Elliptic curve data - 99.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': '99a', 'Clabel': '99a1', 'Cnumber': 1, 'abc_quality': 1.136673290939488, 'absD': 297, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 132, 'ainvs': [1, -1, 1, -2, 0], 'analytic_rank': 1, 'bad_primes': [3, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 99, 'degree': 4, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.83526416397439234511324020037', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [19683, 11], 'lmfdb_iso': '99.a', 'lmfdb_label': '99.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -2, 0], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.b.1', '44.6.0.e.1', '66.6.0.a.1', '132.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.30257138456149499917614303481', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1099172361414197679620515096', 'prec': 103}, 'szpiro_ratio': 2.868988817262553, '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, 0, 4, -1, 0, -2, 2, 0, -1, 2, 0, -6, 4], 'aplist': [-1, 0, -4, -2, -1, -2, 2, -6, 4, -6, 4, -6, -10, 6, -8, 0, 4, -6, 8, 0, -2, -10, 12, 0, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 99, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '99.a', 'trace_hash': 93090483740669463}
• 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': '5.3149751054214535503218232396', 'prec': 100}, 'conductor': 99, 'gens': [[0, 0, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.30257138456149499917614303481', 'prec': 103}], 'lmfdb_label': '99.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '4.4984528865882752706337785999', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.68055155913983414332871941400680984869', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[-1, 0, 1]], 'xcoord_integral_points': [-1, 0, 2, 3, 26]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '99.a2'}
• ec_torsion_growth •

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

  
  
  • id: 3592
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '99.a2', 'torsion': [2, 2]}
  • id: 3593
    {'degree': 4, 'field': [6, -6, 3, 0, 1], 'lmfdb_label': '99.a2', 'torsion': [4]}
  • id: 3596
    {'degree': 8, 'field': [1, -1, 1, -2, -1, -2, 1, -1, 1], 'lmfdb_label': '99.a2', 'torsion': [6]}
  • id: 3595
    {'degree': 8, 'field': [16, 0, 4, 0, 0, 0, 1, 0, 1], 'lmfdb_label': '99.a2', 'torsion': [2, 4]}
  • id: 3594
    {'degree': 8, 'field': [36, 0, -63, 0, 30, 0, -6, 0, 1], 'lmfdb_label': '99.a2', 'torsion': [2, 4]}
  • id: 3598
    {'degree': 16, 'field': [1, 0, 2, 0, 139, 0, 92, 0, -83, 0, -52, 0, -5, 0, 2, 0, 1], 'lmfdb_label': '99.a2', 'torsion': [2, 6]}
  • id: 3597
    {'degree': 16, 'field': [52, 120, 20, -192, -202, 384, 1514, 1704, 217, -900, -434, 192, 152, -12, -20, 0, 1], 'lmfdb_label': '99.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: 597
    {'conductor': 99, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '99.a2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 598
    {'conductor': 99, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '99.a2', 'prime': 11, '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: 1666160
    {'adelic_gens': [[1, 2, 2, 5], [92, 1, 43, 0], [37, 100, 32, 99], [3, 4, 8, 11], [26, 1, 119, 0], [1, 4, 0, 1], [129, 4, 128, 5], [1, 0, 4, 1]], 'adelic_image': '132.12.0.?', 'conductor': 99, 'lmfdb_label': '99.a2', 'prime': 0}
  • id: 340
    {'conductor': 99, 'elladic_image': '2.3.0.1', 'lmfdb_label': '99.a2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 248
    {'lmfdb_iso': '99.a', 'p': 5, 'prec': 20, 'unit': 79851983860429, 'val': -1}
  • id: 249
    {'lmfdb_iso': '99.a', 'p': 7, 'prec': 20, 'unit': 6757918838304996, 'val': 1}
  • id: 254
    {'lmfdb_iso': '99.a', 'p': 13, 'prec': 20, 'unit': 204504363136755794629, 'val': 1}
  • id: 256
    {'lmfdb_iso': '99.a', 'p': 17, 'prec': 20, 'unit': 69849321055288643762097, 'val': 1}
  • id: 257
    {'lmfdb_iso': '99.a', 'p': 19, 'prec': 20, 'unit': 1229498702861567748879789, 'val': 1}
  • id: 260
    {'lmfdb_iso': '99.a', 'p': 23, 'prec': 20, 'unit': 17314448134227815387266192, 'val': 1}
  • id: 253
    {'lmfdb_iso': '99.a', 'p': 29, 'prec': 20, 'unit': 2748842842437898109965551974, 'val': 1}
  • id: 250
    {'lmfdb_iso': '99.a', 'p': 31, 'prec': 20, 'unit': 8580556801770509612565565302, 'val': 1}
  • id: 263
    {'lmfdb_iso': '99.a', 'p': 37, 'prec': 20, 'unit': 361333917218247423277752813325, 'val': 1}
  • id: 251
    {'lmfdb_iso': '99.a', 'p': 41, 'prec': 20, 'unit': 2094109168275800708914330168936, 'val': 1}
  • id: 252
    {'lmfdb_iso': '99.a', 'p': 43, 'prec': 20, 'unit': 1948854787464442599718548607135, 'val': 1}
  • id: 261
    {'lmfdb_iso': '99.a', 'p': 47, 'prec': 20, 'unit': 9410029597860694007871997863013, 'val': 1}
  • id: 258
    {'lmfdb_iso': '99.a', 'p': 59, 'prec': 20, 'unit': 1286762570590104631529302093721584, 'val': 1}
  • id: 262
    {'lmfdb_iso': '99.a', 'p': 61, 'prec': 20, 'unit': 1169081119812000012484121894825427, 'val': 1}
  • id: 247
    {'lmfdb_iso': '99.a', 'p': 67, 'prec': 20, 'unit': 24426469796916896901088905319688515, 'val': 1}
  • id: 259
    {'lmfdb_iso': '99.a', 'p': 73, 'prec': 20, 'unit': 204330547222598763507265875968714350, 'val': 1}
  • id: 255
    {'lmfdb_iso': '99.a', 'p': 79, 'prec': 20, 'unit': 82151975926510459848639924325010557, 'val': 1}
  • id: 246
    {'lmfdb_iso': '99.a', 'p': 83, 'prec': 20, 'unit': 1796503720339289935688394546260531132, 'val': 1}
  • id: 245
    {'lmfdb_iso': '99.a', 'p': 97, 'prec': 20, 'unit': 3585515941648102445188851684175572623, 'val': 1}