Elliptic curve data - 1694.e4

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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': '1694f', 'Clabel': '1694f2', 'Cnumber': 2, 'abc_quality': 0.9676277689392396, 'absD': 173612978, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 5544, 'ainvs': [1, 0, 0, -1273, -17577], 'analytic_rank': 1, 'bad_primes': [2, 7, 11], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 1694, 'degree': 960, 'elladic_images': ['8.6.0.6', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.51343632815416003821650890690', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [128787625, 98], 'lmfdb_iso': '1694.e', 'lmfdb_label': '1694.e4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -11, 12], 'min_quad_twist_disc': -11, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.b.1', '9.12.0.a.1', '18.36.0.a.1', '24.24.0.y.1', '28.6.0.c.1', '33.8.0-3.a.1.2', '56.12.0.k.1', '63.36.0.d.2', '66.24.0-6.a.1.2', '72.72.1.?', '84.24.0.?', '99.24.0.?', '126.108.2.?', '168.48.1.?', '198.72.0.?', '252.216.7.?', '264.48.0.?', '504.432.21.?', '693.72.0.?', '792.144.1.?', '924.48.0.?', '1386.216.2.?', '1848.96.1.?', '2772.432.7.?', '5544.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.7877388104792596581026099467', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.68551130824502523381446288208', 'prec': 107}, 'szpiro_ratio': 4.4467684449661435, '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, 0, -2, -1, 1, 1, 0, 0, -2, 4, -1, 0, 1, -6, 1, -2, 0], 'aplist': [1, -2, 0, -1, 0, 4, -6, -2, 0, 6, -4, 2, -6, -8, -12, 6, -6, -8, -4, 0, -2, -8, 6, -6, -10], 'class_deg': 18, 'class_size': 6, 'conductor': 1694, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '1694.e', 'trace_hash': 2247578083762146412}
• 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': '0.35812519167027493452243476848', 'prec': 103}, 'conductor': 1694, 'gens': [[403, 7099, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '3.7877388104792596581026099467', 'prec': 100}], 'lmfdb_label': '1694.e4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.79930129180542664585369427087', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0275445242376223389398066114230505597', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-81, 81, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [3, 0], '5': [1, 3, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [3, 0], '23': [1, 3, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1694.e4'}
• ec_torsion_growth •

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

  
  
  • id: 85959
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '1694.e4', 'torsion': [2, 2]}
  • id: 85960
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '1694.e4', 'torsion': [6]}
  • id: 85962
    {'degree': 4, 'field': [23, -2, 3, -2, 1], 'lmfdb_label': '1694.e4', 'torsion': [2, 6]}
  • id: 85961
    {'degree': 4, 'field': [242, 0, 11, 0, 1], 'lmfdb_label': '1694.e4', 'torsion': [4]}
  • id: 85963
    {'degree': 6, 'field': [-1338, -228, 226, 5, -15, -1, 1], 'lmfdb_label': '1694.e4', 'torsion': [6]}
  • id: 85964
    {'degree': 6, 'field': [71, -4, 29, -3, 4, -1, 1], 'lmfdb_label': '1694.e4', 'torsion': [18]}
  • id: 85967
    {'degree': 8, 'field': [324, 0, 90, 0, 23, 0, 5, 0, 1], 'lmfdb_label': '1694.e4', 'torsion': [12]}
  • id: 85965
    {'degree': 8, 'field': [784, 0, -480, 0, 70, 0, -8, 0, 1], 'lmfdb_label': '1694.e4', 'torsion': [2, 4]}
  • id: 85966
    {'degree': 8, 'field': [4489, 0, 14, 0, 106, 0, 14, 0, 1], 'lmfdb_label': '1694.e4', 'torsion': [2, 4]}
  • id: 85969
    {'degree': 12, 'field': [388, 808, 1236, 606, 832, 150, 437, 0, 117, -4, 17, 0, 1], 'lmfdb_label': '1694.e4', 'torsion': [18]}
  • id: 85968
    {'degree': 12, 'field': [1296, -6480, 11808, -5040, 1216, 24, -445, 201, 24, 21, -4, -3, 1], 'lmfdb_label': '1694.e4', 'torsion': [3, 6]}
  • id: 85970
    {'degree': 12, 'field': [2304, 0, 5376, 0, 2992, 0, -1106, 0, -312, 0, -14, 0, 1], 'lmfdb_label': '1694.e4', 'torsion': [2, 6]}
  • id: 85971
    {'degree': 12, 'field': [23017, -6468, 16070, -2186, 3607, -352, 647, -106, 82, 6, -3, -2, 1], 'lmfdb_label': '1694.e4', 'torsion': [2, 18]}
  • id: 85974
    {'degree': 16, 'field': [7393, 1796, -6610, 7272, 6936, -27704, 40326, -39864, 29029, -16896, 7986, -3064, 996, -252, 56, -8, 1], 'lmfdb_label': '1694.e4', 'torsion': [2, 12]}
  • id: 85973
    {'degree': 16, 'field': [199103, -148560, 221812, -168808, 145348, -88408, 57312, -28968, 14401, -6056, 2628, -960, 342, -112, 36, -8, 1], 'lmfdb_label': '1694.e4', 'torsion': [2, 12]}
  • id: 85972
    {'degree': 16, 'field': [1032256, 0, -1715968, 0, 860050, 0, -109252, 0, -5475, 0, 2286, 0, 156, 0, -30, 0, 1], 'lmfdb_label': '1694.e4', 'torsion': [8]}
• 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: 26968
    {'conductor': 1694, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1694.e4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 26969
    {'conductor': 1694, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1694.e4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 26970
    {'conductor': 1694, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1694.e4', 'prime': 11, '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: 1675133
    {'adelic_gens': [[1, 36, 0, 1], [4060, 4059, 561, 298], [3023, 0, 0, 5543], [1, 0, 36, 1], [5509, 36, 5508, 37], [4159, 3564, 5302, 2377], [1321, 3564, 2442, 265], [19, 36, 3240, 595], [4313, 3564, 0, 1], [1, 18, 14, 253]], 'adelic_image': '5544.864.21.?', 'conductor': 1694, 'lmfdb_label': '1694.e4', 'prime': 0}
  • id: 8321
    {'conductor': 1694, 'elladic_image': '8.6.0.6', 'lmfdb_label': '1694.e4', 'modell_image': '2B', 'prime': 2}
  • id: 8322
    {'conductor': 1694, 'elladic_image': '9.12.0.1', 'lmfdb_label': '1694.e4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 46691
    {'lmfdb_iso': '1694.e', 'p': 13, 'prec': 20, 'unit': 105898426721130192619, 'val': 1}
  • id: 46693
    {'lmfdb_iso': '1694.e', 'p': 17, 'prec': 20, 'unit': 231929144814762946066278, 'val': 1}
  • id: 46694
    {'lmfdb_iso': '1694.e', 'p': 19, 'prec': 20, 'unit': 35505556246686322247601, 'val': 2}
  • id: 46690
    {'lmfdb_iso': '1694.e', 'p': 29, 'prec': 20, 'unit': 4870879903328811682356064428, 'val': 1}
  • id: 46701
    {'lmfdb_iso': '1694.e', 'p': 31, 'prec': 20, 'unit': 21520923167555804278885719942, 'val': 1}
  • id: 46687
    {'lmfdb_iso': '1694.e', 'p': 37, 'prec': 20, 'unit': 273224145942635340144896541845, 'val': 1}
  • id: 46688
    {'lmfdb_iso': '1694.e', 'p': 41, 'prec': 20, 'unit': 2359883043272849762307047401714, 'val': 1}
  • id: 46689
    {'lmfdb_iso': '1694.e', 'p': 43, 'prec': 20, 'unit': 6881455500023729403984903881635, 'val': 1}
  • id: 46699
    {'lmfdb_iso': '1694.e', 'p': 47, 'prec': 20, 'unit': 36018152038025786098542925990563, 'val': 1}
  • id: 46695
    {'lmfdb_iso': '1694.e', 'p': 53, 'prec': 20, 'unit': 69279119903799718274345587591428, 'val': 1}
  • id: 46696
    {'lmfdb_iso': '1694.e', 'p': 59, 'prec': 20, 'unit': 198193843830817372891844295850696, 'val': 1}
  • id: 46700
    {'lmfdb_iso': '1694.e', 'p': 61, 'prec': 20, 'unit': 6109473882155979380522515250745350, 'val': 1}
  • id: 46686
    {'lmfdb_iso': '1694.e', 'p': 67, 'prec': 20, 'unit': 10580777450679191427779369432313492, 'val': 1}
  • id: 46697
    {'lmfdb_iso': '1694.e', 'p': 73, 'prec': 20, 'unit': 247891272205539239113566628449964389, 'val': 1}
  • id: 46692
    {'lmfdb_iso': '1694.e', 'p': 79, 'prec': 20, 'unit': 54427993981528232313749396866566287, 'val': 1}
  • id: 46685
    {'lmfdb_iso': '1694.e', 'p': 83, 'prec': 20, 'unit': 787393689445737862905894207964555192, 'val': 1}
  • id: 46698
    {'lmfdb_iso': '1694.e', 'p': 89, 'prec': 20, 'unit': 6205822749895243675455385452504023481, 'val': 1}
  • id: 46684
    {'lmfdb_iso': '1694.e', 'p': 97, 'prec': 20, 'unit': 48506406891033633117572143378244342400, 'val': 1}