Elliptic curve data - 6720.c4

Formats: - HTML - YAML - JSON - 2023-03-22T09:03:07.944558

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '6720bi', 'Clabel': '6720bi1', 'Cnumber': 1, 'absD': 6405501887389080000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, -1, 0, -1600156, -768989294], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6720, 'degree': 215040, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4134139676079163624642537069', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [7079962908642659949376, 100085966990454375], 'lmfdb_iso': '6720.c', 'lmfdb_label': '6720.c4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -6400625, -6158314977], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['1.1.0.1', '2.3.0.1', '4.6.0.1', '8.12.0.8', '24.24.0.191', '28.12.0.10', '56.24.0.?', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.0668403773279437077556376462', 'prec': 100}, '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, -1, 0, 1, 0, -4, 0, 6, 0, 1, 0, 6, 0, -4, 0], 'aplist': [0, -1, -1, -1, -4, 6, 6, -4, 4, 2, -8, -6, 6, 8, 0, -6, -4, -10, 8, -12, -14, 16, -12, 14, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 6720, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '6720.c', 'trace_hash': 684933320784037904}
• 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': '0.0080118952514981572467045581056', 'prec': 110}, 'conductor': 6720, 'gens': [], 'heights': [], 'lmfdb_label': '6720.c4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.13434783023631520269455342285', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2091304721268368242509808056261648594', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[1459, 0, 1]], 'xcoord_integral_points': [1459]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [0, 0], '7': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '6720.c4'}
• ec_torsion_growth •

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

  
  
  • id: 352447
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [4]}
  • id: 352446
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [2, 2]}
  • id: 352448
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [4]}
  • id: 352449
    {'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [2, 4]}
  • id: 352453
    {'degree': 8, 'field': [-48, 0, -1856, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [6]}
  • id: 352450
    {'degree': 8, 'field': [1, 0, 4, 0, -1, 0, 4, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [2, 4]}
  • id: 352452
    {'degree': 8, 'field': [49, 0, 14, 0, -3, 0, 2, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [8]}
  • id: 352451
    {'degree': 8, 'field': [676, 0, -976, 0, 348, 0, -40, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [8]}
  • id: 352455
    {'degree': 16, 'field': [-311, -1492, 8872, 140, -27376, 8024, 29748, -11644, -14047, 6568, 2928, -1700, -202, 196, -8, -8, 1], 'lmfdb_label': '6720.c4', 'torsion': [2, 8]}
  • id: 352454
    {'degree': 16, 'field': [16, 0, 0, 0, -24, 0, 0, 0, 73, 0, 0, 0, 15, 0, 0, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [4, 4]}
  • id: 352456
    {'degree': 16, 'field': [49, 196, 812, -280, -152, 1212, 440, -244, 967, 148, 200, 132, 40, -8, 20, -4, 1], 'lmfdb_label': '6720.c4', 'torsion': [2, 8]}
  • id: 352459
    {'degree': 16, 'field': [225, 0, -900, 0, 900, 0, 268, 0, -358, 0, -68, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [12]}
  • id: 352458
    {'degree': 16, 'field': [900, 0, -175536, 0, 94320, 0, -23048, 0, 8492, 0, -2480, 0, 340, 0, -28, 0, 1], 'lmfdb_label': '6720.c4', 'torsion': [12]}
  • id: 352457
    {'degree': 16, 'field': [693889, 0, -72082136, 0, 2756740, 0, 1120728, 0, -98490, 0, -18312, 0, 1540, 0, -56, 0, 1], 'lmfdb_label': '6720.c4', '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: 136582
    {'conductor': 6720, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '6720.c4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 136583
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 28, 'j_denominator_valuation': 28, 'kodaira_symbol': 32, 'lmfdb_label': '6720.c4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 136584
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6720.c4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 136585
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6720.c4', 'prime': 7, '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: 1708302
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [104, 13, 101, 72], [7, 6, 162, 163], [161, 8, 160, 9], [113, 8, 116, 33], [13, 18, 142, 61], [124, 1, 167, 6], [1, 4, 4, 17]], 'adelic_image': '168.48.0.?', 'conductor': 6720, 'lmfdb_label': '6720.c4', 'prime': 0}
  • id: 33170
    {'conductor': 6720, 'elladic_image': '8.12.0.8', 'lmfdb_label': '6720.c4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6720.c does not appear in ec_padic