Elliptic curve data - 199920.gt1

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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': '199920et', 'Clabel': '199920et3', 'Cnumber': 3, 'abc_quality': 1.0554528133897931, 'absD': 37179613453500000000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 1, 0, -1321646440, 18493139642900], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 199920, 'degree': 61931520, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7393180815798797368722989549', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 175, 'isogeny_degrees': [1, 2, 4], 'jinv': [1059623036730633329075378, 154307373046875], 'lmfdb_iso': '199920.gt', 'lmfdb_label': '199920.gt1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -26972376, 53908152624], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.s.1', '40.12.0.bb.1', '56.12.0-4.c.1.2', '84.12.0.?', '120.24.0.?', '168.24.0.?', '280.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.64941678081209157419383349920', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 147], [3, 4, 13328], [5, 6, 39984], [7, 26, 1360], [17, 18, 11760]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1309780915389398840204931385', 'prec': 100}, 'szpiro_ratio': 6.113553753880004, '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, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 1, 0, 4, 0], 'aplist': [0, 1, 1, 0, 0, -2, 1, 4, -8, -6, 0, -6, -2, -4, 8, 10, 8, -6, -4, 8, -10, 0, 12, 14, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 199920, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '199920.gt', 'trace_hash': 2122527007866901920}
• 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': '0.00056502749563582531726502133969', 'prec': 113}, 'conductor': 199920, 'gens': [[21020, 7650, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.64941678081209157419383349920', 'prec': 103}], 'lmfdb_label': '199920.gt1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.090262807532345544156025400576', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.8478545583124987716662247735599317662', 'prec': 130}, 'tamagawa_product': 672, 'torsion_generators': [[20995, 0, 1]], 'xcoord_integral_points': [20995, 21020, 23495, 51620]}
• lmfdb_label 199920.gt1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8763522
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [4]}
  • id: 8763521
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [2, 2]}
  • id: 8763523
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '199920.gt1', 'torsion': [4]}
  • id: 8763524
    {'degree': 4, 'field': [4, 0, -10, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [2, 4]}
  • id: 8763528
    {'degree': 8, 'field': [-28812, 0, 15092, 0, 588, 0, 0, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [6]}
  • id: 8763527
    {'degree': 8, 'field': [1, 3, 17, 6, 24, -6, 17, -3, 1], 'lmfdb_label': '199920.gt1', 'torsion': [8]}
  • id: 8763525
    {'degree': 8, 'field': [48344545, 5696496, 499592, 8160, -13806, -816, 8, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [2, 4]}
  • id: 8763526
    {'degree': 8, 'field': [194896025, -10788200, -8060200, 183600, 108606, -680, -568, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [8]}
  • id: 8763532
    {'degree': 16, 'field': [-66835341, 101270844, 146421450, -435055068, 392420280, -168566940, 34189128, -2314020, 720420, -634524, 133450, -2592, 210, -340, 12, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [2, 6]}
  • id: 8763534
    {'degree': 16, 'field': [144, 0, -2640, 0, -1376, 0, 2640, 0, -6180, 0, 4840, 0, 276, 0, 0, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [12]}
  • id: 8763530
    {'degree': 16, 'field': [15625, -33750, 53475, -65550, 68725, -55920, 50394, -28116, 19026, -9300, 4302, -1608, 553, -150, 39, -6, 1], 'lmfdb_label': '199920.gt1', 'torsion': [2, 8]}
  • id: 8763533
    {'degree': 16, 'field': [156275001, 0, -5276988, 0, 2018628, 0, -642980, 0, -16642, 0, -8900, 0, -92, 0, -28, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [12]}
  • id: 8763529
    {'degree': 16, 'field': [8802347265625, -2106243900000, 251993203200, 4972136880, 20526485146, -3661817544, 289980288, -5658144, 17565951, -2105688, 83232, -4896, 6982, -408, 0, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [4, 4]}
  • id: 8763531
    {'degree': 16, 'field': [16506872008225, 0, -8044338624880, 0, 898168770956, 0, -44493472752, 0, 1163864774, 0, -17061456, 0, 139724, 0, -592, 0, 1], 'lmfdb_label': '199920.gt1', 'torsion': [2, 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: 4947080
    {'conductor': 199920, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '199920.gt1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4947081
    {'conductor': 199920, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '199920.gt1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 4947082
    {'conductor': 199920, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '199920.gt1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 4947083
    {'conductor': 199920, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '199920.gt1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4947084
    {'conductor': 199920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '199920.gt1', '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: 2944398
    {'adelic_gens': [[833, 8, 832, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [552, 7, 287, 720], [337, 728, 28, 393], [599, 0, 0, 839], [7, 6, 834, 835], [764, 721, 343, 246], [736, 203, 49, 78]], 'adelic_image': '840.48.0.?', 'conductor': 199920, 'lmfdb_label': '199920.gt1', 'prime': 0}
  • id: 741004
    {'conductor': 199920, 'elladic_image': '4.6.0.1', 'lmfdb_label': '199920.gt1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 199920.gt does not appear in ec_padic