Elliptic curve data - 327600.kl2

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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': '327600kl', 'Clabel': '327600kl4', 'Cnumber': 4, 'abc_quality': 0.8969869824853101, 'absD': 2730513240000000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 10920, 'ainvs': [0, 0, 0, -840675, -285830750], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 327600, 'degree': 4718592, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3026709384850497958025553970', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 271, 'isogeny_degrees': [1, 2, 4], 'jinv': [1408317602329, 58524375], 'lmfdb_iso': '327600.kl', 'lmfdb_label': '327600.kl2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -234, -1343], 'min_quad_twist_disc': 60, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '20.12.0-4.c.1.1', '156.12.0.?', '168.12.0.?', '728.12.0.?', '780.24.0.?', '840.24.0.?', '2184.24.0.?', '3640.24.0.?', '10920.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 15, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '3.1683864138517685733674374205', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 2925], [3, 8, 36400], [5, 18, 13104], [7, 8, 46800], [13, 14, 25200]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.25549865737399945338732099047', 'prec': 103}, 'szpiro_ratio': 4.137114303677414, '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, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, 0, 1, 0, -1, 2, -4, -8, -6, 0, -2, -6, -8, -4, -6, -4, -10, 12, -4, 6, 8, 0, -6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 327600, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '327600.kl', 'trace_hash': 456814712891706409}
• 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': '0.0099982832375604495222961288306', 'prec': 110}, 'conductor': 327600, 'gens': [[-505, 3150, 1], [1070, 6300, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0953719991873817393236973535', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.9325192217110538570230132916', 'prec': 100}], 'lmfdb_label': '327600.kl2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.15807203590526794803710918572', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '16.026665311108477254319462023474767952', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-610, 0, 1]], 'xcoord_integral_points': [-610, -561, -529, -505, 1070, 1154, 2015, 5015]}
• lmfdb_label 327600.kl2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13756452
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '327600.kl2', 'torsion': [2, 2]}
  • id: 13756454
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '327600.kl2', 'torsion': [4]}
  • id: 13756453
    {'degree': 2, 'field': [49, -1, 1], 'lmfdb_label': '327600.kl2', 'torsion': [4]}
  • id: 13756455
    {'degree': 4, 'field': [121, 0, -17, 0, 1], 'lmfdb_label': '327600.kl2', 'torsion': [2, 4]}
  • id: 13756459
    {'degree': 8, 'field': [-1366875, 0, 0, 0, 4050, 0, -55, 0, 1], 'lmfdb_label': '327600.kl2', 'torsion': [6]}
  • id: 13756458
    {'degree': 8, 'field': [2830, -910, 1189, -544, 238, 38, -8, -4, 1], 'lmfdb_label': '327600.kl2', 'torsion': [8]}
  • id: 13756456
    {'degree': 8, 'field': [120745, 5620, -6316, 1396, -707, 8, 2, -4, 1], 'lmfdb_label': '327600.kl2', 'torsion': [2, 4]}
  • id: 13756457
    {'degree': 8, 'field': [389376, 0, -81120, 0, 15028, 0, -130, 0, 1], 'lmfdb_label': '327600.kl2', 'torsion': [8]}
  • id: 13756465
    {'degree': 16, 'field': [1238769, 0, 24113390, 0, -4198313, 0, 542076, 0, 40505, 0, 15904, 0, 1695, 0, 62, 0, 1], 'lmfdb_label': '327600.kl2', 'torsion': [12]}
  • id: 13756461
    {'degree': 16, 'field': [54264820, -106264140, 99823046, -49648410, 15099391, -3510132, 931607, -492396, 205939, -52926, 12368, -1428, 769, -162, 59, -6, 1], 'lmfdb_label': '327600.kl2', 'torsion': [2, 8]}
  • id: 13756463
    {'degree': 16, 'field': [1207493001, 0, -26914120857, 0, 1127658753, 0, -11107044, 0, -5117580, 0, -68094, 0, 4588, 0, 133, 0, 1], 'lmfdb_label': '327600.kl2', 'torsion': [2, 6]}
  • id: 13756460
    {'degree': 16, 'field': [14579355025, 0, 1556835240, 0, -146532614, 0, -7375068, 0, 738699, 0, 4356, 0, -1346, 0, 12, 0, 1], 'lmfdb_label': '327600.kl2', 'torsion': [4, 4]}
  • id: 13756464
    {'degree': 16, 'field': [38372108544, 0, 13095793728, 0, 2039888160, 0, 184100496, 0, 10261725, 0, 353229, 0, 7378, 0, 100, 0, 1], 'lmfdb_label': '327600.kl2', 'torsion': [12]}
  • id: 13756462
    {'degree': 16, 'field': [338765905296, 0, 58202748240, 0, 6578934076, 0, 214998420, 0, 13092261, 0, 196040, 0, 18291, 0, 0, 0, 1], 'lmfdb_label': '327600.kl2', '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: 8112244
    {'conductor': 327600, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '327600.kl2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8112245
    {'conductor': 327600, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '327600.kl2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8112246
    {'conductor': 327600, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '327600.kl2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 8112247
    {'conductor': 327600, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '327600.kl2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8112248
    {'conductor': 327600, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '327600.kl2', '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: 3715930
    {'adelic_gens': [[2183, 10912, 8732, 10887], [1, 0, 8, 1], [10913, 8, 10912, 9], [1, 8, 0, 1], [1, 4, 4, 17], [5884, 1, 9263, 6], [4099, 4098, 1378, 6835], [7, 6, 10914, 10915], [3632, 10917, 3635, 10918], [9552, 4087, 9527, 9480], [7801, 8, 9364, 33]], 'adelic_image': '10920.48.0.?', 'conductor': 327600, 'lmfdb_label': '327600.kl2', 'prime': 0}
  • id: 1142920
    {'conductor': 327600, 'elladic_image': '4.6.0.1', 'lmfdb_label': '327600.kl2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 327600.kl does not appear in ec_padic