Elliptic curve data - 104222.b2

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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': '104222a', 'Clabel': '104222a3', 'Cnumber': 3, 'abc_quality': 1.1790775616093738, 'absD': 8773642037505122, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 10168, 'ainvs': [1, -1, 1, -51586, -152945], 'analytic_rank': 0, 'bad_primes': [2, 31, 41], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 104222, 'degree': 552960, 'elladic_images': ['8.12.0.15'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7487083478331193748955622116', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [3196010817, 1847042], 'lmfdb_iso': '104222.b', 'lmfdb_label': '104222.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -31, 5], 'min_quad_twist_disc': 41, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.k.1', '164.12.0.?', '248.24.0.?', '328.24.0.?', '10168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1681], [31, 32, 3362], [41, 842, 62]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.10807768551903452703781947492', 'prec': 107}, 'szpiro_ratio': 3.8225321969756787, '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, -2, 0, 0, 1, -3, -2, 0, 0, -2, 0, 0, 1, 6, -3, -4, -2], 'aplist': [1, 0, -2, 0, 0, -2, 6, -4, 8, -2, -1, 10, 0, 8, 8, 6, -12, -6, 12, -8, 10, 8, 8, 6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 104222, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '104222.b', 'trace_hash': 684204629250634135}
• 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': '0.030275493301137257789166292366', 'prec': 107}, 'conductor': 104222, 'gens': [], 'heights': [], 'lmfdb_label': '104222.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.34631239977510640726542099797', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7704991982008512581233679837949032588', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-901, 897, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 1], '31': [0, 0], '41': 'a'}, 'iwp0': 3, 'lmfdb_label': '104222.b2'}
• ec_torsion_growth •

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

  
  
  • id: 4822369
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [2, 2]}
  • id: 4822370
    {'degree': 2, 'field': [41, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [4]}
  • id: 4822371
    {'degree': 2, 'field': [82, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [4]}
  • id: 4822372
    {'degree': 4, 'field': [441, 0, 40, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [2, 4]}
  • id: 4822376
    {'degree': 8, 'field': [-524064, -81552, 42792, -4440, -3252, -78, -6, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [6]}
  • id: 4822373
    {'degree': 8, 'field': [9522, 4248, -3652, -1152, 477, 116, -34, -4, 1], 'lmfdb_label': '104222.b2', 'torsion': [2, 4]}
  • id: 4822375
    {'degree': 8, 'field': [2214092, 553040, 181864, 21824, 2792, -248, -12, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [8]}
  • id: 4822374
    {'degree': 8, 'field': [2389250, -169806, 266659, -11062, 10557, -250, 173, -2, 1], 'lmfdb_label': '104222.b2', 'torsion': [8]}
  • id: 4822377
    {'degree': 16, 'field': [44363682, 44101992, -24151036, -34914456, 5719346, 12102976, -917880, -2305912, 142163, 255480, -18272, -16344, 1450, 560, -60, -8, 1], 'lmfdb_label': '104222.b2', 'torsion': [4, 4]}
  • id: 4822381
    {'degree': 16, 'field': [119202724, 0, 97527832, 0, 32849524, 0, 6335341, 0, 771910, 0, 60337, 0, 2941, 0, 82, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [12]}
  • id: 4822379
    {'degree': 16, 'field': [20461322722, -6663246796, 9923185598, -2464531468, 1971931303, -367132980, 215885042, -29412316, 14257385, -1386436, 575978, -38868, 13861, -604, 182, -4, 1], 'lmfdb_label': '104222.b2', 'torsion': [2, 8]}
  • id: 4822382
    {'degree': 16, 'field': [30515897344, 0, 12483562496, 0, 2102369536, 0, 202730912, 0, 12350560, 0, 482696, 0, 11764, 0, 164, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [12]}
  • id: 4822378
    {'degree': 16, 'field': [35433591426, 24852491928, 14720501340, 5134695912, 1644841570, 350637528, 66559480, 4901472, 159875, -33976, 66560, 15128, 1834, -248, -36, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [2, 8]}
  • id: 4822380
    {'degree': 16, 'field': [456121935424, 0, -40271854144, 0, 2896148176, 0, 132632024, 0, 3080440, 0, -102202, 0, -2456, 0, -16, 0, 1], 'lmfdb_label': '104222.b2', 'torsion': [2, 6]}
• 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: 2559671
    {'conductor': 104222, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '104222.b2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2559672
    {'conductor': 104222, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '104222.b2', 'prime': 31, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2559673
    {'conductor': 104222, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '104222.b2', 'prime': 41, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2348025
    {'adelic_gens': [[4463, 0, 0, 10167], [1272, 5371, 3321, 10046], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [10161, 8, 10160, 9], [2297, 9184, 8692, 6233], [7, 6, 10162, 10163], [5987, 6232, 8610, 5741]], 'adelic_image': '10168.48.0.?', 'conductor': 104222, 'lmfdb_label': '104222.b2', 'prime': 0}
  • id: 416633
    {'conductor': 104222, 'elladic_image': '8.12.0.15', 'lmfdb_label': '104222.b2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 104222.b does not appear in ec_padic