Elliptic curve data - 6720.c2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '6720bi', 'Clabel': '6720bi2', 'Cnumber': 2, 'abc_quality': 1.0964009209698897, 'absD': 374984769600000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, -1, 0, -25515001, -49598319815], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6720, 'degree': 430080, 'elladic_images': ['8.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7599875578878890171728697676', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2], 'jinv': [448487713888272974160064, 91549016015625], 'lmfdb_iso': '6720.c', 'lmfdb_label': '6720.c2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -6378750, 6202979352], 'min_quad_twist_disc': -8, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0-2.a.1.1', '12.12.0-2.a.1.1', '24.24.0-24.a.1.3', '28.12.0.a.1', '56.24.0-28.a.1.2', '84.24.0.?', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.0668403773279437077556376461', 'prec': 100}, 'szpiro_ratio': 7.123459628044274, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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': '0.0040059476257490786233522790528', 'prec': 110}, 'conductor': 6720, 'gens': [], 'heights': [], 'lmfdb_label': '6720.c2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.067173915118157601347276711424', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2091304721268368242509808056261648594', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-2915, 0, 1], [5833, 0, 1]], 'xcoord_integral_points': [-2917, -2915, 5833]}
• 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.c2'}
• ec_torsion_growth •

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

  
  
  • id: 352460
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '6720.c2', 'torsion': [2, 4]}
  • id: 352462
    {'degree': 4, 'field': [9, 0, 8, 0, 1], 'lmfdb_label': '6720.c2', 'torsion': [2, 4]}
  • id: 352461
    {'degree': 4, 'field': [49, 0, -28, 0, 1], 'lmfdb_label': '6720.c2', 'torsion': [2, 4]}
  • id: 352463
    {'degree': 8, 'field': [-48, 0, -1856, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '6720.c2', 'torsion': [2, 6]}
  • id: 352465
    {'degree': 16, 'field': [36, 0, -288, 0, 912, 0, -1200, 0, 604, 0, -80, 0, 72, 0, -8, 0, 1], 'lmfdb_label': '6720.c2', 'torsion': [2, 8]}
  • id: 352467
    {'degree': 16, 'field': [49, 0, 392, 0, 1120, 0, 1512, 0, 786, 0, -24, 0, -32, 0, 8, 0, 1], 'lmfdb_label': '6720.c2', 'torsion': [2, 8]}
  • id: 352464
    {'degree': 16, 'field': [256, 0, 0, 0, -16, 0, 0, 0, -15, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '6720.c2', 'torsion': [4, 4]}
  • id: 352466
    {'degree': 16, 'field': [46656, 0, -435456, 0, 1057536, 0, -483840, 0, 105552, 0, -6048, 0, -192, 0, 0, 0, 1], 'lmfdb_label': '6720.c2', '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: 136586
    {'conductor': 6720, 'conductor_valuation': 6, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '6720.c2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 136587
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '6720.c2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 136588
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '6720.c2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 136589
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6720.c2', 'prime': 7, '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: 1708300
    {'adelic_gens': [[45, 4, 8, 11], [73, 2, 0, 1], [1, 4, 0, 1], [1, 0, 4, 1], [3, 2, 110, 167], [81, 166, 2, 1], [165, 4, 164, 5]], 'adelic_image': '168.48.0.?', 'conductor': 6720, 'lmfdb_label': '6720.c2', 'prime': 0}
  • id: 33168
    {'conductor': 6720, 'elladic_image': '8.12.0.1', 'lmfdb_label': '6720.c2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 6720.c does not appear in ec_padic