Elliptic curve data - 491970.y1

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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': '491970y', 'Clabel': '491970y2', 'Cnumber': 2, 'abc_quality': 0.9193561650234463, 'absD': 1184771707743184664640, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 21390, 'ainvs': [1, 0, 1, -21973349, 39608935952], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 23, 31], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 491970, 'degree': 49600512, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9626195519529661001494207662', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 24, 'isogeny_degrees': [1, 3], 'jinv': [28322662967161, 28599360], 'lmfdb_iso': '491970.y', 'lmfdb_label': '491970.y1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -41538, -3259052], 'min_quad_twist_disc': -23, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '69.8.0-3.a.1.1', '930.8.0.?', '21390.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 2, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.34970770534534135781046007302', 'prec': 103}, 'szpiro_ratio': 4.755745669259909, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 1, 1, -1, -1, -2, -1, 1, 1, 3, 1, 5, 2, -1, 1, -6, -1, 1, -1], 'aplist': [-1, 1, -1, -2, 3, 5, -6, 1, 0, -9, 1, -5, 12, 1, -9, 6, 0, 4, -8, -6, -13, 10, 12, -15, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 491970, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '491970.y', 'trace_hash': 1874596280907820727}
• 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': '0.0026711689219144604823281205549', 'prec': 110}, 'conductor': 491970, 'gens': [], 'heights': [], 'lmfdb_label': '491970.y1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15321790571964732868475230758', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.91930743431788397210851384547286369754', 'prec': 133}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 491970.y1 does not appear in ec_iwasawa
• lmfdb_label 491970.y1 does not appear in ec_torsion_growth
• 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: 12127263
    {'conductor': 491970, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '491970.y1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 12127264
    {'conductor': 491970, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '491970.y1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 12127265
    {'conductor': 491970, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '491970.y1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12127266
    {'conductor': 491970, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '491970.y1', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 12127267
    {'conductor': 491970, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '491970.y1', 'prime': 31, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 4678088
    {'adelic_gens': [[4, 3, 9, 7], [4808, 11937, 14881, 10696], [8557, 3726, 6141, 11179], [21385, 6, 21384, 7], [1, 6, 0, 1], [16739, 0, 0, 21389], [3, 4, 8, 11], [5521, 3726, 18423, 11179], [1, 0, 6, 1]], 'adelic_image': '21390.16.0.?', 'conductor': 491970, 'lmfdb_label': '491970.y1', 'prime': 0}
  • id: 1627066
    {'conductor': 491970, 'elladic_image': '3.4.0.1', 'lmfdb_label': '491970.y1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 491970.y does not appear in ec_padic