Elliptic curve data - 323400.r5

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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': '323400r', 'Clabel': '323400r1', 'Cnumber': 1, 'abc_quality': 1.0588833402519044, 'absD': 1137426855468750000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 6160, 'ainvs': [0, -1, 0, -214783, -63966188], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 323400, 'degree': 4718592, 'elladic_images': ['8.24.0.92'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1599149809608857573615076655', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-37256083456, 38671875], 'lmfdb_iso': '323400.r', 'lmfdb_label': '323400.r5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -175, 1552], 'min_quad_twist_disc': -35, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.ba.1', '22.6.0.a.1', '44.12.0.g.1', '80.48.0.?', '88.48.0.?', '112.48.0.?', '140.12.0.?', '280.48.0.?', '560.96.0.?', '880.96.1.?', '1232.96.0.?', '1540.24.0.?', '3080.96.0.?', '6160.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 13475], [3, 4, 107800], [5, 18, 12936], [7, 26, 6600], [11, 12, 29400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.15119189002953048103604092001', 'prec': 103}, 'szpiro_ratio': 3.8996213963824857, '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, 0, 0, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, -1, 0, 0, -1, -2, -6, 4, 0, 6, 8, -6, -10, 4, -8, 10, 12, -6, 4, 0, -14, 0, 4, 6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 323400, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '323400.r', 'trace_hash': 181961398656165144}
• 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': '0.013302145221362310458231820711', 'prec': 107}, 'conductor': 323400, 'gens': [], 'heights': [], 'lmfdb_label': '323400.r5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10647223291449922601244321795', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.85177786331599380809954574361196394396', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[572, 0, 1]], 'xcoord_integral_points': [572]}
• lmfdb_label 323400.r5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13586459
    {'degree': 2, 'field': [-96, -1, 1], 'lmfdb_label': '323400.r5', 'torsion': [4]}
  • id: 13586458
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '323400.r5', 'torsion': [2, 2]}
  • id: 13586460
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '323400.r5', 'torsion': [4]}
  • id: 13586461
    {'degree': 4, 'field': [36, 0, 23, 0, 1], 'lmfdb_label': '323400.r5', 'torsion': [2, 4]}
  • id: 13586462
    {'degree': 4, 'field': [81, 0, -17, 0, 1], 'lmfdb_label': '323400.r5', 'torsion': [8]}
  • id: 13586463
    {'degree': 4, 'field': [389, 4, -3, -2, 1], 'lmfdb_label': '323400.r5', 'torsion': [8]}
  • id: 13586467
    {'degree': 8, 'field': [-4501875, 0, -336140, 0, -7350, 0, 0, 0, 1], 'lmfdb_label': '323400.r5', 'torsion': [6]}
  • id: 13586465
    {'degree': 8, 'field': [1390, 5080, -4696, -734, 283, 98, -28, -4, 1], 'lmfdb_label': '323400.r5', 'torsion': [8]}
  • id: 13586466
    {'degree': 8, 'field': [17460, 3300, -2914, -750, 321, 62, -16, -4, 1], 'lmfdb_label': '323400.r5', 'torsion': [2, 8]}
  • id: 13586464
    {'degree': 8, 'field': [1752976, 0, -129920, 0, 7548, 0, -140, 0, 1], 'lmfdb_label': '323400.r5', 'torsion': [2, 4]}
  • id: 13586468
    {'degree': 16, 'field': [1932100, 0, 38861280, 0, 30296596, 0, 4270212, 0, 530349, 0, 40716, 0, 2134, 0, 72, 0, 1], 'lmfdb_label': '323400.r5', 'torsion': [4, 8]}
  • id: 13586472
    {'degree': 16, 'field': [4312746, -70282548, 330064146, -2023577202, -821531598, -224733240, 43511122, 15376742, 2281731, -367816, -93302, -1230, -758, 686, -66, -4, 1], 'lmfdb_label': '323400.r5', 'torsion': [12]}
  • id: 13586470
    {'degree': 16, 'field': [5013121, 0, 17352840, 0, 12254736, 0, 4058880, 0, 816066, 0, 106120, 0, 6976, 0, 160, 0, 1], 'lmfdb_label': '323400.r5', 'torsion': [16]}
  • id: 13586469
    {'degree': 16, 'field': [325794625, 494774700, 79504740, -38300400, 80240576, -4770420, -254328, 112320, 810069, -38220, 12036, -1080, 2114, -120, 12, 0, 1], 'lmfdb_label': '323400.r5', 'torsion': [16]}
  • id: 13586473
    {'degree': 16, 'field': [331174461, 172310952, -180525136, 9085880, 14646650, -25398776, 12534124, -3725408, 1246035, -235800, 74220, -16112, 3838, -560, 100, -8, 1], 'lmfdb_label': '323400.r5', 'torsion': [12]}
  • id: 13586471
    {'degree': 16, 'field': [13842781384161, -2624226894936, 2819244410468, -396414144952, 214225052426, -19417510616, 6797210980, -274574576, 63858999, 3348288, -827820, 85792, -13874, -224, 52, -8, 1], 'lmfdb_label': '323400.r5', '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: 8002902
    {'conductor': 323400, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '323400.r5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8002903
    {'conductor': 323400, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '323400.r5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8002904
    {'conductor': 323400, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '323400.r5', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 8002905
    {'conductor': 323400, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '323400.r5', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8002906
    {'conductor': 323400, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '323400.r5', 'prime': 11, '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: 3690196
    {'adelic_gens': [[879, 0, 0, 6159], [1, 16, 0, 1], [15, 2, 6062, 6147], [5, 4, 6156, 6157], [1688, 3521, 5999, 890], [5405, 896, 4074, 4859], [1, 0, 16, 1], [2463, 5264, 3864, 5151], [6145, 16, 6144, 17], [1, 896, 1540, 1541]], 'adelic_image': '6160.192.1.?', 'conductor': 323400, 'lmfdb_label': '323400.r5', 'prime': 0}
  • id: 1129405
    {'conductor': 323400, 'elladic_image': '8.24.0.92', 'lmfdb_label': '323400.r5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 323400.r does not appear in ec_padic