Elliptic curve data - 8712.u5

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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': '8712y', 'Clabel': '8712y1', 'Cnumber': 1, 'abc_quality': 1.1757189916348774, 'absD': 61990462512, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 528, 'ainvs': [0, 0, 0, 726, 9317], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 8712, 'degree': 5120, 'elladic_images': ['16.48.0.150'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.75632790437341019036096766989', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [2048, 3], 'lmfdb_iso': '8712.u', 'lmfdb_label': '8712.u5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 1, 0], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '6.6.0.a.1', '8.24.0.ba.1', '12.12.0.g.1', '16.48.0.y.1', '24.48.0.bi.2', '44.12.0-4.c.1.2', '48.96.1.dt.1', '88.48.0.?', '132.24.0.?', '176.96.0.?', '264.96.0.?', '528.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1089], [3, 8, 968], [11, 62, 72]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2229749365464783638400374447', 'prec': 103}, 'szpiro_ratio': 3.50537221043494, '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, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, 2, 0, 0, 2, 2, 4, 8, 6, 8, 6, -6, -4, 0, 2, -4, 2, -4, -8, -10, 8, -4, 6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 8712, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '8712.u', 'trace_hash': 585696540465894845}
• 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': '0.22032406169281447760984808086', 'prec': 103}, 'conductor': 8712, 'gens': [], 'heights': [], 'lmfdb_label': '8712.u5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.75080237789704370014537591006', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0032095115881748005815036402275811442', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-11, 0, 1]], 'xcoord_integral_points': [-11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '8712.u5'}
• ec_torsion_growth •

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

  
  
  • id: 454771
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '8712.u5', 'torsion': [4]}
  • id: 454770
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '8712.u5', 'torsion': [2, 2]}
  • id: 454772
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '8712.u5', 'torsion': [4]}
  • id: 454774
    {'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [8]}
  • id: 454773
    {'degree': 4, 'field': [9, -3, -2, -1, 1], 'lmfdb_label': '8712.u5', 'torsion': [2, 4]}
  • id: 454775
    {'degree': 4, 'field': [64, 0, 17, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [8]}
  • id: 454779
    {'degree': 8, 'field': [-659, -666, 34, 266, 36, -16, -14, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [6]}
  • id: 454778
    {'degree': 8, 'field': [81, 0, 45, 0, 16, 0, 5, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [2, 8]}
  • id: 454777
    {'degree': 8, 'field': [157, 162, 134, 42, 39, -6, 8, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [8]}
  • id: 454776
    {'degree': 8, 'field': [625, -250, -250, 170, 214, 34, -10, -2, 1], 'lmfdb_label': '8712.u5', 'torsion': [2, 4]}
  • id: 454780
    {'degree': 16, 'field': [484, 0, 10032, 0, 13924, 0, 9324, 0, 4437, 0, 1332, 0, 238, 0, 24, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [4, 8]}
  • id: 454783
    {'degree': 16, 'field': [529, -1104, -686, -3780, 6286, 4716, 13558, 2772, 6139, 180, 1702, -12, 304, 0, 28, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [16]}
  • id: 454781
    {'degree': 16, 'field': [958, -9880, 28376, -14448, -41626, 38620, 17524, -20628, -689, 2592, 520, -244, -202, 84, 8, -8, 1], 'lmfdb_label': '8712.u5', 'torsion': [16]}
  • id: 454786
    {'degree': 16, 'field': [6561, 0, 7290, -3888, 2916, 702, 792, 864, -401, 288, 88, 26, 36, -16, 10, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [12]}
  • id: 454785
    {'degree': 16, 'field': [125962, -454940, 710222, -574358, 177168, 118288, -174488, 103448, -34701, 6284, -1006, 754, -454, 144, -16, -4, 1], 'lmfdb_label': '8712.u5', 'torsion': [12]}
  • id: 454784
    {'degree': 16, 'field': [434281, -438894, 465962, -327944, 202036, -67540, 77328, -19988, 6687, -6206, 828, -490, 160, -32, 14, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [2, 6]}
  • id: 454782
    {'degree': 16, 'field': [722500, 0, -849800, 0, 674528, 0, -211700, 0, 50941, 0, -8020, 0, 758, 0, -40, 0, 1], 'lmfdb_label': '8712.u5', 'torsion': [16]}
• 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: 181909
    {'conductor': 8712, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '8712.u5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 181910
    {'conductor': 8712, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '8712.u5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 181911
    {'conductor': 8712, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '8712.u5', 'prime': 11, 'reduction_type': 0, '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: 1721564
    {'adelic_gens': [[1, 16, 0, 1], [5, 4, 524, 525], [15, 2, 430, 515], [45, 352, 506, 155], [1, 0, 16, 1], [383, 0, 0, 527], [513, 16, 512, 17], [296, 143, 385, 230], [1, 352, 132, 133]], 'adelic_image': '528.192.1.?', 'conductor': 8712, 'lmfdb_label': '8712.u5', 'prime': 0}
  • id: 42595
    {'conductor': 8712, 'elladic_image': '16.48.0.150', 'lmfdb_label': '8712.u5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 8712.u does not appear in ec_padic