Elliptic curve data - 678.f2

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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': '678e', 'Clabel': '678e2', 'Cnumber': 2, 'abc_quality': 1.0161232819454147, 'absD': 335109636, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 904, 'ainvs': [1, 0, 0, -212, 780], 'analytic_rank': 0, 'bad_primes': [2, 3, 113], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 678, 'degree': 320, 'elladic_images': ['8.24.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.33966802209266390939765348116', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [1054045415233, 335109636], 'lmfdb_iso': '678.f', 'lmfdb_label': '678.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -212, 780], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '8.24.0-8.b.1.2', '452.24.0.?', '904.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.33966802209266390939765348116', 'prec': 103}, 'szpiro_ratio': 4.246514985907296, '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, 1, 1, 1, 2, 1, 0, 1, 1, 2, 4, 1, -2, 0, 2, 1, -6, 1, -4, 2], 'aplist': [1, 1, 2, 0, 4, -2, -6, -4, -4, 10, 0, 10, -6, 4, -4, -2, -4, -10, 12, -12, -6, 12, 12, -6, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 678, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '678.f', 'trace_hash': 2245482726988613032}
• 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': '0.50695347535604031044752751722', 'prec': 103}, 'conductor': 678, 'gens': [], 'heights': [], 'lmfdb_label': '678.f2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.5811051550471475702804096420', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1622103100942951405608192840568615602', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[4, -2, 1], [12, -6, 1]], 'xcoord_integral_points': [4, 12]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 1], '3': [5, 0], '113': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '678.f2'}
• ec_torsion_growth •

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

  
  
  • id: 31433
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '678.f2', 'torsion': [2, 4]}
  • id: 31435
    {'degree': 4, 'field': [674, 60, -59, -2, 1], 'lmfdb_label': '678.f2', 'torsion': [2, 4]}
  • id: 31434
    {'degree': 4, 'field': [784, 0, 57, 0, 1], 'lmfdb_label': '678.f2', 'torsion': [2, 4]}
  • id: 31438
    {'degree': 8, 'field': [-38, -148, 118, 59, -26, -7, 7, -4, 1], 'lmfdb_label': '678.f2', 'torsion': [2, 6]}
  • id: 31437
    {'degree': 8, 'field': [144, 0, 128, 0, 58, 0, 8, 0, 1], 'lmfdb_label': '678.f2', 'torsion': [2, 8]}
  • id: 31436
    {'degree': 8, 'field': [614656, 0, 0, 0, 1681, 0, 0, 0, 1], 'lmfdb_label': '678.f2', 'torsion': [4, 4]}
  • id: 31439
    {'degree': 16, 'field': [29952, 64512, -128, -93824, -30504, 66296, 18542, -27510, -2111, 5710, -812, -258, 134, -70, 30, -8, 1], 'lmfdb_label': '678.f2', 'torsion': [2, 8]}
  • id: 31441
    {'degree': 16, 'field': [312012, -224856, 271908, -95508, 50130, -792, 261, -7128, 11368, -7586, 2989, -1172, 529, -182, 46, -8, 1], 'lmfdb_label': '678.f2', 'torsion': [2, 12]}
  • id: 31440
    {'degree': 16, 'field': [419904, 0, -1171584, 0, 1068640, 0, -466464, 0, 94196, 0, -5424, 0, -388, 0, 0, 0, 1], 'lmfdb_label': '678.f2', '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: 8340
    {'conductor': 678, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '678.f2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8341
    {'conductor': 678, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '678.f2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 8342
    {'conductor': 678, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '678.f2', 'prime': 113, '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: 1669000
    {'adelic_gens': [[1, 0, 4, 1], [229, 4, 454, 3], [1, 4, 0, 1], [453, 4, 2, 9], [901, 4, 900, 5], [681, 2, 0, 1]], 'adelic_image': '904.48.0.?', 'conductor': 678, 'lmfdb_label': '678.f2', 'prime': 0}
  • id: 3091
    {'conductor': 678, 'elladic_image': '8.24.0.4', 'lmfdb_label': '678.f2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 678.f does not appear in ec_padic