Elliptic curve data - 330330.bg3

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '330330bg', 'Clabel': '330330bg6', 'Cnumber': 6, 'abc_quality': 1.0265231881197245, 'absD': 43553576659081138650, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 240240, 'ainvs': [1, 1, 0, -70787, 317572479], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 7, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 330330, 'degree': 10485760, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4473864831327349181273850948', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-22143063655441, 24584858584650], 'lmfdb_iso': '330330.bg', 'lmfdb_label': '330330.bg3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -585, -238863], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '40.24.0.ca.1', '44.12.0-4.c.1.1', '88.24.0.?', '104.24.0.?', '336.24.0.?', '440.48.0.?', '520.48.0.?', '1144.48.0.?', '1680.48.0.?', '3696.48.0.?', '4368.48.0.?', '5720.96.0.?', '18480.96.0.?', '21840.96.1.?', '48048.96.0.?', '240240.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 10, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '4.0744541952506647082407767123', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1573], [3, 4, 110110], [5, 6, 66066], [7, 8, 47190], [11, 62, 2730], [13, 14, 25410]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2484388467335496460964133058', 'prec': 100}, 'szpiro_ratio': 4.145136681548175, '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, -1, 1, 1, 1, 1, -1, 1, -1, 0, -1, -1, -1, -1, 1, -2, -1, -4, 1], 'aplist': [-1, -1, 1, 1, 0, -1, -2, -4, 0, -6, -8, 6, -10, -4, 0, 6, 4, -6, -4, 0, 6, 0, -12, -6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 330330, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '330330.bg', 'trace_hash': 1874070525972424535}
• 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': '0.0074856085166496886393718721687', 'prec': 110}, 'conductor': 330330, 'gens': [[765, 26298, 1], [-117, 18066, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8914200708025754155021986567', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.2993065580610044871132583446', 'prec': 100}], 'lmfdb_label': '330330.bg3', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.16356096776126276930984791230', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.662746740386172978804529583329532052', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-2869, 2869, 2]], 'xcoord_integral_points': [-117, 275, 765, 1733, 8213]}
• lmfdb_label 330330.bg3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13849511
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [4]}
  • id: 13849510
    {'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 2]}
  • id: 13849512
    {'degree': 2, 'field': [286, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [4]}
  • id: 13849515
    {'degree': 4, 'field': [16, 0, -3, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [8]}
  • id: 13849513
    {'degree': 4, 'field': [1369, 0, 30, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 4]}
  • id: 13849514
    {'degree': 4, 'field': [14161, 0, -282, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [8]}
  • id: 13849519
    {'degree': 8, 'field': [-11244288, 0, 2917552, 0, -11616, 0, 0, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [6]}
  • id: 13849517
    {'degree': 8, 'field': [10169, -3436, 3282, 296, -117, -40, 18, -4, 1], 'lmfdb_label': '330330.bg3', 'torsion': [8]}
  • id: 13849516
    {'degree': 8, 'field': [427131, 20692, -19338, -2720, 1391, -40, 18, -4, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 4]}
  • id: 13849518
    {'degree': 8, 'field': [592900, 0, 69740, 0, 3941, 0, 98, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 8]}
  • id: 13849521
    {'degree': 16, 'field': [881721, 0, 1684780, 0, 974830, 0, 135200, 0, -12049, 0, -520, 0, 290, 0, -20, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 8]}
  • id: 13849525
    {'degree': 16, 'field': [695324161, 0, 461952008, 0, 18963196, 0, -24900264, 0, 2054406, 0, -74376, 0, 3196, 0, -88, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [12]}
  • id: 13849523
    {'degree': 16, 'field': [63980480116, -202933358880, 206168355568, -29968357440, 22229658488, -6778430400, -831850464, -2419200, 66189065, -7505400, 1705476, -68880, 23558, -840, 148, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [16]}
  • id: 13849520
    {'degree': 16, 'field': [182440891161, 0, 16947877420, 0, 1674801166, 0, 44164640, 0, 2040911, 0, 11960, 0, 2786, 0, -20, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [4, 4]}
  • id: 13849526
    {'degree': 16, 'field': [614825746662400, 0, 78885271088000, 0, 3969892201600, 0, 109797201696, 0, 1872582192, 0, 20543016, 0, 142636, 0, 572, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [12]}
  • id: 13849524
    {'degree': 16, 'field': [7108297506918400, 0, -288177213833600, 0, 4812385052800, 0, 9114140256, 0, 708347952, 0, 2231736, 0, -60164, 0, 52, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [2, 6]}
  • id: 13849522
    {'degree': 16, 'field': [21873460788097681, 0, 107168653888072, 0, -1442016433912, 0, -184716506496, 0, -195637570, 0, 9424824, 0, 62408, 0, -608, 0, 1], 'lmfdb_label': '330330.bg3', 'torsion': [16]}
• 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: 8173518
    {'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '330330.bg3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 8173519
    {'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '330330.bg3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8173520
    {'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '330330.bg3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8173521
    {'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '330330.bg3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 8173522
    {'conductor': 330330, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '330330.bg3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8173523
    {'conductor': 330330, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '330330.bg3', 'prime': 13, '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: 3730793
    {'adelic_gens': [[1, 16, 0, 1], [5, 4, 240236, 240237], [15, 2, 240142, 240227], [171601, 218416, 40568, 65649], [215678, 223861, 177529, 32770], [43679, 0, 0, 240239], [80081, 218416, 29128, 65649], [114676, 223861, 98439, 32770], [1, 0, 16, 1], [120968, 43681, 124399, 152890], [91741, 218416, 12848, 130725], [240225, 16, 240224, 17]], 'adelic_image': '240240.192.1.?', 'conductor': 330330, 'lmfdb_label': '330330.bg3', 'prime': 0}
  • id: 1150047
    {'conductor': 330330, 'elladic_image': '8.12.0.5', 'lmfdb_label': '330330.bg3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 330330.bg does not appear in ec_padic