Elliptic curve data - 6720.c3

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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': '6720bi', 'Clabel': '6720bi4', 'Cnumber': 4, 'abc_quality': 1.0644623952717098, 'absD': 26254935000000000000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, -1, 0, -25427521, -49955395679], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6720, 'degree': 860160, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1065611481678616718814858284', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [-55486311952875723077768, 801237030029296875], 'lmfdb_iso': '6720.c', 'lmfdb_label': '6720.c3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -6356880, 6247602900], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '12.12.0-4.c.1.1', '24.24.0-24.v.1.4', '56.24.0-56.ba.1.3', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3], [3, 4, 2240], [5, 6, 1344], [7, 8, 320]], 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2401271724679300351099456766', 'prec': 100}, 'szpiro_ratio': 7.125087156542699, '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': '0.0020029738128745393116761395264', 'prec': 110}, 'conductor': 6720, 'gens': [], 'heights': [], 'lmfdb_label': '6720.c3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.033586957559078800673638355712', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2091304721268368242509808056261648594', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[5831, 0, 1]], 'xcoord_integral_points': [5831]}
• 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.c3'}
• ec_torsion_growth •

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

  
  
  • id: 352483
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [4]}
  • id: 352484
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [4]}
  • id: 352482
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [2, 2]}
  • id: 352485
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [2, 4]}
  • id: 352489
    {'degree': 8, 'field': [-48, 0, -1856, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [6]}
  • id: 352486
    {'degree': 8, 'field': [36, 0, 0, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [2, 4]}
  • id: 352488
    {'degree': 8, 'field': [57, -12, -20, -4, 40, -12, 4, -4, 1], 'lmfdb_label': '6720.c3', 'torsion': [8]}
  • id: 352487
    {'degree': 8, 'field': [1089, 0, -828, 0, 258, 0, -36, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [8]}
  • id: 352490
    {'degree': 16, 'field': [81, 0, -324, 0, 648, 0, -864, 0, 711, 0, -288, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [4, 4]}
  • id: 352495
    {'degree': 16, 'field': [196, 0, 784, 0, 784, 0, 312, 0, 396, 0, -48, 0, 4, 0, 4, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [12]}
  • id: 352492
    {'degree': 16, 'field': [225, -540, 972, -1236, 1828, -2208, 1920, -892, 149, -112, 260, -244, 162, -84, 32, -8, 1], 'lmfdb_label': '6720.c3', 'torsion': [2, 8]}
  • id: 352493
    {'degree': 16, 'field': [2025, 0, -1236, 0, -1220, 0, 2652, 0, 1602, 0, 140, 0, 60, 0, 12, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [2, 6]}
  • id: 352494
    {'degree': 16, 'field': [65536, 0, -131072, 0, -52736, 0, 37376, 0, -44155, 0, 2336, 0, -206, 0, -32, 0, 1], 'lmfdb_label': '6720.c3', 'torsion': [12]}
  • id: 352491
    {'degree': 16, 'field': [810000, 0, 907200, 0, 387504, 0, 72576, 0, 5409, 0, 504, 0, 108, 0, 0, 0, 1], 'lmfdb_label': '6720.c3', '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: 136594
    {'conductor': 6720, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '6720.c3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 136595
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '6720.c3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 136596
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '6720.c3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 136597
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6720.c3', '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: 1708301
    {'adelic_gens': [[73, 8, 124, 33], [143, 144, 50, 137], [144, 55, 29, 42], [1, 0, 8, 1], [161, 8, 160, 9], [7, 6, 162, 163], [1, 4, 4, 17], [116, 1, 79, 6], [1, 8, 0, 1]], 'adelic_image': '168.48.0.?', 'conductor': 6720, 'lmfdb_label': '6720.c3', 'prime': 0}
  • id: 33169
    {'conductor': 6720, 'elladic_image': '8.12.0.7', 'lmfdb_label': '6720.c3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6720.c does not appear in ec_padic