Elliptic curve data - 178752.b1

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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': '178752id', 'Clabel': '178752id1', 'Cnumber': 1, 'abc_quality': 1.0271363895982601, 'absD': 28045263582508032, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1596, 'ainvs': [0, -1, 0, -20861325, 36681178941], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 178752, 'degree': 8847360, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6669501304986281067966088625', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [8334147900493981696, 232793757], 'lmfdb_iso': '178752.b', 'lmfdb_label': '178752.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -106435, -13329764], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '266.6.0.?', '1596.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.9180055045340932446827921638', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 931], [3, 4, 59584], [7, 32, 3648], [19, 20, 9408]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1163724055043503630629057229', 'prec': 100}, 'szpiro_ratio': 5.140986191321506, '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, -1, 0, -4, 0, 0, 0, 1, 0, 0, 0, -2, 0, 4, 0, -4, 0, 1, 0], 'aplist': [0, -1, -4, 0, 0, -2, -4, 1, 4, -4, 0, 10, -10, -4, 6, 0, 4, -10, 4, -2, 2, 4, -14, 6, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 178752, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '178752.b', 'trace_hash': 1346193671866742941}
• 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': '0.0048252136711417053045480141476', 'prec': 110}, 'conductor': 178752, 'gens': [[3484, 79233, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9180055045340932446827921638', 'prec': 100}], 'lmfdb_label': '178752.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.27321998272586535165531936715', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1890296541711398655174051031907920943', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[2637, 0, 1]], 'xcoord_integral_points': [2637, 3484]}
• lmfdb_label 178752.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7916614
    {'degree': 2, 'field': [-33, -1, 1], 'lmfdb_label': '178752.b1', 'torsion': [2, 2]}
  • id: 7916615
    {'degree': 4, 'field': [532, 0, -46, 0, 1], 'lmfdb_label': '178752.b1', 'torsion': [4]}
  • id: 7916618
    {'degree': 8, 'field': [-9408, 0, 3808, 0, 336, 0, 0, 0, 1], 'lmfdb_label': '178752.b1', 'torsion': [6]}
  • id: 7916617
    {'degree': 8, 'field': [11664, 0, 1080, 0, 208, 0, -10, 0, 1], 'lmfdb_label': '178752.b1', 'torsion': [2, 4]}
  • id: 7916616
    {'degree': 8, 'field': [29929, 0, 51006, 0, 2686, 0, -138, 0, 1], 'lmfdb_label': '178752.b1', 'torsion': [2, 4]}
  • id: 7916619
    {'degree': 16, 'field': [16999129, 0, 5994044, 0, -4192046, 0, -2227864, 0, 1163431, 0, -121552, 0, 5710, 0, -124, 0, 1], 'lmfdb_label': '178752.b1', 'torsion': [8]}
  • id: 7916620
    {'degree': 16, 'field': [196364169, 0, -48343878, 0, -32066550, 0, -2880900, 0, 136539, 0, 11044, 0, -846, 0, 0, 0, 1], 'lmfdb_label': '178752.b1', 'torsion': [2, 6]}
• 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: 4424576
    {'conductor': 178752, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '178752.b1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4424577
    {'conductor': 178752, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '178752.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4424578
    {'conductor': 178752, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '178752.b1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4424579
    {'conductor': 178752, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '178752.b1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 2814680
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [533, 4, 1066, 9], [1593, 4, 1592, 5], [422, 1, 587, 0], [230, 1, 683, 0], [401, 1198, 1196, 399]], 'adelic_image': '1596.12.0.?', 'conductor': 178752, 'lmfdb_label': '178752.b1', 'prime': 0}
  • id: 671250
    {'conductor': 178752, 'elladic_image': '2.3.0.1', 'lmfdb_label': '178752.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 178752.b does not appear in ec_padic