Elliptic curve data - 8670.n4

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '8670n', 'Clabel': '8670n1', 'Cnumber': 1, 'abc_quality': 0.9764195258143714, 'absD': 1506763607256000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 2040, 'ainvs': [1, 1, 1, 7219, -1849597], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 8670, 'degree': 41472, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5923066395024754508088421121', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [1723683599, 62424000], 'lmfdb_iso': '8670.n', 'lmfdb_label': '8670.n4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 25, -375], 'min_quad_twist_disc': 17, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '24.24.0-6.a.1.10', '30.24.0.b.1', '51.8.0-3.a.1.2', '102.24.0.?', '120.48.0.?', '136.6.0.?', '408.48.0.?', '510.48.0.?', '2040.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 4335], [3, 4, 289], [5, 6, 1734], [17, 162, 30]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.17569996747436741068407480316', 'prec': 103}, 'szpiro_ratio': 4.6745819577130225, '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, 1, -1, 1, -1, -1, -2, 1, 1, -1, 0, -1, -4, -2, 1, 1, 0, 1, -4, -1], 'aplist': [1, -1, -1, -2, 0, -4, 0, -4, 0, -6, 4, -2, 0, 2, 0, -6, 6, 10, 2, 6, 16, -8, 0, 6, 4], 'class_deg': 6, 'class_size': 4, 'conductor': 8670, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '8670.n', 'trace_hash': 1979418992420591480}
• 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': '0.041394250731881856726625472271', 'prec': 107}, 'conductor': 8670, 'gens': [], 'heights': [], 'lmfdb_label': '8670.n4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.22959008255957119076050549278', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3775404953574271445630329566889871249', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[103, -52, 1]], 'xcoord_integral_points': [103]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [2, 0], '5': [0, 0], '17': 'a'}, 'iwp0': 5, 'lmfdb_label': '8670.n4'}
• ec_torsion_growth •

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

  
  
  • id: 452632
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '8670.n4', 'torsion': [6]}
  • id: 452631
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '8670.n4', 'torsion': [2, 2]}
  • id: 452633
    {'degree': 4, 'field': [-15, 0, -22, 0, 1], 'lmfdb_label': '8670.n4', 'torsion': [4]}
  • id: 452634
    {'degree': 4, 'field': [64, 0, -1, 0, 1], 'lmfdb_label': '8670.n4', 'torsion': [2, 6]}
  • id: 452635
    {'degree': 6, 'field': [4, -14, 19, -11, 8, -3, 1], 'lmfdb_label': '8670.n4', 'torsion': [6]}
  • id: 452638
    {'degree': 8, 'field': [8, 8, 18, -40, -9, 32, -6, -4, 1], 'lmfdb_label': '8670.n4', 'torsion': [12]}
  • id: 452637
    {'degree': 8, 'field': [9726, -4800, -203, 142, 269, 52, -1, -2, 1], 'lmfdb_label': '8670.n4', 'torsion': [2, 4]}
  • id: 452636
    {'degree': 8, 'field': [33856, 0, 8578, 0, 549, 0, -8, 0, 1], 'lmfdb_label': '8670.n4', 'torsion': [2, 4]}
  • id: 452639
    {'degree': 12, 'field': [16, -56, 120, -178, 175, 3, -65, 12, 12, -2, 1, -3, 1], 'lmfdb_label': '8670.n4', 'torsion': [3, 6]}
  • id: 452640
    {'degree': 12, 'field': [1104, -1812, 4411, -5584, 3861, -1584, 1061, -522, 219, -70, 25, -6, 1], 'lmfdb_label': '8670.n4', 'torsion': [2, 6]}
  • id: 452642
    {'degree': 16, 'field': [19456, 4096, 32832, 33056, 168, 35856, 12106, -4072, 18303, -6584, 5614, -1500, 768, -128, 48, -4, 1], 'lmfdb_label': '8670.n4', 'torsion': [2, 12]}
  • id: 452643
    {'degree': 16, 'field': [65536, 0, -70144, 0, 126272, 0, -43200, 0, -4204, 0, 1140, 0, 317, 0, 26, 0, 1], 'lmfdb_label': '8670.n4', 'torsion': [2, 12]}
  • id: 452641
    {'degree': 16, 'field': [2401824, 19475904, -18533264, -5381168, 10842382, -8155912, 71660, 2130512, -333697, -173680, 76844, -24320, 5206, -560, 100, -8, 1], 'lmfdb_label': '8670.n4', 'torsion': [8]}
  • id: 452644
    {'degree': 18, 'field': [-3123997456, -3476428032, 554925216, 1992812516, 410385936, -370696356, -101976184, 28511394, -222498, -1714685, 892647, 73914, 15178, 3168, -12, 212, -12, -3, 1], 'lmfdb_label': '8670.n4', 'torsion': [18]}
• 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: 180903
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '8670.n4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 180904
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '8670.n4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 180905
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '8670.n4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 180906
    {'conductor': 8670, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '8670.n4', 'prime': 17, '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: 1721284
    {'adelic_gens': [[1, 6, 6, 37], [1, 12, 0, 1], [11, 2, 1990, 2031], [1799, 2028, 594, 1967], [1706, 11, 669, 2020], [10, 3, 381, 2032], [2029, 12, 2028, 13], [435, 88, 398, 77], [1021, 12, 6, 73], [1, 0, 12, 1]], 'adelic_image': '2040.96.1.?', 'conductor': 8670, 'lmfdb_label': '8670.n4', 'prime': 0}
  • id: 42413
    {'conductor': 8670, 'elladic_image': '2.3.0.1', 'lmfdb_label': '8670.n4', 'modell_image': '2B', 'prime': 2}
  • id: 42414
    {'conductor': 8670, 'elladic_image': '3.4.0.1', 'lmfdb_label': '8670.n4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 8670.n does not appear in ec_padic