Elliptic curve data - 388416.gb1

Formats: - HTML - YAML - JSON - 2025-10-29T03:04:56.689420

• 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': '388416gb', 'Clabel': '388416gb1', 'Cnumber': 1, 'abc_quality': 1.1802104601903138, 'absD': 174190166225687937024, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 24, 'ainvs': [0, 1, 0, -111361, 635118431], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 388416, 'degree': 14100480, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5628971644172588181738566749', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 157, 'isogeny_degrees': [1], 'jinv': [-83521, 95256], 'lmfdb_iso': '388416.gb', 'lmfdb_label': '388416.gb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -6, 252], 'min_quad_twist_disc': 136, 'modell_images': [], 'modm_images': ['24.2.0.b.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 867], [3, 4, 129472], [5, 2, 129472], [7, 8, 55488], [17, 98, 1344]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.36563250246013653278501458587', 'prec': 107}, 'szpiro_ratio': 4.200669102615829, '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, -1, 0, 1, 0, 1, 0, 5, 0, 2, 0, -1, 0, 0, 0, 2, 0], 'aplist': [0, 1, -1, 1, 5, 2, 0, 2, -4, -9, 9, -10, -8, 10, -12, -9, -5, -12, 12, -2, 3, 9, -12, 12, -7], 'class_deg': 1, 'class_size': 1, 'conductor': 388416, 'isogeny_matrix': [[1]], 'lmfdb_iso': '388416.gb', 'trace_hash': 2183906311139366669}
• 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': '0.0059414959799805316015211817734', 'prec': 110}, 'conductor': 388416, 'gens': [], 'heights': [], 'lmfdb_label': '388416.gb1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14569802443738617004963186604', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9139604887477234009926373208881616935', 'prec': 130}, 'tamagawa_product': 20, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 388416.gb1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16059926
    {'degree': 3, 'field': [39, -11, -1, 1], 'lmfdb_label': '388416.gb1', 'torsion': [2]}
  • id: 16059927
    {'degree': 6, 'field': [24, -120, 142, 52, 15, -2, 1], 'lmfdb_label': '388416.gb1', 'torsion': [2, 2]}
  • id: 16059928
    {'degree': 8, 'field': [-15552, 0, 4824, 0, -432, 0, 0, 0, 1], 'lmfdb_label': '388416.gb1', 'torsion': [3]}
  • id: 16059929
    {'degree': 12, 'field': [340500, -282000, -23880, 62736, -22684, -2008, 4516, -1136, -149, 80, -4, -4, 1], 'lmfdb_label': '388416.gb1', '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: 9609725
    {'conductor': 388416, 'conductor_valuation': 6, 'discriminant_valuation': 21, 'j_denominator_valuation': 3, 'kodaira_symbol': -15, 'lmfdb_label': '388416.gb1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9609726
    {'conductor': 388416, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '388416.gb1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 9609727
    {'conductor': 388416, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '388416.gb1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9609728
    {'conductor': 388416, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '388416.gb1', 'prime': 17, 'reduction_type': 0, '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

  
  {'adelic_gens': [[7, 2, 0, 1], [1, 2, 0, 1], [17, 2, 17, 3], [1, 0, 2, 1], [23, 2, 22, 3], [13, 2, 13, 3], [1, 1, 23, 0]], 'adelic_image': '24.2.0.?', 'conductor': 388416, 'lmfdb_label': '388416.gb1', 'prime': 0}
• lmfdb_iso 388416.gb does not appear in ec_padic