Elliptic curve data - 8400.z3

Formats: - HTML - YAML - JSON - 2024-06-12T13:02:49.984392

• 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': '8400e', 'Clabel': '8400e2', 'Cnumber': 2, 'abc_quality': 0.9068964182020077, 'absD': 1102500000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 420, 'ainvs': [0, -1, 0, -5908, 169312], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 8400, 'degree': 12288, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0706189933838534641886531097', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2], 'jinv': [5702413264, 275625], 'lmfdb_iso': '8400.z', 'lmfdb_label': '8400.z3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -236, -1260], 'min_quad_twist_disc': -20, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0.b.1', '20.12.0-2.a.1.1', '28.12.0.a.1', '60.24.0-12.b.1.2', '84.24.0.?', '140.24.0.?', '420.48.0.?'], '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': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.19619808320649359605654797122', 'prec': 107}, 'szpiro_ratio': 4.168438963463504, '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, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, -1, 0, 1, 0, 2, -6, 4, 4, 6, 0, -6, 6, -4, 8, -14, 4, -2, 12, 12, -10, -8, -4, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 8400, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '8400.z', 'trace_hash': 479355773979978457}
• 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': '0.11750927800533491133082539097', 'prec': 103}, 'conductor': 8400, 'gens': [], 'heights': [], 'lmfdb_label': '8400.z3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.86059523891974557334146764175', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7211904778394911466829352834930475006', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[37, 0, 1], [52, 0, 1]], 'xcoord_integral_points': [-88, 37, 52]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': 'a', '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '8400.z3'}
• ec_torsion_growth •

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

  
  
  • id: 438378
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '8400.z3', 'torsion': [2, 4]}
  • id: 438376
    {'degree': 4, 'field': [9, 0, -1, 0, 1], 'lmfdb_label': '8400.z3', 'torsion': [2, 4]}
  • id: 438377
    {'degree': 4, 'field': [25, 0, -25, 0, 1], 'lmfdb_label': '8400.z3', 'torsion': [2, 4]}
  • id: 438379
    {'degree': 8, 'field': [-1875, 0, 1240, 0, -150, 0, 0, 0, 1], 'lmfdb_label': '8400.z3', 'torsion': [2, 6]}
  • id: 438380
    {'degree': 16, 'field': [256, 0, 576, 0, 704, 0, 1044, 0, 1029, 0, 261, 0, 44, 0, 9, 0, 1], 'lmfdb_label': '8400.z3', 'torsion': [4, 4]}
  • id: 438381
    {'degree': 16, 'field': [1764, 3528, 3472, -11032, 16102, -15072, 14316, -11430, 6813, -2754, 762, -78, -72, 42, -2, -4, 1], 'lmfdb_label': '8400.z3', 'torsion': [2, 8]}
  • id: 438383
    {'degree': 16, 'field': [35929, -15540, 32978, -38152, 29504, -18936, 17594, -11160, 5365, -2736, 1414, -296, -72, 28, 16, -8, 1], 'lmfdb_label': '8400.z3', 'torsion': [2, 8]}
  • id: 438382
    {'degree': 16, 'field': [2059225, 0, -12268620, 0, 10574116, 0, -3213378, 0, 511338, 0, -47436, 0, 2593, 0, -78, 0, 1], 'lmfdb_label': '8400.z3', '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: 174658
    {'conductor': 8400, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '8400.z3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 174659
    {'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8400.z3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 174660
    {'conductor': 8400, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '8400.z3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 174661
    {'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8400.z3', '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: 1719617
    {'adelic_gens': [[1, 0, 4, 1], [1, 4, 0, 1], [417, 4, 416, 5], [83, 0, 0, 419], [281, 340, 310, 261], [39, 250, 260, 89], [51, 170, 190, 251]], 'adelic_image': '420.48.0.?', 'conductor': 8400, 'lmfdb_label': '8400.z3', 'prime': 0}
  • id: 41215
    {'conductor': 8400, 'elladic_image': '2.6.0.1', 'lmfdb_label': '8400.z3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 8400.z does not appear in ec_padic