Elliptic curve data - 221.a1

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• 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': '221a', 'Clabel': '221a2', 'Cnumber': 2, 'abc_quality': 1.287884882140366, 'absD': 634933, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [1, -1, 1, -11718, 491144], 'analytic_rank': 0, 'bad_primes': [13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 221, 'degree': 240, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.75517255567276285909025831691', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [177930109857804849, 634933], 'lmfdb_iso': '221.a', 'lmfdb_label': '221.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -11718, 491144], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '26.6.0.b.1', '68.6.0.c.1', '884.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 13], [3, 2, 17], [13, 14, 17], [17, 18, 13]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.75517255567276285909025831691', 'prec': 103}, 'szpiro_ratio': 7.358090043429584, '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, -1, 0, -1, 4, 0, -2, 3, -3, -4, 6, 0, -1, 2, 0, -1, 1, 3, 8, -4], 'aplist': [-1, 0, 4, -2, 6, -1, 1, 8, 4, -6, -2, -8, 0, 4, 0, -6, 0, -10, -8, 2, 0, 0, -4, -2, -4], 'class_deg': 2, 'class_size': 2, 'conductor': 221, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '221.a', 'trace_hash': 922098505865849259}
• 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': '0.22083375257352386371251619402', 'prec': 103}, 'conductor': 221, 'gens': [], 'heights': [], 'lmfdb_label': '221.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.9250249682244930363036353622', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.96251248411224651815181768109790560775', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[251, -255, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '13': [0, 0], '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '221.a1'}
• ec_torsion_growth •

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

  
  
  • id: 9360
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '221.a1', 'torsion': [2, 2]}
  • id: 9361
    {'degree': 4, 'field': [52, 0, -15, 0, 1], 'lmfdb_label': '221.a1', 'torsion': [4]}
  • id: 9364
    {'degree': 8, 'field': [1, -4, 4, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '221.a1', 'torsion': [6]}
  • id: 9362
    {'degree': 8, 'field': [16, 0, -68, 0, 77, 0, -17, 0, 1], 'lmfdb_label': '221.a1', 'torsion': [2, 4]}
  • id: 9363
    {'degree': 8, 'field': [107, 244, 285, 118, 0, -32, 3, -2, 1], 'lmfdb_label': '221.a1', 'torsion': [2, 4]}
  • id: 9366
    {'degree': 16, 'field': [14641, 0, -19337, 0, 30472, 0, -22253, 0, 8293, 0, -1919, 0, 295, 0, -26, 0, 1], 'lmfdb_label': '221.a1', 'torsion': [2, 6]}
  • id: 9365
    {'degree': 16, 'field': [456976, 0, -1476384, 0, 2575560, 0, -912600, 0, 170885, 0, -23712, 0, 1902, 0, -72, 0, 1], 'lmfdb_label': '221.a1', 'torsion': [8]}
• 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: 1948
    {'conductor': 221, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '221.a1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1949
    {'conductor': 221, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221.a1', 'prime': 17, '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: 1666704
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [881, 4, 880, 5], [105, 4, 210, 9], [342, 1, 271, 0], [665, 222, 220, 663]], 'adelic_image': '884.12.0.?', 'conductor': 221, 'lmfdb_label': '221.a1', 'prime': 0}
  • id: 933
    {'conductor': 221, 'elladic_image': '2.3.0.1', 'lmfdb_label': '221.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 221.a does not appear in ec_padic