Elliptic curve data - 47040.ff2

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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': '47040gh', 'Clabel': '47040gh2', 'Cnumber': 2, 'abc_quality': 1.0488640833975327, 'absD': 1708019812167782400, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 1, 0, -3889881, -2953553625], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 47040, 'degree': 1474560, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4832121118883163760567578124', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 135, 'isogeny_degrees': [1, 2], 'jinv': [13507798771700416, 3544416225], 'lmfdb_iso': '47040.ff', 'lmfdb_label': '47040.ff2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -19846, -1069280], 'min_quad_twist_disc': 56, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '24.12.0.a.1', '28.12.0-2.a.1.1', '40.12.0.a.1', '60.12.0.a.1', '120.24.0.?', '168.24.0.?', '280.24.0.?', '420.24.0.?', '840.48.0.?'], '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, 49], [3, 4, 15680], [5, 6, 3136], [7, 32, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.81710985680071441408684931922', 'prec': 103}, 'szpiro_ratio': 5.310584560088103, '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, -1, 0, 0, 0, 1, 0, 4, 0, -6, 0, -1, 0, -6, 0, 0, 0], 'aplist': [0, 1, -1, 0, 4, -6, -6, 0, 4, 6, 0, -2, -2, 4, 4, 6, -12, -10, 4, -8, 14, -8, 12, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 47040, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '47040.ff', 'trace_hash': 1201482873593211676}
• 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': '0.0069680196195137695930659770719', 'prec': 110}, 'conductor': 47040, 'gens': [], 'heights': [], 'lmfdb_label': '47040.ff2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10750342605255897295075421709', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1500685210511794590150843418737234258', 'prec': 130}, 'tamagawa_product': 320, 'torsion_generators': [[-1125, 0, 1], [2277, 0, 1]], 'xcoord_integral_points': [-1153, -1125, 2277]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [2, 0], '7': 'a'}, 'iwp0': 7, 'lmfdb_label': '47040.ff2'}
• ec_torsion_growth •

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

  
  
  • id: 2296955
    {'degree': 4, 'field': [49, 0, -56, 0, 1], 'lmfdb_label': '47040.ff2', 'torsion': [2, 4]}
  • id: 2296956
    {'degree': 4, 'field': [81, 0, 24, 0, 1], 'lmfdb_label': '47040.ff2', 'torsion': [2, 4]}
  • id: 2296957
    {'degree': 4, 'field': [134, 16, -15, -2, 1], 'lmfdb_label': '47040.ff2', 'torsion': [2, 4]}
  • id: 2296958
    {'degree': 8, 'field': [-107163, 0, 18144, 0, -1134, 0, 0, 0, 1], 'lmfdb_label': '47040.ff2', 'torsion': [2, 6]}
  • id: 2296959
    {'degree': 16, 'field': [576, -5184, 17712, -28560, 25018, -18900, 17850, -13276, 8321, -4684, 2534, -1204, 504, -168, 44, -8, 1], 'lmfdb_label': '47040.ff2', 'torsion': [4, 4]}
  • id: 2296960
    {'degree': 16, 'field': [1296, 0, 71712, 0, 1921320, 0, -1343688, 0, 275329, 0, -15712, 0, -210, 0, 8, 0, 1], 'lmfdb_label': '47040.ff2', 'torsion': [2, 8]}
  • id: 2296962
    {'degree': 16, 'field': [52796, 66624, -27520, -67760, 8124, 29984, -8648, -1080, 901, -1616, 1652, -912, 334, -112, 36, -8, 1], 'lmfdb_label': '47040.ff2', 'torsion': [2, 8]}
  • id: 2296961
    {'degree': 16, 'field': [853776, 0, -2628864, 0, 3376416, 0, -1079808, 0, 206152, 0, -23488, 0, 1656, 0, -64, 0, 1], 'lmfdb_label': '47040.ff2', '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: 1123482
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '47040.ff2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1123483
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '47040.ff2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 1123484
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '47040.ff2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1123485
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '47040.ff2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1977571
    {'adelic_gens': [[837, 4, 836, 5], [1, 4, 0, 1], [599, 0, 0, 839], [281, 364, 322, 729], [1, 0, 4, 1], [657, 238, 602, 601], [27, 476, 112, 349], [337, 602, 0, 1]], 'adelic_image': '840.48.0.?', 'conductor': 47040, 'lmfdb_label': '47040.ff2', 'prime': 0}
  • id: 203509
    {'conductor': 47040, 'elladic_image': '2.6.0.1', 'lmfdb_label': '47040.ff2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 47040.ff does not appear in ec_padic