Elliptic curve data - 209088.ca1

Formats: - HTML - YAML - JSON - 2026-07-03T05:21:54.491791

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '209088gg', 'Clabel': '209088gg1', 'Cnumber': 1, 'abc_quality': 0.8254556483942886, 'absD': 1517208151523328, 'adelic_genus': 0, 'adelic_index': 6, 'adelic_level': 6, 'ainvs': [0, 0, 0, -47916, 4450864], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 209088, 'degree': 811008, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6473129266451462463773340531', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 52, 'isogeny_degrees': [1], 'jinv': [-8019, 1], 'lmfdb_iso': '209088.ca', 'lmfdb_label': '209088.ca1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -56, 190], 'min_quad_twist_disc': 264, 'modell_images': [], 'modm_images': ['6.6.0.b.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 3267], [3, 6, 7744], [11, 52, 1728]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2656577648940461699719544903', 'prec': 103}, 'szpiro_ratio': 3.603144794738529, '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, -2, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0], 'aplist': [0, 0, -2, 1, 0, -1, -4, 0, -8, -6, 1, 6, 2, 12, -2, 12, -10, 6, 13, 6, 1, 11, -18, -6, 5], 'class_deg': 1, 'class_size': 1, 'conductor': 209088, 'isogeny_matrix': [[1]], 'lmfdb_iso': '209088.ca', 'trace_hash': 823020309948104812}
• 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': '0.037081916529112042314304204056', 'prec': 107}, 'conductor': 209088, 'gens': [], 'heights': [], 'lmfdb_label': '209088.ca1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.46287364579430606806395254794', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.92574729158861213612790509589003171091', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 209088.ca1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9143401
    {'degree': 3, 'field': [-11, 0, 0, 1], 'lmfdb_label': '209088.ca1', 'torsion': [2]}
  • id: 9143402
    {'degree': 6, 'field': [144, -36, -27, 15, 6, -3, 1], 'lmfdb_label': '209088.ca1', 'torsion': [2, 2]}
  • id: 9143403
    {'degree': 8, 'field': [-48, 0, 0, 0, 24, 0, -10, 0, 1], 'lmfdb_label': '209088.ca1', 'torsion': [3]}
  • id: 9143404
    {'degree': 12, 'field': [-48, 0, 162, 0, 165, 0, -186, 0, 66, 0, -12, 0, 1], 'lmfdb_label': '209088.ca1', '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: 5181746
    {'conductor': 209088, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '209088.ca1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5181747
    {'conductor': 209088, 'conductor_valuation': 3, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '209088.ca1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5181748
    {'conductor': 209088, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '209088.ca1', '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': [[0, 5, 1, 5], [3, 2, 5, 5]], 'adelic_image': '6.6.0.?', 'conductor': 209088, 'lmfdb_label': '209088.ca1', 'prime': 0}
• lmfdb_iso 209088.ca does not appear in ec_padic