Elliptic curve data - 130.b3

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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': '130b', 'Clabel': '130b4', 'Cnumber': 4, 'abc_quality': 1.0488536278953087, 'absD': 71402500, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 1040, 'ainvs': [1, -1, 1, -67, -441], 'analytic_rank': 0, 'bad_primes': [2, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 130, 'degree': 32, 'elladic_images': ['4.48.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.19578703008235126746546993134', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [-32798729601, 71402500], 'lmfdb_iso': '130.b', 'lmfdb_label': '130.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -67, -441], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.48.0-4.c.1.1', '520.96.1.?', '1040.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [5, 6, 26], [13, 14, 10]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.19578703008235126746546993134', 'prec': 103}, 'szpiro_ratio': 5.295142682875964, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [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, 1, 0, 1, 1, 0, 0, 1, -3, 1, 0, 0, 1, 0, 0, 1, 2, -3, -8, 1], 'aplist': [1, 0, 1, 0, 0, 1, 2, -8, -4, -2, -4, 6, 10, 0, 8, 6, 8, -2, 4, -12, 10, -8, 12, 10, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 130, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '130.b', 'trace_hash': 1845375246341445412}
• 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': '0.67599198456306252375168429457', 'prec': 103}, 'conductor': 130, 'gens': [], 'heights': [], 'lmfdb_label': '130.b3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.78235687720051918418978631529', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5647137544010383683795726305806570641', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[27, 116, 1]], 'xcoord_integral_points': [27]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 2], '5': [1, 0], '13': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '130.b3'}
• ec_torsion_growth •

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

  
  
  • id: 5142
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '130.b3', 'torsion': [4, 4]}
  • id: 5143
    {'degree': 4, 'field': [-64, 0, -2, 0, 1], 'lmfdb_label': '130.b3', 'torsion': [8]}
  • id: 5146
    {'degree': 8, 'field': [4, -16, 16, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '130.b3', 'torsion': [12]}
  • id: 5144
    {'degree': 8, 'field': [64, 0, -80, 0, 34, 0, -6, 0, 1], 'lmfdb_label': '130.b3', 'torsion': [4, 8]}
  • id: 5145
    {'degree': 8, 'field': [256, 0, 0, 0, 33, 0, 0, 0, 1], 'lmfdb_label': '130.b3', 'torsion': [4, 8]}
  • id: 5148
    {'degree': 16, 'field': [16, 0, 128, 0, 256, 0, 41, 0, 106, 0, -31, 0, 1, 0, 2, 0, 1], 'lmfdb_label': '130.b3', 'torsion': [4, 12]}
  • id: 5147
    {'degree': 16, 'field': [4096, 0, 0, 0, 58496, 0, 0, 0, 14176, 0, 0, 0, -654, 0, 0, 0, 1], 'lmfdb_label': '130.b3', 'torsion': [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: 927
    {'conductor': 130, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '130.b3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 928
    {'conductor': 130, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '130.b3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 929
    {'conductor': 130, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '130.b3', 'prime': 13, '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: 1666299
    {'adelic_gens': [[5, 16, 64, 205], [1, 16, 0, 1], [1025, 16, 1024, 17], [470, 751, 19, 362], [417, 16, 844, 193], [1, 12, 4, 49], [1, 0, 16, 1], [273, 132, 136, 261], [561, 16, 164, 65]], 'adelic_image': '1040.192.3.?', 'conductor': 130, 'lmfdb_label': '130.b3', 'prime': 0}
  • id: 499
    {'conductor': 130, 'elladic_image': '4.48.0.2', 'lmfdb_label': '130.b3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 130.b does not appear in ec_padic