Elliptic curve data - 1690.f1

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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': '1690f', 'Clabel': '1690f3', 'Cnumber': 3, 'abc_quality': 0.9543225417743602, 'absD': 217180147159040, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [1, 0, 0, -35071, -2429415], 'analytic_rank': 0, 'bad_primes': [2, 5, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 1690, 'degree': 12096, 'elladic_images': ['4.6.0.3', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5129240812084319536165801655', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [988345570681, 44994560], 'lmfdb_iso': '1690.f', 'lmfdb_label': '1690.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -208, -1122], 'min_quad_twist_disc': 13, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.b.1', '6.12.0.a.1', '12.24.0.f.1', '24.48.0.br.2', '30.24.0-6.a.1.4', '39.8.0-3.a.1.2', '40.12.0-4.b.1.1', '60.48.0-12.f.1.6', '78.24.0.?', '104.12.0.?', '120.96.0.?', '130.6.0.?', '156.48.0.?', '260.24.0.?', '312.96.0.?', '390.48.0.?', '520.48.0.?', '780.192.3.?', '1560.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 845], [3, 2, 845], [5, 6, 338], [13, 98, 10]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.23044940247766358558983644472', 'prec': 103}, 'szpiro_ratio': 5.78662470012936, '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, -2, 1, -1, -2, 4, 1, 1, -1, 6, -2, 0, 4, 2, 1, -6, 1, -2, -1], 'aplist': [1, -2, -1, 4, 6, 0, -6, -2, 6, -6, -2, -2, 6, 2, 12, 6, -6, 2, 4, 6, 10, -4, 0, 6, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 1690, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '1690.f', 'trace_hash': 1016874537208526182}
• 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': '0.048516653811777303164044401751', 'prec': 107}, 'conductor': 1690, 'gens': [], 'heights': [], 'lmfdb_label': '1690.f1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.34985209475164546343263775056', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0991125685098727805958265033746967327', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-90, 45, 1]], 'xcoord_integral_points': [-90]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [2, 1], '5': [0, 0], '13': 'a'}, 'iwp0': 5, 'lmfdb_label': '1690.f1'}
• ec_torsion_growth •

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

  
  
  • id: 85751
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '1690.f1', 'torsion': [2, 2]}
  • id: 85752
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '1690.f1', 'torsion': [6]}
  • id: 85753
    {'degree': 4, 'field': [4, -4, 1, 0, 1], 'lmfdb_label': '1690.f1', 'torsion': [4]}
  • id: 85754
    {'degree': 4, 'field': [40, 25, -1, -1, 1], 'lmfdb_label': '1690.f1', 'torsion': [2, 6]}
  • id: 85755
    {'degree': 6, 'field': [48, -132, 33, 7, -6, -3, 1], 'lmfdb_label': '1690.f1', 'torsion': [6]}
  • id: 85757
    {'degree': 8, 'field': [16, -56, 98, -86, 33, 6, 8, -4, 1], 'lmfdb_label': '1690.f1', 'torsion': [2, 4]}
  • id: 85756
    {'degree': 8, 'field': [16, 0, -32, 0, -41, 0, -8, 0, 1], 'lmfdb_label': '1690.f1', 'torsion': [2, 4]}
  • id: 85758
    {'degree': 8, 'field': [256, -256, 48, -56, 74, -14, 3, -4, 1], 'lmfdb_label': '1690.f1', 'torsion': [12]}
  • id: 85760
    {'degree': 12, 'field': [-16, 3288, -2568, -890, -795, 1128, 171, -366, -30, 70, -3, -6, 1], 'lmfdb_label': '1690.f1', 'torsion': [2, 6]}
  • id: 85759
    {'degree': 12, 'field': [2304, -6336, 15840, -5028, 2301, -1497, -53, 24, 24, 4, 15, -3, 1], 'lmfdb_label': '1690.f1', 'torsion': [3, 6]}
  • id: 85762
    {'degree': 16, 'field': [832, -1664, 1296, 608, -1252, 860, -114, -494, 347, -44, -57, 86, -10, 2, 9, -2, 1], 'lmfdb_label': '1690.f1', 'torsion': [8]}
  • id: 85761
    {'degree': 16, 'field': [4096, 1024, 1152, -12928, 1152, -1136, 4882, -34, 2405, -246, 84, -198, 2, -2, 2, 0, 1], 'lmfdb_label': '1690.f1', 'torsion': [4, 4]}
  • id: 85764
    {'degree': 16, 'field': [8836, 0, -22283, 0, 22087, 0, -9643, 0, 2343, 0, -329, 0, 13, 0, -1, 0, 1], 'lmfdb_label': '1690.f1', 'torsion': [2, 12]}
  • id: 85763
    {'degree': 16, 'field': [65536, -82944, 111488, -77408, 43152, -13772, 4622, -2624, 3925, -2678, 1176, -298, -22, 18, 10, -6, 1], 'lmfdb_label': '1690.f1', 'torsion': [2, 12]}
  • id: 85765
    {'degree': 18, 'field': [314706432, 546405120, 737634816, 165132000, 201216912, 48267864, 21451468, 9429768, 854442, 1169843, 37593, 40824, 13896, -2346, 1314, -184, 54, -9, 1], 'lmfdb_label': '1690.f1', '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: 26900
    {'conductor': 1690, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '1690.f1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 26901
    {'conductor': 1690, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1690.f1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 26902
    {'conductor': 1690, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '1690.f1', 'prime': 13, '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: 1675107
    {'adelic_gens': [[952, 3, 477, 1474], [1, 24, 0, 1], [1, 0, 24, 1], [7, 24, 492, 127], [1537, 24, 1536, 25], [1, 12, 12, 145], [521, 24, 520, 1], [391, 24, 12, 289], [781, 24, 780, 1], [822, 1559, 1417, 1552], [21, 4, 1460, 1541]], 'adelic_image': '1560.384.9.?', 'conductor': 1690, 'lmfdb_label': '1690.f1', 'prime': 0}
  • id: 8292
    {'conductor': 1690, 'elladic_image': '4.6.0.3', 'lmfdb_label': '1690.f1', 'modell_image': '2B', 'prime': 2}
  • id: 8293
    {'conductor': 1690, 'elladic_image': '3.4.0.1', 'lmfdb_label': '1690.f1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 1690.f does not appear in ec_padic