Elliptic curve data - 115056.v1

Formats: - HTML - YAML - JSON - 2025-11-02T07:31:11.909481

• 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': '115056w', 'Clabel': '115056w2', 'Cnumber': 2, 'abc_quality': 1.0212077352422504, 'absD': 6610892935053312, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 564, 'ainvs': [0, 0, 0, -769729395, -8219685891278], 'analytic_rank': 0, 'bad_primes': [2, 3, 17, 47], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 115056, 'degree': 16318464, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3646246525544195059545100490', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2], 'jinv': [16890809037822478057344625, 2213974668], 'lmfdb_iso': '115056.v', 'lmfdb_label': '115056.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5345343, -4758989895], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '188.6.0.?', '564.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 12784], [17, 18, 6768], [47, 48, 2448]], 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1221713276604193508396553091', 'prec': 100}, 'szpiro_ratio': 6.264237556547191, '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, 0, 0, 0, 0, 4, 0, 0, 0, -4, 0, 2, 0, 0, 0, -1, 0, -2, 0], 'aplist': [0, 0, 0, 4, -4, 2, -1, -2, -4, 0, -2, 10, 12, -10, 1, -10, 4, -14, 2, 0, 6, -4, 4, -6, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 115056, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '115056.v', 'trace_hash': 312486314258038858}
• 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': '0.0011954300245996515784308625970', 'prec': 110}, 'conductor': 115056, 'gens': [], 'heights': [], 'lmfdb_label': '115056.v1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.028662563947416320968950913354', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0637046042139751097644657614649554882', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-16018, 0, 1]], 'xcoord_integral_points': [-16018]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '17': [0, 0], '47': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '115056.v1'}
• ec_torsion_growth •

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

  
  
  • id: 5278162
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '115056.v1', 'torsion': [2, 2]}
  • id: 5278163
    {'degree': 4, 'field': [12, 0, -1, 0, 1], 'lmfdb_label': '115056.v1', 'torsion': [4]}
  • id: 5278166
    {'degree': 8, 'field': [-84672, 0, 17364, 0, -1008, 0, 0, 0, 1], 'lmfdb_label': '115056.v1', 'torsion': [6]}
  • id: 5278165
    {'degree': 8, 'field': [-2, 16, -40, 46, -17, -10, 8, -4, 1], 'lmfdb_label': '115056.v1', 'torsion': [2, 4]}
  • id: 5278164
    {'degree': 8, 'field': [324, 0, 312, 0, 85, 0, -14, 0, 1], 'lmfdb_label': '115056.v1', 'torsion': [2, 4]}
  • id: 5278167
    {'degree': 16, 'field': [318096, 0, -318096, 0, 1656844, 0, 5452, 0, 2225, 0, 532, 0, -70, 0, -8, 0, 1], 'lmfdb_label': '115056.v1', 'torsion': [8]}
  • id: 5278168
    {'degree': 16, 'field': [226803600, 0, -24246288, 0, 3777012, 0, -4742787, 0, 1062474, 0, -100443, 0, 4741, 0, -110, 0, 1], 'lmfdb_label': '115056.v1', '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: 2829809
    {'conductor': 115056, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '115056.v1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2829810
    {'conductor': 115056, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '115056.v1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2829811
    {'conductor': 115056, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '115056.v1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2829812
    {'conductor': 115056, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '115056.v1', 'prime': 47, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 2416301
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [424, 145, 141, 424], [1, 4, 0, 1], [561, 4, 560, 5], [190, 1, 187, 0], [193, 4, 386, 9]], 'adelic_image': '564.12.0.?', 'conductor': 115056, 'lmfdb_label': '115056.v1', 'prime': 0}
  • id: 454268
    {'conductor': 115056, 'elladic_image': '2.3.0.1', 'lmfdb_label': '115056.v1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 115056.v does not appear in ec_padic