Elliptic curve data - 7056.bg1

Formats: - HTML - YAML - JSON - 2024-05-08T12:38:14.608152

• 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': '7056bq', 'Clabel': '7056bq4', 'Cnumber': 4, 'abc_quality': 1.1980441775334598, 'absD': 120495224844288, 'ainvs': [0, 0, 0, -262395, 51731946], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 14, 'class_size': 4, 'cm': -28, 'conductor': 7056, 'degree': 28672, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7628436006460070452518354626', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 14, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [16581375, 1], 'lmfdb_iso': '7056.bg', 'lmfdb_label': '7056.bg1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -37, -78], 'min_quad_twist_disc': -84, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.93904233603947808869203383490', 'prec': 107}, 'szpiro_ratio': 5.534693048977438, '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, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, 0, 0, 4, 0, 0, 0, 8, -2, 0, -6, 0, 12, 0, 10, 0, 0, -4, 16, 0, -8, 0, 0, 0], 'class_deg': 14, 'class_size': 4, 'conductor': 7056, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '7056.bg', 'trace_hash': 520392068974718912}
• 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': '0.029431575001681825812489267668', 'prec': 107}, 'conductor': 7056, 'gens': [], 'heights': [], 'lmfdb_label': '7056.bg1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.55809901683266033382036113112', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2323960673306413352814445244990738053', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[294, 0, 1]], 'xcoord_integral_points': [294]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0, 0], '7': 'a'}, 'iwp0': 11, 'lmfdb_label': '7056.bg1'}
• ec_torsion_growth •

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

  
  
  • id: 371454
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '7056.bg1', 'torsion': [2, 2]}
  • id: 371455
    {'degree': 4, 'field': [16, 10, -4, -1, 1], 'lmfdb_label': '7056.bg1', 'torsion': [4]}
  • id: 371456
    {'degree': 6, 'field': [1, -16, 23, 18, -12, -2, 1], 'lmfdb_label': '7056.bg1', 'torsion': [14]}
  • id: 371461
    {'degree': 8, 'field': [-147, 0, -147, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '7056.bg1', 'torsion': [6]}
  • id: 371457
    {'degree': 8, 'field': [36, -72, 72, -24, 13, -10, 2, -2, 1], 'lmfdb_label': '7056.bg1', 'torsion': [2, 4]}
  • id: 371458
    {'degree': 8, 'field': [36, 0, -60, 0, 13, 0, -4, 0, 1], 'lmfdb_label': '7056.bg1', 'torsion': [2, 4]}
  • id: 371460
    {'degree': 8, 'field': [58, -44, 3, -4, 20, -16, 6, -2, 1], 'lmfdb_label': '7056.bg1', 'torsion': [8]}
  • id: 371459
    {'degree': 8, 'field': [214, 24, 23, -82, 12, 32, -6, -4, 1], 'lmfdb_label': '7056.bg1', 'torsion': [8]}
  • id: 371462
    {'degree': 12, 'field': [1, 0, -16, 0, 60, 0, -78, 0, 44, 0, -11, 0, 1], 'lmfdb_label': '7056.bg1', 'torsion': [2, 14]}
  • id: 371468
    {'degree': 16, 'field': [9, 0, -63, 0, 144, 0, -63, 0, 3, 0, 0, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '7056.bg1', 'torsion': [2, 6]}
  • id: 371465
    {'degree': 16, 'field': [46, -284, 3806, -8776, 9773, -8650, 7387, -5388, 3257, -1570, 605, -248, 113, -28, 6, -4, 1], 'lmfdb_label': '7056.bg1', 'torsion': [16]}
  • id: 371464
    {'degree': 16, 'field': [232, 488, -388, -924, 2530, -3200, 2268, -1090, 473, -350, 334, -222, 128, -70, 30, -8, 1], 'lmfdb_label': '7056.bg1', 'torsion': [2, 8]}
  • id: 371463
    {'degree': 16, 'field': [256, 0, 1088, 0, 1892, 0, 2004, 0, 1601, 0, 144, 0, -34, 0, -4, 0, 1], 'lmfdb_label': '7056.bg1', 'torsion': [4, 4]}
  • id: 371467
    {'degree': 16, 'field': [21609, 0, -21609, 0, 15435, 0, -6174, 0, 1911, 0, -294, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '7056.bg1', 'torsion': [3, 6]}
  • id: 371466
    {'degree': 16, 'field': [208378, -34616, -169856, 21876, 98181, -20356, -30918, 8246, 6415, -1442, -983, 56, 131, 18, -15, -2, 1], 'lmfdb_label': '7056.bg1', 'torsion': [16]}
  • id: 371469
    {'degree': 20, 'field': [10916801973, 0, 0, 0, 346565142, 0, 0, 0, 2750517, 0, -166698, 0, 31752, 0, 2646, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '7056.bg1', 'torsion': [22]}
• 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: 144768
    {'conductor': 7056, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '7056.bg1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 144769
    {'conductor': 7056, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '7056.bg1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 144770
    {'conductor': 7056, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '7056.bg1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 7056.bg1 does not appear in ec_galrep
• lmfdb_iso 7056.bg does not appear in ec_padic