Elliptic curve data - 21.a6

Formats: - HTML - YAML - JSON - 2022-06-25T14:37:27.769273

• 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': '21a', 'Clabel': '21a4', 'Cnumber': 4, 'absD': 63, 'ainvs': [1, 0, 0, 1, 0], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21, 'degree': 2, 'elladic_images': ['16.48.0.27'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.96551538744897819336758232752', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [103823, 63], 'lmfdb_iso': '21.a', 'lmfdb_label': '21.a6', 'lmfdb_number': 6, 'manin_constant': 2, 'min_quad_twist_ainvs': [1, 0, 0, 1, 0], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.96551538744897819336758232752', 'prec': 107}, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, -1, 1, -1, -2, -1, -1, 3, 1, 2, 4, -1, -2, 1, -2, -1, -6, -1, 4, 2], 'aplist': [-1, 1, -2, -1, 4, -2, -6, 4, 0, -2, 0, 6, 2, -4, 0, 6, 12, -2, 4, 0, -6, -16, -12, -14, 18], 'class_deg': 8, 'class_size': 6, 'conductor': 21, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '21.a', 'trace_hash': 1161919666425559947}
• 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': '6.8966154370970158450892581367', 'prec': 100}, 'conductor': 21, 'gens': [], 'heights': [], 'lmfdb_label': '21.a6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.6089232431079364447472012512', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.45111540538849205559340015640263020881', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[1, 1, 1]], 'xcoord_integral_points': [0, 1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [1, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '21.a6'}
• ec_torsion_growth •

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

  
  
  • id: 435
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '21.a6', 'torsion': [8]}
  • id: 436
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '21.a6', 'torsion': [8]}
  • id: 434
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '21.a6', 'torsion': [2, 4]}
  • id: 438
    {'degree': 4, 'field': [1, 2, 0, -1, 1], 'lmfdb_label': '21.a6', 'torsion': [16]}
  • id: 437
    {'degree': 4, 'field': [4, -2, -1, -1, 1], 'lmfdb_label': '21.a6', 'torsion': [2, 8]}
  • id: 443
    {'degree': 8, 'field': [-3, 0, -1, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '21.a6', 'torsion': [12]}
  • id: 441
    {'degree': 8, 'field': [-3, 24, -54, 30, -2, -10, 15, -4, 1], 'lmfdb_label': '21.a6', 'torsion': [16]}
  • id: 442
    {'degree': 8, 'field': [1, -3, 4, -3, 3, -3, 4, -3, 1], 'lmfdb_label': '21.a6', 'torsion': [2, 16]}
  • id: 440
    {'degree': 8, 'field': [1, -2, 2, 4, -1, 4, 2, -2, 1], 'lmfdb_label': '21.a6', 'torsion': [2, 8]}
  • id: 439
    {'degree': 8, 'field': [36, -72, 72, -24, 13, -10, 2, -2, 1], 'lmfdb_label': '21.a6', 'torsion': [4, 4]}
  • id: 444
    {'degree': 16, 'field': [1, -2, 2, -12, 13, 8, 30, -26, -12, -26, 30, 8, 13, -12, 2, -2, 1], 'lmfdb_label': '21.a6', 'torsion': [4, 8]}
  • id: 447
    {'degree': 16, 'field': [1, -2, 5, 7, -18, 40, 3, -53, 103, -102, 67, -47, 32, -21, 11, -4, 1], 'lmfdb_label': '21.a6', 'torsion': [2, 12]}
  • id: 446
    {'degree': 16, 'field': [3, 6, -9, -114, 501, -1062, 1485, -1572, 1393, -1106, 802, -512, 274, -116, 37, -8, 1], 'lmfdb_label': '21.a6', 'torsion': [32]}
  • id: 445
    {'degree': 16, 'field': [9, -72, 198, -126, -354, 486, 462, -1188, 457, 350, -142, -160, 67, 28, -13, -2, 1], 'lmfdb_label': '21.a6', 'torsion': [2, 16]}
  • id: 449
    {'degree': 16, 'field': [9, 0, -3, 0, -17, 0, -6, 0, 39, 0, -2, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '21.a6', 'torsion': [24]}
  • id: 448
    {'degree': 16, 'field': [9, 45, -432, 882, -990, 540, 309, -669, 531, -120, -123, 153, -71, 14, 6, -4, 1], 'lmfdb_label': '21.a6', 'torsion': [24]}
• 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: 52
    {'conductor': 21, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21.a6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 53
    {'conductor': 21, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21.a6', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  {'conductor': 21, 'elladic_image': '16.48.0.27', 'lmfdb_label': '21.a6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 21.a does not appear in ec_padic