Elliptic curve data - 171.a4

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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': '171a', 'Clabel': '171a4', 'Cnumber': 4, 'abc_quality': 0.9747386105988611, 'absD': 285012027, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [1, -1, 1, 76, -790], 'analytic_rank': 0, 'bad_primes': [3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 171, 'degree': 48, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.30429748213122875202819024859', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [67419143, 390963], 'lmfdb_iso': '171.a', 'lmfdb_label': '171.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 8, 29], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '6.6.0.a.1', '12.24.0-12.g.1.1', '152.24.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.24500866220282609366943236987', 'prec': 107}, 'szpiro_ratio': 5.215749745602377, '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, -1, 0, -1, 2, 0, 0, 3, 0, -2, 0, 0, 6, 0, 0, -1, 6, 0, -1, -2], 'aplist': [-1, 0, 2, 0, 0, 6, 6, -1, -4, -2, 8, -10, 2, -4, -12, 6, 12, -2, -4, 0, 10, 0, -16, 2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 171, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '171.a', 'trace_hash': 679434992409306156}
• 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': '0.54411483303622839218427142867', 'prec': 103}, 'conductor': 171, 'gens': [], 'heights': [], 'lmfdb_label': '171.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.86836134047839452207664078170', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.86836134047839452207664078170361972629', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[27, -31, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 2], '3': 'a', '19': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '171.a4'}
• ec_torsion_growth •

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

  
  
  • id: 6800
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [4]}
  • id: 6799
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '171.a4', 'torsion': [2, 2]}
  • id: 6801
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [4]}
  • id: 6803
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [2, 4]}
  • id: 6802
    {'degree': 4, 'field': [3, 0, -3, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [2, 4]}
  • id: 6804
    {'degree': 8, 'field': [1, -4, 8, -10, 7, -2, 2, -2, 1], 'lmfdb_label': '171.a4', 'torsion': [4, 4]}
  • id: 6807
    {'degree': 8, 'field': [3, -12, 21, -21, 12, -3, 4, -4, 1], 'lmfdb_label': '171.a4', 'torsion': [6]}
  • id: 6805
    {'degree': 8, 'field': [16, 0, 0, 0, -11, 0, 0, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [8]}
  • id: 6806
    {'degree': 8, 'field': [144, 0, 0, 0, 33, 0, 0, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [8]}
  • id: 6813
    {'degree': 16, 'field': [1, 0, 8, 0, 46, 0, 89, 0, 73, 0, 89, 0, 46, 0, 8, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [12]}
  • id: 6808
    {'degree': 16, 'field': [9, 0, 0, 0, -72, 0, 0, 0, 141, 0, 0, 0, 24, 0, 0, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [2, 8]}
  • id: 6811
    {'degree': 16, 'field': [9, 0, 33, 0, 103, 0, 66, 0, 39, 0, 22, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [2, 6]}
  • id: 6810
    {'degree': 16, 'field': [256, 0, 0, 0, 176, 0, 0, 0, 105, 0, 0, 0, 11, 0, 0, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [2, 8]}
  • id: 6812
    {'degree': 16, 'field': [729, 0, -957, 0, 37, 0, 888, 0, 18, 0, -217, 0, 15, 0, 3, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [12]}
  • id: 6809
    {'degree': 16, 'field': [20736, 0, 0, 0, -4752, 0, 0, 0, 945, 0, 0, 0, -33, 0, 0, 0, 1], 'lmfdb_label': '171.a4', 'torsion': [2, 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: 1325
    {'conductor': 171, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '171.a4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1326
    {'conductor': 171, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '171.a4', 'prime': 19, '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: 1666462
    {'adelic_gens': [[7, 6, 450, 451], [97, 8, 388, 33], [1, 0, 8, 1], [296, 453, 299, 454], [449, 8, 448, 9], [403, 402, 298, 67], [1, 8, 0, 1], [1, 4, 4, 17], [179, 172, 218, 405]], 'adelic_image': '456.48.0.?', 'conductor': 171, 'lmfdb_label': '171.a4', 'prime': 0}
  • id: 687
    {'conductor': 171, 'elladic_image': '4.12.0.8', 'lmfdb_label': '171.a4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 171.a does not appear in ec_padic