Elliptic curve data - 8670.g3

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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': '8670e', 'Clabel': '8670e6', 'Cnumber': 6, 'abc_quality': 1.0522127879225598, 'absD': 217238121000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 2040, 'ainvs': [1, 1, 0, -96387, -11536371], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 55296, 'elladic_images': ['2.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6341990669644870657053935698', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 6, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4102915888729, 9000000], 'lmfdb_iso': '8670.g', 'lmfdb_label': '8670.g3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -334, -2368], 'min_quad_twist_disc': 17, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1', '12.48.0.a.1', '24.96.1.cp.2', '40.12.0.a.1', '51.8.0-3.a.1.1', '60.96.1.h.3', '102.48.0.?', '120.192.5.?', '136.12.0.?', '204.96.0.?', '340.12.0.?', '408.192.1.?', '680.24.0.?', '1020.192.1.?', '2040.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.21759239493637902558062626086', 'prec': 103}, 'szpiro_ratio': 5.077625488141365, '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, 1, 1, 4, -1, 1, -1, 0, -1, 2, -4, -1, 1, 0, -1, -4, 1], 'aplist': [-1, -1, 1, 4, 0, 2, 0, -4, 0, 6, -8, -2, 6, -4, 0, -6, 0, 10, -4, 0, -2, -8, 12, 18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 8670, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '8670.g', 'trace_hash': 1247736579813721573}
• 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': '0.038067357069003131284230393789', 'prec': 107}, 'conductor': 8670, 'gens': [], 'heights': [], 'lmfdb_label': '8670.g3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.27098895538152820488065760633', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6259337322891692292839456379704312739', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-186, 93, 1], [358, -179, 1]], 'xcoord_integral_points': [-186, 358]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [0, 1], '5': [1, 0], '17': 'a'}, 'iwp0': 5, 'lmfdb_label': '8670.g3'}
• ec_torsion_growth •

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

  
  
  • id: 452520
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 6]}
  • id: 452522
    {'degree': 4, 'field': [36, 0, -22, 0, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 4]}
  • id: 452523
    {'degree': 4, 'field': [100, 0, 14, 0, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 12]}
  • id: 452521
    {'degree': 4, 'field': [1156, 0, 17, 0, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 4]}
  • id: 452524
    {'degree': 6, 'field': [-16, -129, 45, 17, -9, -3, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 6]}
  • id: 452526
    {'degree': 8, 'field': [735, 1470, 1261, -422, 458, 106, -7, -2, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 12]}
  • id: 452525
    {'degree': 8, 'field': [4761, 0, 1365, 0, 208, 0, 5, 0, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 12]}
  • id: 452527
    {'degree': 12, 'field': [4996, 4326, -99, -7180, 645, 2886, 47, -726, 15, 100, -9, -6, 1], 'lmfdb_label': '8670.g3', 'torsion': [6, 6]}
  • id: 452528
    {'degree': 16, 'field': [748225, 0, -239580, 0, 256046, 0, 68208, 0, 4659, 0, -336, 0, 14, 0, -12, 0, 1], 'lmfdb_label': '8670.g3', 'torsion': [4, 12]}
  • id: 452531
    {'degree': 16, 'field': [20566225, 0, 60999440, 0, 27534724, 0, 5501936, 0, 622678, 0, 45872, 0, 2404, 0, 80, 0, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 24]}
  • id: 452530
    {'degree': 16, 'field': [25341660, 7570800, -13156920, 10425600, -3106944, -3147912, 1940180, -485600, -204219, 183720, -4624, -15960, 1386, 560, -60, -8, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 8]}
  • id: 452529
    {'degree': 16, 'field': [79673476, 0, -9079560, 0, 1103461, 0, -223410, 0, -2229, 0, 540, 0, 331, 0, 30, 0, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 8]}
  • id: 452532
    {'degree': 18, 'field': [2220119775, 939060675, -530672625, -273196560, 103233690, 51974670, -14065328, -3522624, 1404183, -39095, -24699, 7848, -2092, 1626, -330, -76, 45, -9, 1], 'lmfdb_label': '8670.g3', 'torsion': [2, 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: 180851
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '8670.g3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 180852
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8670.g3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 180853
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '8670.g3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 180854
    {'conductor': 8670, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '8670.g3', '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: 1721267
    {'adelic_gens': [[1, 0, 12, 1], [1799, 0, 0, 2039], [817, 612, 714, 1327], [817, 1326, 0, 1], [9, 4, 2024, 2033], [1021, 612, 1326, 1633], [1, 12, 0, 1], [2029, 12, 2028, 13], [647, 1326, 1054, 715]], 'adelic_image': '2040.384.5.?', 'conductor': 8670, 'lmfdb_label': '8670.g3', 'prime': 0}
  • id: 42391
    {'conductor': 8670, 'elladic_image': '2.6.0.1', 'lmfdb_label': '8670.g3', 'modell_image': '2Cs', 'prime': 2}
  • id: 42392
    {'conductor': 8670, 'elladic_image': '3.4.0.1', 'lmfdb_label': '8670.g3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 8670.g does not appear in ec_padic