Elliptic curve data - 176176.bo1

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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': '176176ba', 'Clabel': '176176ba4', 'Cnumber': 4, 'abc_quality': 0.9711976019732098, 'absD': 32388259387387904, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 616, 'ainvs': [0, 0, 0, -19196771, -32373553630], 'analytic_rank': 2, 'bad_primes': [2, 7, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 176176, 'degree': 4669440, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6543227351424128908883378138', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 40, 'isogeny_degrees': [1, 2, 4], 'jinv': [107818231938348177, 4463459], 'lmfdb_iso': '176176.bo', 'lmfdb_label': '176176.bo1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -9916, -377564], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '44.24.0-44.h.1.1', '56.24.0-56.z.1.5', '616.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '37.310375436814005511899449408', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.76222791818328230944013390336', 'prec': 103}, 'szpiro_ratio': 5.126511871055599, '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, -3, 0, 0, 0, 1, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, -2, -1, 0, 1, 2, -4, 0, -6, 4, 6, -6, 12, -4, -10, 0, -10, -12, 0, -14, 0, -4, -14, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 176176, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '176176.bo', 'trace_hash': 1703845031474575321}
• 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': '0.0049486252399186641121296719116', 'prec': 110}, 'conductor': 176176, 'gens': [[-22766, 910, 3], [131231, 13403754, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '5.2585260381351806737481546654', 'prec': 100}, {'__RealLiteral__': 0, 'data': '8.2565075268897003257986651795', 'prec': 100}], 'lmfdb_label': '176176.bo1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.072126109971701843858886575454', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.764208967364520725189361107896928844', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-2530, 0, 1]], 'xcoord_integral_points': [-2530]}
• lmfdb_label 176176.bo1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7802571
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [2, 2]}
  • id: 7802573
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [4]}
  • id: 7802572
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '176176.bo1', 'torsion': [4]}
  • id: 7802575
    {'degree': 4, 'field': [-1859, 0, 0, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [2, 4]}
  • id: 7802574
    {'degree': 4, 'field': [9, 0, -5, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [2, 4]}
  • id: 7802579
    {'degree': 8, 'field': [-1263603, 0, -99, 0, 3894, 0, 0, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [6]}
  • id: 7802578
    {'degree': 8, 'field': [1, 0, 334, 0, 171, 0, 26, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [8]}
  • id: 7802577
    {'degree': 8, 'field': [456976, 0, 0, 0, 6084, 0, 0, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [8]}
  • id: 7802576
    {'degree': 8, 'field': [3452164, 0, 22312, 0, -3712, 0, 4, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [4, 4]}
  • id: 7802580
    {'degree': 16, 'field': [130321, 0, 0, 0, 51742, 0, 0, 0, 4443, 0, 0, 0, 122, 0, 0, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [2, 8]}
  • id: 7802583
    {'degree': 16, 'field': [73805281, 0, -93143380, 0, 61717744, 0, -14157121, 0, 781660, 0, 5357, 0, -803, 0, -22, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [2, 6]}
  • id: 7802585
    {'degree': 16, 'field': [528862009, 0, -273558103, 0, 56764396, 0, -5593015, 0, 176269, 0, 12611, 0, -1013, 0, 2, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [12]}
  • id: 7802581
    {'degree': 16, 'field': [731215681, 0, 528955812, 0, -68951634, 0, 7739580, 0, 2422347, 0, 6140, 0, -3014, 0, 8, 0, 1], 'lmfdb_label': '176176.bo1', 'torsion': [2, 8]}
  • id: 7802584
    {'degree': 16, 'field': [5537761773, 1115219418, -1012165086, -203165274, 94188087, 8947548, -3026430, -117744, 215314, -111122, 9790, 6304, -626, -224, 52, -8, 1], 'lmfdb_label': '176176.bo1', 'torsion': [12]}
  • id: 7802582
    {'degree': 16, 'field': [50597553721, 0, 0, 0, -3345292808, 0, 0, 0, -12074205, 0, 0, 0, -14872, 0, 0, 0, 1], 'lmfdb_label': '176176.bo1', '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: 4356255
    {'conductor': 176176, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '176176.bo1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4356256
    {'conductor': 176176, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '176176.bo1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4356257
    {'conductor': 176176, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '176176.bo1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4356258
    {'conductor': 176176, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '176176.bo1', 'prime': 13, '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: 2798202
    {'adelic_gens': [[384, 69, 381, 352], [609, 8, 608, 9], [353, 8, 180, 33], [388, 615, 537, 610], [1, 0, 8, 1], [235, 234, 90, 395], [7, 6, 610, 611], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '616.48.0.?', 'conductor': 176176, 'lmfdb_label': '176176.bo1', 'prime': 0}
  • id: 662067
    {'conductor': 176176, 'elladic_image': '4.12.0.8', 'lmfdb_label': '176176.bo1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 176176.bo does not appear in ec_padic