Elliptic curve data - 1690.e1

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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': '1690e', 'Clabel': '1690e1', 'Cnumber': 1, 'abc_quality': 0.9795846641235626, 'absD': 50198813600000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 520, 'ainvs': [1, 1, 0, -142132, -20681136], 'analytic_rank': 0, 'bad_primes': [2, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1690, 'degree': 13440, 'elladic_images': ['4.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6394255894137786361689688850', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [65787589563409, 10400000], 'lmfdb_iso': '1690.e', 'lmfdb_label': '1690.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -841, -9737], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.b.1', '40.12.0-4.b.1.4', '104.12.0.?', '130.6.0.?', '260.24.0.?', '520.48.0.?'], '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, 4, 845], [5, 6, 338], [13, 98, 10]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.35695091068301026814222516422', 'prec': 103}, 'szpiro_ratio': 6.351463345604078, '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, 2, 2, 0, -4, 2, 1, 2, -1, -6, 1], 'aplist': [-1, 2, 1, 4, 2, 0, 2, -6, 6, 2, 6, 2, -10, -10, 12, 2, -10, 2, 12, -10, -10, -4, 0, 14, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 1690, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1690.e', 'trace_hash': 728748789144977232}
• 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': '0.037671509785489964594259507658', 'prec': 107}, 'conductor': 1690, 'gens': [], 'heights': [], 'lmfdb_label': '1690.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.24588402276127733405466664147', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4588402276127733405466664146717231226', 'prec': 130}, 'tamagawa_product': 40, 'torsion_generators': [[-216, 108, 1]], 'xcoord_integral_points': [-216]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [0, 0], '5': [1, 0], '13': 'a'}, 'iwp0': 7, 'lmfdb_label': '1690.e1'}
• ec_torsion_growth •

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

  
  
  • id: 85707
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '1690.e1', 'torsion': [2, 2]}
  • id: 85708
    {'degree': 4, 'field': [5, -2, -3, 0, 1], 'lmfdb_label': '1690.e1', 'torsion': [4]}
  • id: 85711
    {'degree': 8, 'field': [-10, -35, 50, -31, 19, -7, 7, -4, 1], 'lmfdb_label': '1690.e1', 'torsion': [6]}
  • id: 85710
    {'degree': 8, 'field': [-10, 60, -115, 45, 71, -16, -19, -1, 1], 'lmfdb_label': '1690.e1', 'torsion': [2, 4]}
  • id: 85709
    {'degree': 8, 'field': [196, -84, 18, -62, 29, -2, 8, -4, 1], 'lmfdb_label': '1690.e1', 'torsion': [2, 4]}
  • id: 85712
    {'degree': 16, 'field': [100, 0, 1300, 0, 6405, 0, 16055, 0, 10951, 0, 3094, 0, 471, 0, 39, 0, 1], 'lmfdb_label': '1690.e1', 'torsion': [4, 4]}
  • id: 85713
    {'degree': 16, 'field': [1745, 4860, -1236, -8848, 6837, 13864, -8574, -9272, 9288, -1408, -770, 136, 125, -20, -4, 0, 1], 'lmfdb_label': '1690.e1', 'torsion': [8]}
  • id: 85714
    {'degree': 16, 'field': [2304, 0, -362532, 0, -115340, 0, 66996, 0, 23685, 0, 1004, 0, -342, 0, 0, 0, 1], 'lmfdb_label': '1690.e1', 'torsion': [2, 6]}
• 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: 26888
    {'conductor': 1690, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '1690.e1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 26889
    {'conductor': 1690, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '1690.e1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 26890
    {'conductor': 1690, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1690.e1', 'prime': 13, '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: 1675105
    {'adelic_gens': [[513, 8, 512, 9], [1, 0, 8, 1], [192, 517, 315, 518], [1, 8, 0, 1], [422, 1, 231, 4], [1, 4, 4, 17], [3, 8, 28, 75], [391, 8, 264, 33], [5, 8, 48, 77], [261, 8, 0, 1]], 'adelic_image': '520.48.0.?', 'conductor': 1690, 'lmfdb_label': '1690.e1', 'prime': 0}
  • id: 8290
    {'conductor': 1690, 'elladic_image': '4.6.0.3', 'lmfdb_label': '1690.e1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1690.e does not appear in ec_padic