Elliptic curve data - 151725.b1

Formats: - HTML - YAML - JSON - 2024-05-02T09:33:39.290120

• 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': '151725h', 'Clabel': '151725h1', 'Cnumber': 1, 'abc_quality': 0.8729498068381875, 'absD': 1425054918994875, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 1190, 'ainvs': [0, -1, 1, -68878, 7213908], 'analytic_rank': 2, 'bad_primes': [3, 5, 7, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 151725, 'degree': 1437696, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6764967432145496034224933590', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [-11977551872, 472311], 'lmfdb_iso': '151725.b', 'lmfdb_label': '151725.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -238, 1384], 'min_quad_twist_disc': 17, 'modell_images': [], 'modm_images': ['1190.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 16, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.71118648048306898214389590487', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.14246940692208353035246378324', 'prec': 107}, 'szpiro_ratio': 3.7804253708591897, '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, -1, 2, 0, 2, -1, 0, 1, 0, 0, -2, -5, 2, 0, -4, 0, -2, 4, 0], 'aplist': [-2, -1, 0, -1, 0, -5, 0, 4, 3, -6, 7, -9, 9, 0, -11, -12, 8, -1, -2, -14, -12, 8, 1, -12, 6], 'class_deg': 1, 'class_size': 1, 'conductor': 151725, 'isogeny_matrix': [[1]], 'lmfdb_iso': '151725.b', 'trace_hash': 2004893574101570834}
• 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': '0.034979486600998709953591876312', 'prec': 107}, 'conductor': 151725, 'gens': [[91, 1300, 1], [397, 6502, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.57509506435651150573593458663', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.2553565147541104304939419625', 'prec': 100}], 'lmfdb_label': '151725.b1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.47587986616104668927355625355', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.4150292343652593700688714437700315769', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [], 'xcoord_integral_points': [-198, -143, 91, 108, 168, 172, 397, 18298]}
• lmfdb_label 151725.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 6815823
    {'degree': 3, 'field': [-9, -1, -1, 1], 'lmfdb_label': '151725.b1', 'torsion': [2]}
  • id: 6815824
    {'degree': 6, 'field': [2380, 0, 16, 0, -8, 0, 1], 'lmfdb_label': '151725.b1', 'torsion': [2, 2]}
  • id: 6815825
    {'degree': 8, 'field': [-21675, 0, -5525, 0, -510, 0, 0, 0, 1], 'lmfdb_label': '151725.b1', 'torsion': [3]}
  • id: 6815826
    {'degree': 12, 'field': [-19278000, 0, -160000, 0, 253200, 0, -1000, 0, -860, 0, 0, 0, 1], 'lmfdb_label': '151725.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: 3752272
    {'conductor': 151725, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '151725.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3752273
    {'conductor': 151725, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '151725.b1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3752274
    {'conductor': 151725, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '151725.b1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3752275
    {'conductor': 151725, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '151725.b1', 'prime': 17, '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, 1, 1189, 0], [1189, 2, 1188, 3], [171, 2, 171, 3], [71, 2, 71, 3], [477, 2, 477, 3], [1, 0, 2, 1], [1, 2, 0, 1]], 'adelic_image': '1190.2.0.?', 'conductor': 151725, 'lmfdb_label': '151725.b1', 'prime': 0}
• lmfdb_iso 151725.b does not appear in ec_padic