Elliptic curve data - 1680.j2

Formats: - HTML - YAML - JSON - 2024-06-08T02:48:43.259116

• 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': '1680p', 'Clabel': '1680p5', 'Cnumber': 5, 'abc_quality': 1.05504045380176, 'absD': 531284060160000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 1680, 'ainvs': [0, -1, 0, -1920800, 1025280000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 1680, 'degree': 24576, 'elladic_images': ['8.96.0.43'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1410030071755357016616543081', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [191342053882402567201, 129708022500], 'lmfdb_iso': '1680.j', 'lmfdb_label': '1680.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -120050, -16020000], 'min_quad_twist_disc': -4, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '8.96.0-8.l.1.5', '24.192.1-24.ch.1.3', '80.192.2.?', '112.192.1.?', '240.384.5.?', '336.384.5.?', '560.384.5.?', '1680.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4478558266155903922444221866', 'prec': 100}, 'szpiro_ratio': 7.408334609879248, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
• 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, -2, 0, -1, 0, 2, 0, -4, 0], 'aplist': [0, -1, 1, 1, 4, -2, 2, -4, 8, -2, 0, 6, -6, 4, 0, -10, -12, 14, 12, 8, 10, -16, 12, 10, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 1680, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '1680.j', 'trace_hash': 1852342526424412922}
• 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': '0.013814921341146231099223053349', 'prec': 107}, 'conductor': 1680, 'gens': [], 'heights': [], 'lmfdb_label': '1680.j2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.43090287435849486501128292544', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7236114974339794600451317017589934449', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[800, 0, 1], [850, 2450, 1]], 'xcoord_integral_points': [-1600, 752, 800, 801, 850]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [1, 0], '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1680.j2'}
• ec_torsion_growth •

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

  
  
  • id: 85073
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [2, 8]}
  • id: 85075
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [2, 8]}
  • id: 85074
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [4, 4]}
  • id: 85079
    {'degree': 8, 'field': [-959, -3080, -2344, 560, 742, -40, -56, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [2, 16]}
  • id: 85081
    {'degree': 8, 'field': [-768, 0, -188, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [2, 12]}
  • id: 85078
    {'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [4, 8]}
  • id: 85077
    {'degree': 8, 'field': [22201, 0, 1804, 0, -294, 0, 4, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [4, 8]}
  • id: 85076
    {'degree': 8, 'field': [22801, 0, -1796, 0, 306, 0, 4, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [4, 8]}
  • id: 85080
    {'degree': 8, 'field': [135646, -59192, 64016, -9776, 5209, -388, 134, -4, 1], 'lmfdb_label': '1680.j2', 'torsion': [2, 16]}
  • id: 85083
    {'degree': 16, 'field': [148, -640, 236, 4416, -8422, -2000, 21538, -29112, 23653, -14796, 7258, -2896, 968, -252, 56, -8, 1], 'lmfdb_label': '1680.j2', 'torsion': [2, 16]}
  • id: 85084
    {'degree': 16, 'field': [519841, 0, -143824, 0, -77396, 0, -64092, 0, 3426, 0, -192, 0, 184, 0, -4, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [2, 24]}
  • id: 85082
    {'degree': 16, 'field': [31640625, 0, -25312500, 0, 10125000, 0, -2700000, 0, 444375, 0, -36000, 0, 1800, 0, -60, 0, 1], 'lmfdb_label': '1680.j2', 'torsion': [8, 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: 26681
    {'conductor': 1680, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '1680.j2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 26682
    {'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1680.j2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 26683
    {'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1680.j2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 26684
    {'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '1680.j2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1675005
    {'adelic_gens': [[1353, 16, 1076, 121], [1, 16, 0, 1], [1, 16, 6, 517], [9, 16, 754, 345], [1665, 16, 1664, 17], [1, 16, 4, 65], [1, 0, 16, 1], [489, 8, 1156, 1641], [1679, 1664, 1674, 113]], 'adelic_image': '1680.768.13.?', 'conductor': 1680, 'lmfdb_label': '1680.j2', 'prime': 0}
  • id: 8193
    {'conductor': 1680, 'elladic_image': '8.96.0.43', 'lmfdb_label': '1680.j2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 1680.j does not appear in ec_padic