Elliptic curve data - 327600.hl6

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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': '327600hl', 'Clabel': '327600hl1', 'Cnumber': 1, 'abc_quality': 1.0143277708927247, 'absD': 4794047424006750000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 21840, 'ainvs': [0, 0, 0, 162150, -102302125], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 327600, 'degree': 4718592, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2655930564397923409719711639', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 193, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [2587063175168, 26304786963], 'lmfdb_iso': '327600.hl', 'lmfdb_label': '327600.hl6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 721, -30552], 'min_quad_twist_disc': 60, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '6.6.0.a.1', '8.12.0.n.1', '12.12.0.g.1', '20.12.0-4.c.1.1', '24.24.0.bh.1', '40.24.0-8.n.1.10', '60.24.0-12.g.1.1', '104.24.0.?', '112.24.0.?', '120.48.0.?', '312.48.0.?', '336.48.0.?', '520.48.0.?', '560.48.0.?', '1456.48.0.?', '1560.96.0.?', '1680.96.0.?', '4368.96.1.?', '7280.96.0.?', '21840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4045525809826284566728542941', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 6, 36400], [5, 14, 13104], [7, 8, 46800], [13, 14, 25200]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.68051889570203887150155817167', 'prec': 103}, 'szpiro_ratio': 3.9694345845173977, '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, -4, 0, -1, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 0, 1, -4, -1, -6, -4, 0, -6, 0, -6, 6, 4, 0, -2, 4, -2, 4, 0, 6, -8, -12, -10, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 327600, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '327600.hl', 'trace_hash': 1682542305695705094}
• 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': '0.010767896554476433345095083322', 'prec': 107}, 'conductor': 327600, 'gens': [[2455, 122850, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4045525809826284566728542941', 'prec': 100}], 'lmfdb_label': '327600.hl6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12021246283857271348101966544', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.4030311982782596822168482124612134367', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[355, 0, 1]], 'xcoord_integral_points': [355, 2455]}
• lmfdb_label 327600.hl6 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13754488
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '327600.hl6', 'torsion': [4]}
  • id: 13754487
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '327600.hl6', 'torsion': [2, 2]}
  • id: 13754489
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '327600.hl6', 'torsion': [4]}
  • id: 13754490
    {'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '327600.hl6', 'torsion': [2, 4]}
  • id: 13754491
    {'degree': 4, 'field': [36, 0, -27, 0, 1], 'lmfdb_label': '327600.hl6', 'torsion': [8]}
  • id: 13754492
    {'degree': 4, 'field': [49, 0, -1, 0, 1], 'lmfdb_label': '327600.hl6', 'torsion': [8]}
  • id: 13754496
    {'degree': 8, 'field': [-8449, -5912, 682, 1246, 980, 68, 20, -2, 1], 'lmfdb_label': '327600.hl6', 'torsion': [6]}
  • id: 13754494
    {'degree': 8, 'field': [6, -24, 36, -30, 31, -22, 12, -4, 1], 'lmfdb_label': '327600.hl6', 'torsion': [8]}
  • id: 13754495
    {'degree': 8, 'field': [16, 0, -36, 0, 77, 0, -9, 0, 1], 'lmfdb_label': '327600.hl6', 'torsion': [2, 8]}
  • id: 13754493
    {'degree': 8, 'field': [321556, -44456, 46958, -5078, 2725, -226, 80, -4, 1], 'lmfdb_label': '327600.hl6', 'torsion': [2, 4]}
  • id: 13754498
    {'degree': 16, 'field': [1, -2, 2, -4, -22, 2, 48, 114, 163, 114, 48, 2, -22, -4, 2, -2, 1], 'lmfdb_label': '327600.hl6', 'torsion': [2, 8]}
  • id: 13754502
    {'degree': 16, 'field': [9, 0, 0, 0, 1116, 0, -14640, 0, -11490, 0, -480, 0, -272, 0, 80, 0, 1], 'lmfdb_label': '327600.hl6', 'torsion': [12]}
  • id: 13754503
    {'degree': 16, 'field': [59049, 0, 0, 0, -2916, 0, 11880, 0, 3390, 0, -2160, 0, 912, 0, 40, 0, 1], 'lmfdb_label': '327600.hl6', 'torsion': [12]}
  • id: 13754501
    {'degree': 16, 'field': [3490711, 474712, 2096906, -346458, -2012458, -1271410, -197980, 321370, 410613, 201646, 35056, -838, 354, 362, 8, -4, 1], 'lmfdb_label': '327600.hl6', 'torsion': [2, 6]}
  • id: 13754497
    {'degree': 16, 'field': [260305956, 0, -46753920, 0, -3039900, 0, 600348, 0, 124813, 0, -1100, 0, -474, 0, -8, 0, 1], 'lmfdb_label': '327600.hl6', 'torsion': [4, 4]}
  • id: 13754500
    {'degree': 16, 'field': [567117932689, -148640295776, 161242827200, -25557361844, 13675822220, -1123167828, 454155008, -72622236, 23578009, -3784308, 928796, -97100, 18974, -1316, 208, -8, 1], 'lmfdb_label': '327600.hl6', 'torsion': [16]}
  • id: 13754499
    {'degree': 16, 'field': [3855636780394, 177189607168, -200726838312, 48794931080, -28704875542, 5185490268, -1753534268, 16140412, 2766699, -4767368, 1181464, -118212, 14606, 2324, -312, -8, 1], 'lmfdb_label': '327600.hl6', '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: 8111294
    {'conductor': 327600, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '327600.hl6', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 8111295
    {'conductor': 327600, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '327600.hl6', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8111296
    {'conductor': 327600, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '327600.hl6', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8111297
    {'conductor': 327600, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '327600.hl6', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 8111298
    {'conductor': 327600, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '327600.hl6', 'prime': 13, '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: 3715741
    {'adelic_gens': [[4899, 8720, 10150, 9589], [7264, 21835, 45, 14], [1, 16, 0, 1], [21825, 16, 21824, 17], [4381, 13120, 3440, 8421], [15, 2, 21742, 21827], [18721, 13120, 14360, 17601], [1, 0, 16, 1], [1, 13120, 5460, 5461], [5, 4, 21836, 21837], [13103, 0, 0, 21839]], 'adelic_image': '21840.192.1.?', 'conductor': 327600, 'lmfdb_label': '327600.hl6', 'prime': 0}
  • id: 1142722
    {'conductor': 327600, 'elladic_image': '8.12.0.5', 'lmfdb_label': '327600.hl6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 327600.hl does not appear in ec_padic