Elliptic curve data - 87120.fa1

Formats: - HTML - YAML - JSON - 2025-10-15T09:23:56.907210

• 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': '87120by', 'Clabel': '87120by1', 'Cnumber': 1, 'abc_quality': 1.1033068405579607, 'absD': 5166189175587484822272000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 120, 'ainvs': [0, 0, 0, -255148707, 1564877428994], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 87120, 'degree': 17233920, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6141146777220954215163270921', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 130, 'isogeny_degrees': [1], 'jinv': [5739907130357378, 16142520375], 'lmfdb_iso': '87120.fa', 'lmfdb_label': '87120.fa1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -234296, -43623120], 'min_quad_twist_disc': -132, 'modell_images': [], 'modm_images': ['120.2.0.?'], '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, 5445], [3, 8, 1936], [5, 6, 17424], [11, 42, 720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.83082676934251034614494597699', 'prec': 103}, 'szpiro_ratio': 6.126190638349533, '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, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0, 0, -1, 0, -5, 0], 'aplist': [0, 0, 1, 1, 0, -3, -1, -5, 4, -9, -6, -11, -2, 2, -6, -4, 4, -4, 6, 5, -6, -14, -7, -4, -14], 'class_deg': 1, 'class_size': 1, 'conductor': 87120, 'isogeny_matrix': [[1]], 'lmfdb_iso': '87120.fa', 'trace_hash': 1895932794716621345}
• 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': '0.00072580486849482831839020431948', 'prec': 113}, 'conductor': 87120, 'gens': [], 'heights': [], 'lmfdb_label': '87120.fa1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.076843164790012481905690035860', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.92211797748014978286828043031993980765', 'prec': 133}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [2, 0], '11': 'a', '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '87120.fa1'}
• ec_torsion_growth •

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

  
  
  • id: 4079133
    {'degree': 3, 'field': [-22, -33, 0, 1], 'lmfdb_label': '87120.fa1', 'torsion': [2]}
  • id: 4079134
    {'degree': 6, 'field': [-750, 0, 301, 0, -32, 0, 1], 'lmfdb_label': '87120.fa1', 'torsion': [2, 2]}
  • id: 4079135
    {'degree': 8, 'field': [10, -72, 190, -244, 126, -22, 22, 0, 1], 'lmfdb_label': '87120.fa1', 'torsion': [3]}
  • id: 4079136
    {'degree': 12, 'field': [243000, 0, 498070, 0, -15159, 0, -8584, 0, 1046, 0, -54, 0, 1], 'lmfdb_label': '87120.fa1', '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: 2126603
    {'conductor': 87120, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '87120.fa1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2126604
    {'conductor': 87120, 'conductor_valuation': 2, 'discriminant_valuation': 23, 'j_denominator_valuation': 17, 'kodaira_symbol': -21, 'lmfdb_label': '87120.fa1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2126605
    {'conductor': 87120, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '87120.fa1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2126606
    {'conductor': 87120, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '87120.fa1', 'prime': 11, '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': [[1, 0, 2, 1], [119, 2, 118, 3], [61, 2, 61, 3], [31, 2, 31, 3], [1, 2, 0, 1], [1, 1, 119, 0], [97, 2, 97, 3], [41, 2, 41, 3]], 'adelic_image': '120.2.0.?', 'conductor': 87120, 'lmfdb_label': '87120.fa1', 'prime': 0}
• lmfdb_iso 87120.fa does not appear in ec_padic