Elliptic curve data - 388416.n2

Formats: - HTML - YAML - JSON - 2025-09-22T02:30:55.565289

• 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': '388416n', 'Clabel': '388416n1', 'Cnumber': 1, 'abc_quality': 1.0426921261059747, 'absD': 1970427581175636688896, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 24, 'ainvs': [0, -1, 0, 2135903, 1764959521], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 388416, 'degree': 17418240, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7707838756844744216388566812', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 13, 'isogeny_degrees': [1, 3], 'jinv': [49218965184023, 89996344704], 'lmfdb_iso': '388416.n', 'lmfdb_label': '388416.n2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 33373, 3451358], 'min_quad_twist_disc': 8, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0-3.a.1.2', '24.16.0-24.d.1.1'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2343595689887221198140513477', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 867], [3, 4, 129472], [5, 2, 129472], [7, 8, 55488], [17, 114, 1344]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.78665865682581776409649695972', 'prec': 103}, 'szpiro_ratio': 4.359554843385552, '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, 0, -1, 0, -3, 0, 1, 0, 1, 0, 3, 0, -2, 0, 3, 0, 0, 0, -2, 0], 'aplist': [0, -1, -3, 1, 3, -2, 0, -2, 0, -3, 5, -2, 0, 10, 12, -3, -3, 4, 4, 6, 11, 5, -12, 0, -7], 'class_deg': 3, 'class_size': 2, 'conductor': 388416, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '388416.n', 'trace_hash': 214791745156867919}
• 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': '0.0039203758433548822523850303519', 'prec': 110}, 'conductor': 388416, 'gens': [[3321, 213248, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2343595689887221198140513477', 'prec': 100}], 'lmfdb_label': '388416.n2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10143911445872341261277170893', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.4396349454541814635995410858571299146', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': [3321]}
• lmfdb_label 388416.n2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16057311
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '388416.n2', 'torsion': [3]}
  • id: 16057312
    {'degree': 3, 'field': [39, -11, -1, 1], 'lmfdb_label': '388416.n2', 'torsion': [2]}
  • id: 16057315
    {'degree': 6, 'field': [-98, 0, -3, 0, -12, 0, 1], 'lmfdb_label': '388416.n2', 'torsion': [6]}
  • id: 16057313
    {'degree': 6, 'field': [24, -120, 142, 52, 15, -2, 1], 'lmfdb_label': '388416.n2', 'torsion': [2, 2]}
  • id: 16057314
    {'degree': 6, 'field': [151591, 65866, 7031, -536, -139, -2, 1], 'lmfdb_label': '388416.n2', 'torsion': [3]}
  • id: 16057316
    {'degree': 12, 'field': [1764, -3864, -516, -4592, 209, 1794, -396, -514, 354, -98, 40, -6, 1], 'lmfdb_label': '388416.n2', 'torsion': [4]}
  • id: 16057318
    {'degree': 12, 'field': [9604, 0, -294, 0, -1167, 0, -232, 0, 147, 0, 12, 0, 1], 'lmfdb_label': '388416.n2', 'torsion': [2, 6]}
  • id: 16057317
    {'degree': 12, 'field': [11005898281, 0, 238053662, 0, 7507143, 0, 225196, 0, 2271, 0, -10, 0, 1], 'lmfdb_label': '388416.n2', 'torsion': [3, 3]}
  • id: 16057320
    {'degree': 18, 'field': [351318624, 0, 23906992, 0, 29246472, 0, -717276, 0, -39648, 0, 35392, 0, 6972, 0, 408, 0, 6, 0, 1], 'lmfdb_label': '388416.n2', 'torsion': [2, 6]}
  • id: 16057319
    {'degree': 18, 'field': [469343528048, -191409555552, -96080173008, 77875312432, -30793921368, 8611584624, -1720641220, 297055704, 2587320, -16934236, 5313348, -1019544, 139645, -26532, 4614, -398, 15, -6, 1], 'lmfdb_label': '388416.n2', 'torsion': [9]}
• 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: 9608585
    {'conductor': 388416, 'conductor_valuation': 6, 'discriminant_valuation': 25, 'j_denominator_valuation': 7, 'kodaira_symbol': -19, 'lmfdb_label': '388416.n2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 9608586
    {'conductor': 388416, 'conductor_valuation': 1, 'discriminant_valuation': 15, 'j_denominator_valuation': 15, 'kodaira_symbol': 19, 'lmfdb_label': '388416.n2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9608587
    {'conductor': 388416, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '388416.n2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9608588
    {'conductor': 388416, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '388416.n2', 'prime': 17, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 4076574
    {'adelic_gens': [[19, 6, 18, 7], [1, 0, 6, 1], [4, 3, 9, 7], [3, 4, 8, 11], [7, 6, 0, 1], [11, 18, 9, 5], [1, 6, 0, 1], [6, 1, 19, 6]], 'adelic_image': '24.16.0.?', 'conductor': 388416, 'lmfdb_label': '388416.n2', 'prime': 0}
  • id: 1325648
    {'conductor': 388416, 'elladic_image': '3.4.0.1', 'lmfdb_label': '388416.n2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 388416.n does not appear in ec_padic