Elliptic curve data - 11.a2

Formats: - HTML - YAML - JSON - 2022-06-27T04:52:47.391407

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  absD	numeric
  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[]
  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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '11a', 'Clabel': '11a1', 'Cnumber': 1, 'absD': 161051, 'ainvs': [0, -1, 1, -10, -20], 'analytic_rank': 0, 'bad_primes': [11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 11, 'degree': 1, 'elladic_images': ['5.120.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.30800984111840306468901426146', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 5, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5], 'jinv': [-122023936, 161051], 'lmfdb_iso': '11.a', 'lmfdb_label': '11.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -10, -20], 'min_quad_twist_disc': 1, 'modell_images': ['5Cs.1.1'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 1, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.30800984111840306468901426146', 'prec': 107}, 'torsion': 5, 'torsion_primes': [5], 'torsion_structure': [5]}
• 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, -2, -1, 2, 1, 2, -2, 0, -2, -2, 1, -2, 4, 4, -1, -4, -2, 4, 0, 2], 'aplist': [-2, -1, 1, -2, 1, 4, -2, 0, -1, 0, 7, 3, -8, -6, 8, -6, 5, 12, -7, -3, 4, -10, -6, 15, -7], 'class_deg': 25, 'class_size': 3, 'conductor': 11, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '11.a', 'trace_hash': 1428752966040989219}
• 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': '1.8515436234559593177080067118', 'prec': 100}, 'conductor': 11, 'gens': [], 'heights': [], 'lmfdb_label': '11.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2692093042795534216887946168', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.25384186085591068433775892335043887465', 'prec': 133}, 'tamagawa_product': 5, 'torsion_generators': [[5, 5, 1]], 'xcoord_integral_points': [5, 16]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 1, 0], '3': [0, 0], '5': [0, 1], '11': [1, 0]}, 'iwp0': 7, 'lmfdb_label': '11.a2'}
• ec_torsion_growth •

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

  
  
  • id: 0
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '11.a2', 'torsion': [10]}
  • id: 1
    {'degree': 4, 'field': [1, -1, 1, -1, 1], 'lmfdb_label': '11.a2', 'torsion': [5, 5]}
  • id: 2
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '11.a2', 'torsion': [2, 10]}
  • id: 3
    {'degree': 8, 'field': [-1, 1, 2, -7, 7, -7, 7, -4, 1], 'lmfdb_label': '11.a2', 'torsion': [15]}
  • id: 4
    {'degree': 12, 'field': [-1, 6, -10, 4, -3, 12, -8, -4, 5, -2, 6, -4, 1], 'lmfdb_label': '11.a2', 'torsion': [20]}
  • id: 5
    {'degree': 12, 'field': [1, 1, 2, 4, 7, -8, 3, 2, -3, 2, 0, -1, 1], 'lmfdb_label': '11.a2', 'torsion': [5, 10]}
• 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

  
  {'conductor': 11, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '11.a2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
• ec_galrep •

  Column	Type
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  {'conductor': 11, 'elladic_image': '5.120.0.1', 'lmfdb_label': '11.a2', 'modell_image': '5Cs.1.1', 'prime': 5}
• lmfdb_iso 11.a does not appear in ec_padic