Elliptic curve data - 199920.dt4

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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': '199920cw', 'Clabel': '199920cw3', 'Cnumber': 3, 'abc_quality': 1.000933549492738, 'absD': 52813373217479884800, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 952, 'ainvs': [0, -1, 0, 453920, -329388800], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 199920, 'degree': 5308416, 'elladic_images': ['8.12.0.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4666351687984516624740048032', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 97, 'isogeny_degrees': [1, 2, 4], 'jinv': [21464092074671, 109596256200], 'lmfdb_iso': '199920.dt', 'lmfdb_label': '199920.dt4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 579, -14757], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.d.1', '28.12.0-4.c.1.2', '56.24.0-8.d.1.2', '136.24.0.?', '952.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.80053291371084970050409631002', 'prec': 103}, 'szpiro_ratio': 4.3215746678479885, '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, 4, 0, 2, 0, -1, 0, -1, 0, -4, 0], 'aplist': [0, -1, 1, 0, 4, 2, -1, -4, 4, 2, 4, -6, -2, 12, 8, -2, 12, -2, -4, 4, 14, 12, -4, -10, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 199920, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '199920.dt', 'trace_hash': 2133719822790218334}
• 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': '0.0072029087780257332373658501355', 'prec': 110}, 'conductor': 199920, 'gens': [], 'heights': [], 'lmfdb_label': '199920.dt4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10032509010627382048806746457', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2104028834007622556181588662036523992', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[481, 0, 1]], 'xcoord_integral_points': [481]}
• lmfdb_label 199920.dt4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8762425
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '199920.dt4', 'torsion': [4]}
  • id: 8762426
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '199920.dt4', 'torsion': [4]}
  • id: 8762424
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '199920.dt4', 'torsion': [2, 2]}
  • id: 8762427
    {'degree': 4, 'field': [2, -8, 9, -2, 1], 'lmfdb_label': '199920.dt4', 'torsion': [2, 4]}
  • id: 8762431
    {'degree': 8, 'field': [-115248, 0, -30527, 0, -1176, 0, 0, 0, 1], 'lmfdb_label': '199920.dt4', 'torsion': [6]}
  • id: 8762429
    {'degree': 8, 'field': [625, 0, 148, 0, -280, 0, -44, 0, 1], 'lmfdb_label': '199920.dt4', 'torsion': [8]}
  • id: 8762428
    {'degree': 8, 'field': [4881, -680, -1456, 240, 182, -40, 16, 0, 1], 'lmfdb_label': '199920.dt4', 'torsion': [2, 4]}
  • id: 8762430
    {'degree': 8, 'field': [5436, -372, 596, -486, 339, -118, 44, -4, 1], 'lmfdb_label': '199920.dt4', 'torsion': [8]}
  • id: 8762432
    {'degree': 16, 'field': [2466, 89736, 722036, -2003736, 2049818, -1545584, 1041984, -549208, 269123, -103464, 37096, -10008, 2578, -448, 84, -8, 1], 'lmfdb_label': '199920.dt4', 'torsion': [4, 4]}
  • id: 8762437
    {'degree': 16, 'field': [87368, -66704, 84934, -41418, 33541, -17344, 11254, -9368, 8730, -5234, 2270, -1000, 470, -168, 44, -8, 1], 'lmfdb_label': '199920.dt4', 'torsion': [12]}
  • id: 8762433
    {'degree': 16, 'field': [571250, 20200, -73868, 165000, -210014, 101216, 68824, -122456, 78627, -39848, 16400, -5368, 1562, -336, 68, -8, 1], 'lmfdb_label': '199920.dt4', 'torsion': [2, 8]}
  • id: 8762434
    {'degree': 16, 'field': [2827336, -4907168, 6283352, -2632056, 977206, 510308, -334638, 124528, -10863, -12992, 2154, 128, 100, -84, 32, -8, 1], 'lmfdb_label': '199920.dt4', 'torsion': [2, 8]}
  • id: 8762435
    {'degree': 16, 'field': [3467089924, 0, 7307323396, 0, 1309016065, 0, 99718752, 0, 2900940, 0, -51198, 0, -2240, 0, 16, 0, 1], 'lmfdb_label': '199920.dt4', 'torsion': [2, 6]}
  • id: 8762436
    {'degree': 16, 'field': [5072430841, 0, 470347268, 0, 72991996, 0, 1654956, 0, -265074, 0, -29556, 0, -884, 0, -28, 0, 1], 'lmfdb_label': '199920.dt4', 'torsion': [12]}
• 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: 4946510
    {'conductor': 199920, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '199920.dt4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4946511
    {'conductor': 199920, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '199920.dt4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4946512
    {'conductor': 199920, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '199920.dt4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4946513
    {'conductor': 199920, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '199920.dt4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4946514
    {'conductor': 199920, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '199920.dt4', '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: 2944195
    {'adelic_gens': [[785, 280, 420, 169], [7, 6, 946, 947], [543, 0, 0, 951], [1, 0, 8, 1], [48, 791, 567, 384], [945, 8, 944, 9], [120, 875, 497, 526], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '952.48.0.?', 'conductor': 199920, 'lmfdb_label': '199920.dt4', 'prime': 0}
  • id: 740791
    {'conductor': 199920, 'elladic_image': '8.12.0.16', 'lmfdb_label': '199920.dt4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 199920.dt does not appear in ec_padic