Elliptic curve data - 190575.b1

Formats: - HTML - YAML - JSON - 2025-11-07T05:02:38.787073

• 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': '190575g', 'Clabel': '190575g1', 'Cnumber': 1, 'abc_quality': 0.744779716951845, 'absD': 2486075840325, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 154, 'ainvs': [0, 0, 1, -5445, -134764], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 190575, 'degree': 460800, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1048842705475320138065508691', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [552960, 77], 'lmfdb_iso': '190575.b', 'lmfdb_label': '190575.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -5, -4], 'min_quad_twist_disc': 33, 'modell_images': [], 'modm_images': ['154.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.84843531367828129844390339346', 'prec': 103}, 'semistable': False, 'serre_invariants': [[3, 6, 21175], [5, 10, 7623], [7, 8, 27225], [11, 72, 1575]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.91160916225805816635550342721', 'prec': 107}, 'szpiro_ratio': 3.0779383410459342, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, -3, 2, 0, -4, 3, 0, 7, 0], 'aplist': [-2, 0, 0, -1, 0, -3, 3, 7, 4, -4, 2, 3, 5, 4, 8, -9, 12, 9, -13, -3, 3, -10, 12, -10, -4], 'class_deg': 1, 'class_size': 1, 'conductor': 190575, 'isogeny_matrix': [[1]], 'lmfdb_iso': '190575.b', 'trace_hash': 1975824723967029611}
• 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': '0.10972604264622304014182829587', 'prec': 103}, 'conductor': 190575, 'gens': [[99, 544, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.84843531367828129844390339346', 'prec': 103}], 'lmfdb_label': '190575.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.56091741290822968156678412988', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8072171293472310504255515998144354488', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [99, 286]}
• lmfdb_label 190575.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8392324
    {'degree': 3, 'field': [-30, -20, 0, 1], 'lmfdb_label': '190575.b1', 'torsion': [2]}
  • id: 8392325
    {'degree': 6, 'field': [-77, -77, 58, 37, -16, -3, 1], 'lmfdb_label': '190575.b1', 'torsion': [2, 2]}
  • id: 8392326
    {'degree': 8, 'field': [-213719, 113729, 24904, 1166, 220, -154, -41, -1, 1], 'lmfdb_label': '190575.b1', 'torsion': [3]}
  • id: 8392327
    {'degree': 12, 'field': [-59775489, 219827034, 38675124, -7073460, -4801005, -1256796, -105384, 50436, 355, -610, -36, -4, 1], 'lmfdb_label': '190575.b1', 'torsion': [4]}
• 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: 4717739
    {'conductor': 190575, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '190575.b1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4717740
    {'conductor': 190575, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '190575.b1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4717741
    {'conductor': 190575, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '190575.b1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4717742
    {'conductor': 190575, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '190575.b1', 'prime': 11, 'reduction_type': 0, '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

  
  {'adelic_gens': [[1, 2, 0, 1], [1, 0, 2, 1], [45, 2, 45, 3], [153, 2, 152, 3], [57, 2, 57, 3], [1, 1, 153, 0]], 'adelic_image': '154.2.0.?', 'conductor': 190575, 'lmfdb_label': '190575.b1', 'prime': 0}
• lmfdb_iso 190575.b does not appear in ec_padic