Elliptic curve data - 17689.e2

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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': '17689h', 'Clabel': '17689h3', 'Cnumber': 3, 'abc_quality': 0.9802957926219806, 'absD': 1898470992842767, 'ainvs': [1, -1, 1, -38695, -3592802], 'analytic_rank': 1, 'bad_primes': [7, 19], 'class_deg': 14, 'class_size': 4, 'cm': -7, 'conductor': 17689, 'degree': 50400, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6460361750552544654328783779', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 7, 'intrinsic_torsion': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [-3375, 1], 'lmfdb_iso': '17689.e', 'lmfdb_label': '17689.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -2, -1], 'min_quad_twist_disc': 133, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '18.112724879058550287399884762', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 2527], [7, 20, 361], [19, 182, 49]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2856159263194507434006498956', 'prec': 103}, 'szpiro_ratio': 4.469763604940933, '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, 0, -1, 0, 0, 0, 3, -3, 0, 4, 0, 0, 0, 0, -1, 0, 3, 0, 0], 'aplist': [-1, 0, 0, 0, 4, 0, 0, 0, 8, -2, 0, 6, 0, -12, 0, 10, 0, 0, -4, -16, 0, -8, 0, 0, 0], 'class_deg': 14, 'class_size': 4, 'conductor': 17689, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '17689.e', 'trace_hash': 751386599024126472}
• 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': '0.037176726317913885236828548633', 'prec': 107}, 'conductor': 17689, 'gens': [[1227911624, 41587462694622, 1063]], 'heights': [{'__RealLiteral__': 0, 'data': '18.112724879058550287399884762', 'prec': 100}], 'lmfdb_label': '17689.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16763938541380179012307704401', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0364060668946527281325121913591304636', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[233, -117, 1]], 'xcoord_integral_points': [233]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'o?', '3': [3, 1, 0], '5': [1, 1, 0], '7': 'a', '11': [1, 0], '13': [1, 1, 0], '17': [1, 1, 0], '19': 'a', '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '17689.e2'}
• ec_torsion_growth •

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

  
  
  • id: 905762
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '17689.e2', 'torsion': [2, 2]}
  • id: 905763
    {'degree': 4, 'field': [-563, -130, -2, -2, 1], 'lmfdb_label': '17689.e2', 'torsion': [4]}
  • id: 905764
    {'degree': 4, 'field': [632, 66, -32, -1, 1], 'lmfdb_label': '17689.e2', 'torsion': [2, 4]}
  • id: 905765
    {'degree': 6, 'field': [239, -16, 75, -7, 10, -1, 1], 'lmfdb_label': '17689.e2', 'torsion': [14]}
  • id: 905768
    {'degree': 8, 'field': [-74549, 15430, -17849, 3043, -1148, 100, 1, -2, 1], 'lmfdb_label': '17689.e2', 'torsion': [6]}
  • id: 905766
    {'degree': 8, 'field': [30276, -11832, 2312, -416, 349, -66, 2, -2, 1], 'lmfdb_label': '17689.e2', 'torsion': [4, 4]}
  • id: 905767
    {'degree': 8, 'field': [99856, 0, 20507, 0, 1721, 0, 67, 0, 1], 'lmfdb_label': '17689.e2', 'torsion': [2, 8]}
  • id: 905769
    {'degree': 12, 'field': [15625, -3125, -2500, 1125, 275, -280, 1, -56, 11, 9, -4, -1, 1], 'lmfdb_label': '17689.e2', 'torsion': [2, 14]}
  • id: 905771
    {'degree': 16, 'field': [628029256, -3182552, 17932044, -29771644, 15724866, -1448336, 1221556, -641170, 174689, -16590, 10358, -3918, 744, -70, 30, -8, 1], 'lmfdb_label': '17689.e2', 'torsion': [4, 8]}
  • id: 905770
    {'degree': 16, 'field': [902837636, -53494552, 35202228, 37687856, -21527046, 3010008, -654170, -297212, 68829, 8064, -5894, 2148, -176, -112, 36, -8, 1], 'lmfdb_label': '17689.e2', 'torsion': [8]}
  • id: 905772
    {'degree': 16, 'field': [1617567961, 0, 897217187, 0, 190539084, 0, 20524655, 0, 1494906, 0, 78027, 0, 2844, 0, 71, 0, 1], 'lmfdb_label': '17689.e2', 'torsion': [2, 16]}
  • id: 905773
    {'degree': 16, 'field': [5557553401, -1150291070, -1092540201, 178295144, 186051059, -26342127, -12922901, 240964, 1044282, -69758, -18464, -1449, 1349, -202, 3, -2, 1], 'lmfdb_label': '17689.e2', 'torsion': [6, 6]}
  • id: 905774
    {'degree': 20, 'field': [964658227471, -399048852098, 106836459007, -25819961020, 23164696201, -1350280281, 101111009, -13194435, 46160552, 10604317, 1940277, -126135, 225499, -14490, -3202, -3504, -242, 72, 0, -2, 1], 'lmfdb_label': '17689.e2', 'torsion': [2, 22]}
• 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: 396052
    {'conductor': 17689, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '17689.e2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 396053
    {'conductor': 17689, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '17689.e2', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 17689.e2 does not appear in ec_galrep
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 809867
    {'lmfdb_iso': '17689.e', 'p': 11, 'prec': 20, 'unit': 24061028633728794175, 'val': 1}
  • id: 809869
    {'lmfdb_iso': '17689.e', 'p': 23, 'prec': 20, 'unit': 13324299080350237323124663, 'val': 1}
  • id: 809870
    {'lmfdb_iso': '17689.e', 'p': 29, 'prec': 20, 'unit': 715415921969575350990724852, 'val': 1}
  • id: 809863
    {'lmfdb_iso': '17689.e', 'p': 37, 'prec': 20, 'unit': 400496010777342256369790407089, 'val': 1}
  • id: 809865
    {'lmfdb_iso': '17689.e', 'p': 43, 'prec': 20, 'unit': 2547907712410828971512238520129, 'val': 1}
  • id: 809868
    {'lmfdb_iso': '17689.e', 'p': 53, 'prec': 20, 'unit': 432992877826973903703987317568167, 'val': 1}
  • id: 809862
    {'lmfdb_iso': '17689.e', 'p': 67, 'prec': 20, 'unit': 30276598107898751102579516084174833, 'val': 1}
  • id: 809864
    {'lmfdb_iso': '17689.e', 'p': 71, 'prec': 20, 'unit': 29776712410656331350264963159804559, 'val': 1}
  • id: 809866
    {'lmfdb_iso': '17689.e', 'p': 79, 'prec': 20, 'unit': 933145214863650869443703455850501786, 'val': 1}