Elliptic curve data - 85176.bs4

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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': '85176ce', 'Clabel': '85176ce1', 'Cnumber': 1, 'abc_quality': 0.8915192755066496, 'absD': 6305588819712, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2184, 'ainvs': [0, 0, 0, 1521, -118638], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 85176, 'degree': 147456, 'elladic_images': ['8.12.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1366008157062904159605906808', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 44, 'isogeny_degrees': [1, 2, 4], 'jinv': [432, 7], 'lmfdb_iso': '85176.bs', 'lmfdb_label': '85176.bs4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 1, 2], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.p.1', '14.6.0.b.1', '28.12.0.g.1', '56.24.0.bn.1', '156.12.0.?', '312.24.0.?', '1092.24.0.?', '2184.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 10647], [3, 6, 9464], [7, 8, 12168], [13, 86, 504]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1572781277318296707085970727', 'prec': 103}, 'szpiro_ratio': 3.24958300553552, '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, 2, 0, 1, 0, 0, 0, -4, 0, 0, 0, 0, 0, 6, 0, -8, 0], 'aplist': [0, 0, 2, 1, -4, 0, 6, -8, 0, -6, -8, 2, 2, -4, -8, -6, 0, -6, 4, -8, -10, 16, 8, -6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 85176, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '85176.bs', 'trace_hash': 543660258960651909}
• 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': '0.10298194149525314387768268938', 'prec': 103}, 'conductor': 85176, 'gens': [], 'heights': [], 'lmfdb_label': '85176.bs4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.36768810143206036160141536270', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4707524057282414464056614507784919839', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[39, 0, 1]], 'xcoord_integral_points': [39]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': [1, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '85176.bs4'}
• ec_torsion_growth •

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

  
  
  • id: 3994059
    {'degree': 2, 'field': [-68, -1, 1], 'lmfdb_label': '85176.bs4', 'torsion': [4]}
  • id: 3994058
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '85176.bs4', 'torsion': [2, 2]}
  • id: 3994060
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '85176.bs4', 'torsion': [4]}
  • id: 3994061
    {'degree': 4, 'field': [64, 0, 23, 0, 1], 'lmfdb_label': '85176.bs4', 'torsion': [2, 4]}
  • id: 3994065
    {'degree': 8, 'field': [-35909, -21842, -6002, 2614, 1048, -74, -38, -2, 1], 'lmfdb_label': '85176.bs4', 'torsion': [6]}
  • id: 3994064
    {'degree': 8, 'field': [15214, -7276, 5502, -1304, 647, -104, 42, -4, 1], 'lmfdb_label': '85176.bs4', 'torsion': [8]}
  • id: 3994063
    {'degree': 8, 'field': [58564, 0, -26632, 0, 2600, 0, -92, 0, 1], 'lmfdb_label': '85176.bs4', 'torsion': [8]}
  • id: 3994062
    {'degree': 8, 'field': [157621, -39482, 24482, -3756, 1679, -156, 62, -2, 1], 'lmfdb_label': '85176.bs4', 'torsion': [2, 4]}
  • id: 3994069
    {'degree': 16, 'field': [5030398, -20025520, 32615622, -31517174, 23672276, -14918616, 7781812, -3366502, 1239015, -306178, 78130, -4758, 608, 508, -24, -4, 1], 'lmfdb_label': '85176.bs4', 'torsion': [2, 6]}
  • id: 3994071
    {'degree': 16, 'field': [16721779, -6249058, -2533906, -1339788, 1508960, 48952, -25118, -81462, 29980, -15006, 2326, 596, 80, 24, 26, -2, 1], 'lmfdb_label': '85176.bs4', 'torsion': [12]}
  • id: 3994070
    {'degree': 16, 'field': [19085271, 4556034, -27670008, 19857822, -11700084, 5640480, -2032956, 670572, -208832, 57926, -5132, -3670, 892, 104, -32, -4, 1], 'lmfdb_label': '85176.bs4', 'torsion': [12]}
  • id: 3994066
    {'degree': 16, 'field': [60279696, 0, 61326240, 0, 23745340, 0, 5007560, 0, 651873, 0, 53800, 0, 2754, 0, 80, 0, 1], 'lmfdb_label': '85176.bs4', 'torsion': [4, 4]}
  • id: 3994067
    {'degree': 16, 'field': [79100176, -58136704, 80007352, -48715864, 37491390, -17771500, 9458042, -3402832, 1339457, -360512, 108002, -21152, 4860, -644, 112, -8, 1], 'lmfdb_label': '85176.bs4', 'torsion': [2, 8]}
  • id: 3994068
    {'degree': 16, 'field': [524348176, -236794624, 285906952, -104666152, 69043458, -21792532, 10290686, -2853136, 1051193, -247808, 72974, -13904, 3288, -476, 88, -8, 1], 'lmfdb_label': '85176.bs4', '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: 2077403
    {'conductor': 85176, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '85176.bs4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2077404
    {'conductor': 85176, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '85176.bs4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2077405
    {'conductor': 85176, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '85176.bs4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2077406
    {'conductor': 85176, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '85176.bs4', 'prime': 13, 'reduction_type': 0, '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: 2225109
    {'adelic_gens': [[2177, 8, 2176, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [976, 507, 1989, 898], [727, 0, 0, 2183], [1873, 1872, 1014, 703], [7, 6, 2178, 2179], [547, 1326, 1482, 1171], [167, 0, 0, 2183]], 'adelic_image': '2184.48.0.?', 'conductor': 85176, 'lmfdb_label': '85176.bs4', 'prime': 0}
  • id: 347668
    {'conductor': 85176, 'elladic_image': '8.12.0.9', 'lmfdb_label': '85176.bs4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 85176.bs does not appear in ec_padic