Elliptic curve data - 2856.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': '2856h', 'Clabel': '2856h2', 'Cnumber': 2, 'abc_quality': 1.0420651643816399, 'absD': 18502955149722624, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 952, 'ainvs': [0, 1, 0, -11335464, 14685722496], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 2856, 'degree': 69120, 'elladic_images': ['8.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5444337152271206247600773540', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2], 'jinv': [157304700372188331121828, 18069292138401], 'lmfdb_iso': '2856.c', 'lmfdb_label': '2856.c3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -11335464, 14685722496], '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.a.1.2', '476.24.0.?', '952.48.0.?'], '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, 'serre_invariants': [[2, 2, 1], [3, 4, 136], [7, 8, 408], [17, 18, 168]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.9668110647604995335790505861', 'prec': 100}, 'szpiro_ratio': 7.583586615791889, '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, -2, 0, -1, 0, 1, 0, 0, 0, 2, 0, -2, 0, 1, 0, 0, 0], 'aplist': [0, 1, -2, -1, 0, 2, 1, 0, 0, 2, 8, -6, -6, 4, 0, 14, -8, 14, 4, 8, 10, 8, -16, 2, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 2856, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '2856.c', 'trace_hash': 2142708236620293017}
• 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': '0.0061649982239351969731550266650', 'prec': 110}, 'conductor': 2856, 'gens': [], 'heights': [], 'lmfdb_label': '2856.c3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29971136951585998016249400374', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7982682170951598809749640224479207218', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[1943, 0, 1], [1944, 0, 1]], 'xcoord_integral_points': [-3888, 1943, 1944]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '7': [0, 0], '17': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '2856.c3'}
• ec_torsion_growth •

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

  
  
  • id: 148465
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '2856.c3', 'torsion': [2, 4]}
  • id: 148467
    {'degree': 4, 'field': [786, -64, 65, -2, 1], 'lmfdb_label': '2856.c3', 'torsion': [2, 4]}
  • id: 148466
    {'degree': 4, 'field': [900, 0, -59, 0, 1], 'lmfdb_label': '2856.c3', 'torsion': [2, 4]}
  • id: 148470
    {'degree': 8, 'field': [-48, 0, -16, 0, 24, 0, 0, 0, 1], 'lmfdb_label': '2856.c3', 'torsion': [2, 6]}
  • id: 148469
    {'degree': 8, 'field': [376, 1216, 1248, 208, -364, -64, -20, 0, 1], 'lmfdb_label': '2856.c3', 'torsion': [2, 8]}
  • id: 148468
    {'degree': 8, 'field': [810000, 0, 0, 0, 1681, 0, 0, 0, 1], 'lmfdb_label': '2856.c3', 'torsion': [4, 4]}
  • id: 148473
    {'degree': 16, 'field': [729, 0, 1944, 0, 1404, 0, -2660, 0, 734, 0, -8, 0, -32, 0, -4, 0, 1], 'lmfdb_label': '2856.c3', 'torsion': [2, 12]}
  • id: 148471
    {'degree': 16, 'field': [15310233, -3187932, 14511767, -2898416, 5602141, -1167370, 1293464, -195106, 199852, -11986, 20598, -3746, 2155, -318, 81, -6, 1], 'lmfdb_label': '2856.c3', 'torsion': [2, 8]}
  • id: 148472
    {'degree': 16, 'field': [40916790305316, 47540837853792, 23563619583408, 6582871432512, 1110799983268, 100459496496, 4139424552, 35926656, -49091907, 8164656, 1724272, -12576, 13470, -1536, 120, 0, 1], 'lmfdb_label': '2856.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: 50853
    {'conductor': 2856, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '2856.c3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 50854
    {'conductor': 2856, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '2856.c3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 50855
    {'conductor': 2856, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '2856.c3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 50856
    {'conductor': 2856, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2856.c3', 'prime': 17, '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: 1682613
    {'adelic_gens': [[1, 0, 4, 1], [239, 2, 0, 1], [1, 4, 0, 1], [275, 2, 134, 951], [949, 4, 948, 5], [477, 2, 0, 1], [451, 2, 334, 951]], 'adelic_image': '952.48.0.?', 'conductor': 2856, 'lmfdb_label': '2856.c3', 'prime': 0}
  • id: 14279
    {'conductor': 2856, 'elladic_image': '8.24.0.1', 'lmfdb_label': '2856.c3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 2856.c does not appear in ec_padic