Elliptic curve data - 413712.a1

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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': '413712a', 'Clabel': '413712a2', 'Cnumber': 2, 'abc_quality': 1.2247540947788373, 'absD': 308202207835392, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 5304, 'ainvs': [0, 0, 0, -16887, -1690], 'analytic_rank': 2, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 413712, 'degree': 1966080, 'elladic_images': ['4.6.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4696152647219832740412142417', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [1298923792, 751689], 'lmfdb_iso': '413712.a', 'lmfdb_label': '413712.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1876, -688], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.d.1', '26.6.0.b.1', '52.12.0.i.1', '156.24.0.?', '408.12.0.?', '1768.24.0.?', '5304.48.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 19, 'optimality': 2, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.2708833267799627481379711360', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.18302633935075262861460165146', 'prec': 107}, 'szpiro_ratio': 3.1560145924850223, '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, 0, 0, -4, 0, -2, 0, 0, 0, -6, 0, 0, 0, 0, 0, 1, 0, 2, 0], 'aplist': [0, 0, -4, -2, -6, 0, 1, 2, 0, 2, -6, -8, 0, 4, 2, -6, -10, -2, -6, 2, 4, 8, -6, 12, -12], 'class_deg': 2, 'class_size': 2, 'conductor': 413712, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '413712.a', 'trace_hash': 1941701549258908907}
• 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': '0.052906423014553571922408547490', 'prec': 107}, 'conductor': 413712, 'gens': [[-91, 884, 1], [-74, 918, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0262054651045074489944049639', 'prec': 100}, {'__RealLiteral__': 0, 'data': '1.3124543747046929254460273076', 'prec': 100}], 'lmfdb_label': '413712.a1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.45990652716057023896362241128', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.3518005959303168025832331184941930995', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[130, 0, 1]], 'xcoord_integral_points': [-91, -74, -23, 130, 133, 169, 598, 997, 2002, 11401]}
• lmfdb_label 413712.a1 does not appear in ec_iwasawa
• lmfdb_label 413712.a1 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: 10221870
    {'conductor': 413712, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '413712.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 10221871
    {'conductor': 413712, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '413712.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 10221872
    {'conductor': 413712, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '413712.a1', 'prime': 13, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 10221873
    {'conductor': 413712, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '413712.a1', 'prime': 17, '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: 4223145
    {'adelic_gens': [[7, 2, 5258, 5291], [1, 0, 8, 1], [1226, 5, 2839, 5262], [1, 8, 0, 1], [3, 1330, 1334, 11], [1, 4, 4, 17], [5297, 8, 5296, 9], [5303, 1318, 0, 3977], [1873, 8, 2188, 33], [3535, 5296, 3532, 5271]], 'adelic_image': '5304.48.1.?', 'conductor': 413712, 'lmfdb_label': '413712.a1', 'prime': 0}
  • id: 1398785
    {'conductor': 413712, 'elladic_image': '4.6.0.2', 'lmfdb_label': '413712.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 413712.a does not appear in ec_padic