Elliptic curve data - 100022.a2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '100022b', 'Clabel': '100022b1', 'Cnumber': 1, 'abc_quality': 0.9133820749996613, 'absD': 10907589541888, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 200044, 'ainvs': [1, -1, 0, -17669, -913451], 'analytic_rank': 0, 'bad_primes': [2, 13, 3847], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 100022, 'degree': 401184, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2983751562635150080048371350', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [-610061264000475561, 10907589541888], 'lmfdb_iso': '100022.a', 'lmfdb_label': '100022.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -17669, -913451], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '52.6.0.c.1', '7694.6.0.?', '200044.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2983751562635150080048371350', 'prec': 100}, 'szpiro_ratio': 3.5596496281658174, '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, -1, -3, 4, 4, 0, 1, -2, 0, 1, 2, 3, 6, -4], 'aplist': [-1, 0, -4, 2, 4, 1, 2, 6, -8, -6, -8, -2, 8, -4, 4, -10, -6, -2, -12, 0, -16, 8, -6, -18, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 100022, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '100022.a', 'trace_hash': 1808785563289987752}
• 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': '0.074515336738095828427244124643', 'prec': 107}, 'conductor': 100022, 'gens': [], 'heights': [], 'lmfdb_label': '100022.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20682579439766632840839564495', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.20682579439766632840839564494731282735', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[154, -77, 1]], 'xcoord_integral_points': [154]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '13': [1, 0], '3847': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '100022.a2'}
• ec_torsion_growth •

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

  
  
  • id: 4641431
    {'degree': 2, 'field': [962, -1, 1], 'lmfdb_label': '100022.a2', 'torsion': [2, 2]}
  • id: 4641432
    {'degree': 4, 'field': [-237, 59, 22, -1, 1], 'lmfdb_label': '100022.a2', 'torsion': [4]}
  • id: 4641435
    {'degree': 8, 'field': [-4832, 1076, -842, -469, 238, -7, 7, -4, 1], 'lmfdb_label': '100022.a2', 'torsion': [6]}
  • id: 4641433
    {'degree': 8, 'field': [2768896, 0, 183131, 0, 4928, 0, 80, 0, 1], 'lmfdb_label': '100022.a2', 'torsion': [2, 4]}
  • id: 4641434
    {'degree': 8, 'field': [584478976, 0, 657524, 0, -43447, 0, -46, 0, 1], 'lmfdb_label': '100022.a2', 'torsion': [2, 4]}
  • id: 4641437
    {'degree': 16, 'field': [20342553513984, 0, -5146610790672, 0, 319219493229, 0, 7043670504, 0, 161989968, 0, -4748622, 0, 20664, 0, 0, 0, 1], 'lmfdb_label': '100022.a2', 'torsion': [2, 6]}
  • id: 4641436
    {'degree': 16, 'field': [117437488959337, 234359003605016, 22663866427318, -103933677599084, 18692378610313, 1834924714300, -220939878578, -2270212956, -1104763284, -94531504, 20600642, 420236, -34575, 476, -326, -4, 1], 'lmfdb_label': '100022.a2', '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: 2454030
    {'conductor': 100022, 'conductor_valuation': 1, 'discriminant_valuation': 24, 'j_denominator_valuation': 24, 'kodaira_symbol': 28, 'lmfdb_label': '100022.a2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2454031
    {'conductor': 100022, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '100022.a2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2454032
    {'conductor': 100022, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '100022.a2', 'prime': 3847, 'reduction_type': -1, '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

  
  
  • id: 2321203
    {'adelic_gens': [[1, 0, 4, 1], [46165, 4, 92330, 9], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [50013, 150034, 150032, 50011], [30786, 1, 184651, 0], [200041, 4, 200040, 5]], 'adelic_image': '200044.12.0.?', 'conductor': 100022, 'lmfdb_label': '100022.a2', 'prime': 0}
  • id: 401818
    {'conductor': 100022, 'elladic_image': '2.3.0.1', 'lmfdb_label': '100022.a2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 100022.a does not appear in ec_padic