 0, 1], 'lmfdb_label': '90.b2', 'torsion': [24]}
  • id: 3144
    {'degree': 18, 'field': [-6144, 0, 18432, 0, -25344, 0, 20496, 0, -10440, 0, 3564, 0, -942, 0, 204, 0, -24, 0, 1], 'lmfdb_label': '90.b2', 'torsion': [2, 18]}
• 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: 518
    {'conductor': 90, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '90.b2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 519
    {'conductor': 90, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '90.b2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 520
    {'conductor': 90, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '90.b2', '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: 1666125
    {'adelic_gens': [[1, 12, 0, 1], [10, 3, 33, 112], [32, 11, 45, 88], [109, 12, 108, 13], [11, 2, 70, 111], [1, 6, 6, 37], [97, 12, 102, 73], [1, 0, 12, 1], [66, 97, 5, 26]], 'adelic_image': '120.96.1.?', 'conductor': 90, 'lmfdb_label': '90.b2', 'prime': 0}
  • id: 290
    {'conductor': 90, 'elladic_image': '2.3.0.1', 'lmfdb_label': '90.b2', 'modell_image': '2B', 'prime': 2}
  • id: 291
    {'conductor': 90, 'elladic_image': '3.8.0.1', 'lmfdb_label': '90.b2', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 90.b does not appear in ec_padic