Elliptic curve data - 398820.k4

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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': '398820k', 'Clabel': '398820k2', 'Cnumber': 2, 'abc_quality': 0.9093994819073755, 'absD': 297869959895328000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 23460, 'ainvs': [0, -1, 0, 132844, -18543000], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 398820, 'degree': 4644864, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0393219067885505371762263757', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [41957807024, 48205125], 'lmfdb_iso': '398820.k', 'lmfdb_label': '398820.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 460, -3612], 'min_quad_twist_disc': 17, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '20.6.0.a.1', '51.8.0-3.a.1.2', '60.24.0.o.1', '102.24.0.?', '276.24.0.?', '1020.48.0.?', '1380.48.1.?', '4692.48.0.?', '23460.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.5612722814559244403689924095', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1445], [3, 4, 26588], [5, 6, 79764], [17, 146, 1380], [23, 24, 17340]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.16061711438714562410663765246', 'prec': 103}, 'szpiro_ratio': 3.644806164032439, '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, 4, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0], 'aplist': [0, -1, -1, 4, 0, 2, 0, 2, 1, -6, 4, -8, -6, 8, 12, -6, -6, 10, 8, 6, -2, 10, -12, 6, -8], 'class_deg': 6, 'class_size': 4, 'conductor': 398820, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '398820.k', 'trace_hash': 388472360801214827}
• 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': '0.016930410883557564845794023587', 'prec': 107}, 'conductor': 398820, 'gens': [[103966, 47060182, 21]], 'heights': [{'__RealLiteral__': 0, 'data': '8.5612722814559244403689924095', 'prec': 100}], 'lmfdb_label': '398820.k4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16538090023957409726857703208', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.4952255026197590354830860402773842894', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[125, 0, 1]], 'xcoord_integral_points': [125]}
• lmfdb_label 398820.k4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16450406
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '398820.k4', 'torsion': [6]}
  • id: 16450405
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '398820.k4', 'torsion': [2, 2]}
  • id: 16450407
    {'degree': 4, 'field': [-1445, 0, 272, 0, 1], 'lmfdb_label': '398820.k4', 'torsion': [4]}
  • id: 16450408
    {'degree': 4, 'field': [86, -2, 3, -2, 1], 'lmfdb_label': '398820.k4', 'torsion': [2, 6]}
  • id: 16450409
    {'degree': 6, 'field': [10111, -913, -2, 173, 8, -3, 1], 'lmfdb_label': '398820.k4', 'torsion': [6]}
  • id: 16450412
    {'degree': 8, 'field': [5716, 3364, -3134, -476, 279, -52, 22, -4, 1], 'lmfdb_label': '398820.k4', 'torsion': [12]}
  • id: 16450410
    {'degree': 8, 'field': [17892900, 0, -462600, 0, 9420, 0, -160, 0, 1], 'lmfdb_label': '398820.k4', 'torsion': [2, 4]}
  • id: 16450411
    {'degree': 8, 'field': [56177881, -260950, 1573818, -29410, 25823, -170, 208, 0, 1], 'lmfdb_label': '398820.k4', 'torsion': [2, 4]}
  • id: 16450413
    {'degree': 12, 'field': [9025, 31065, 42863, 24852, -1767, -4047, 2284, -1125, 177, -42, 17, -3, 1], 'lmfdb_label': '398820.k4', 'torsion': [3, 6]}
  • id: 16450414
    {'degree': 12, 'field': [121126461, -78922716, 5394235, 6720118, -1331718, -18936, 52127, -1506, -138, 148, 55, -6, 1], 'lmfdb_label': '398820.k4', 'torsion': [2, 6]}
  • id: 16450416
    {'degree': 16, 'field': [4885496, -13163920, 10571304, -694720, -950880, -1134840, 170716, 363700, 26489, -20460, -10764, 860, 1350, -60, -56, 0, 1], 'lmfdb_label': '398820.k4', 'torsion': [2, 12]}
  • id: 16450417
    {'degree': 16, 'field': [810543376, -78303232, 111855328, -69337024, 40740236, -8676064, 5267892, -2161984, 713609, -141200, 55080, -15992, 3818, -560, 100, -8, 1], 'lmfdb_label': '398820.k4', 'torsion': [2, 12]}
  • id: 16450415
    {'degree': 16, 'field': [31269138189813, 3826223686044, -3386680524450, -126426636864, 289893070806, -253662597600, 56353695870, -12743653956, 1631037058, -269188148, 9915026, 1193632, -162002, 10112, -70, -4, 1], 'lmfdb_label': '398820.k4', 'torsion': [8]}
  • id: 16450418
    {'degree': 18, 'field': [-2774006024, 2338914432, 1791564744, -2336861456, 80325360, 579085728, -124278438, -25319652, 2484372, -1320255, 1437087, -244452, 38322, -7422, 990, -136, -6, -3, 1], 'lmfdb_label': '398820.k4', 'torsion': [18]}
• 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: 9865103
    {'conductor': 398820, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '398820.k4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 9865104
    {'conductor': 398820, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '398820.k4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9865105
    {'conductor': 398820, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '398820.k4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9865106
    {'conductor': 398820, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '398820.k4', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9865107
    {'conductor': 398820, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '398820.k4', 'prime': 23, '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: 4137710
    {'adelic_gens': [[1, 6, 6, 37], [11, 2, 23410, 23451], [1, 12, 0, 1], [19330, 22083, 7701, 4132], [12241, 17952, 306, 13873], [13686, 15997, 13685, 21506], [11969, 6902, 21624, 1], [6899, 0, 0, 23459], [1, 0, 12, 1], [23449, 12, 23448, 13]], 'adelic_image': '23460.96.1.?', 'conductor': 398820, 'lmfdb_label': '398820.k4', 'prime': 0}
  • id: 1356325
    {'conductor': 398820, 'elladic_image': '2.3.0.1', 'lmfdb_label': '398820.k4', 'modell_image': '2B', 'prime': 2}
  • id: 1356326
    {'conductor': 398820, 'elladic_image': '3.4.0.1', 'lmfdb_label': '398820.k4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 398820.k does not appear in ec_padic