Elliptic curve data - 4719.k1

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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': '4719j', 'Clabel': '4719j3', 'Cnumber': 3, 'abc_quality': 0.9895637859915349, 'absD': 2279999007, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 6864, 'ainvs': [1, 0, 1, -830547, -291405149], 'analytic_rank': 1, 'bad_primes': [3, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4719, 'degree': 30720, 'elladic_images': ['16.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7400432753061000934007294042', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [35765103905346817, 1287], 'lmfdb_iso': '4719.k', 'lmfdb_label': '4719.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -6864, 218313], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.5', '24.24.0-8.n.1.8', '44.12.0-4.c.1.2', '48.48.0-48.g.1.1', '52.12.0-4.c.1.1', '88.24.0.?', '104.24.0.?', '176.48.0.?', '208.48.0.?', '264.48.0.?', '312.48.0.?', '528.96.0.?', '572.24.0.?', '624.96.0.?', '1144.48.0.?', '2288.96.0.?', '3432.96.0.?', '6864.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '14.990294410579169839749470444', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.54109563890691482136975761522', 'prec': 103}, 'szpiro_ratio': 6.206517887957384, '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, 1, -1, -2, 1, 0, -3, 1, -2, 0, -1, -1, 0, -2, -1, 6, 1, 4, 2], 'aplist': [1, 1, -2, 0, 0, -1, 6, 4, -8, 10, 0, 6, -10, -4, 8, -10, -12, -14, -12, 0, 6, -8, -12, 2, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 4719, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '4719.k', 'trace_hash': 741914974426684793}
• 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': '0.030804744747851848019340200878', 'prec': 107}, 'conductor': 4719, 'gens': [[3837119, 2946422025, 58]], 'heights': [{'__RealLiteral__': 0, 'data': '14.990294410579169839749470444', 'prec': 100}], 'lmfdb_label': '4719.k1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.15814612821832793321081735453', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7413140437718758889883538722168516374', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-2105, 2101, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': [4, 0], '5': [1, 0], '7': [1, 1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [3, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4719.k1'}
• ec_torsion_growth •

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

  
  
  • id: 245493
    {'degree': 2, 'field': [-143, 0, 1], 'lmfdb_label': '4719.k1', 'torsion': [2, 2]}
  • id: 245495
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '4719.k1', 'torsion': [4]}
  • id: 245494
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '4719.k1', 'torsion': [4]}
  • id: 245497
    {'degree': 4, 'field': [9, -3, -2, -1, 1], 'lmfdb_label': '4719.k1', 'torsion': [8]}
  • id: 245496
    {'degree': 4, 'field': [113, -32, 33, -2, 1], 'lmfdb_label': '4719.k1', 'torsion': [2, 4]}
  • id: 245498
    {'degree': 4, 'field': [1725, 72, -71, -2, 1], 'lmfdb_label': '4719.k1', 'torsion': [8]}
  • id: 245503
    {'degree': 8, 'field': [-249, 321, -366, 89, -41, -7, 7, -4, 1], 'lmfdb_label': '4719.k1', 'torsion': [6]}
  • id: 245501
    {'degree': 8, 'field': [42916, 8524, -8054, -926, 429, 38, -8, -4, 1], 'lmfdb_label': '4719.k1', 'torsion': [2, 8]}
  • id: 245500
    {'degree': 8, 'field': [103684, 0, -2788, 0, 2933, 0, 2, 0, 1], 'lmfdb_label': '4719.k1', 'torsion': [8]}
  • id: 245499
    {'degree': 8, 'field': [1616553, 51588, -54108, 5052, -2555, 32, -6, -4, 1], 'lmfdb_label': '4719.k1', 'torsion': [2, 4]}
  • id: 245502
    {'degree': 8, 'field': [1656369, 0, -169884, 0, 6897, 0, -132, 0, 1], 'lmfdb_label': '4719.k1', 'torsion': [16]}
  • id: 245510
    {'degree': 16, 'field': [23409, 0, -36693, 0, -6696, 0, 16871, 0, 6665, 0, 1097, 0, 211, 0, 22, 0, 1], 'lmfdb_label': '4719.k1', 'torsion': [12]}
  • id: 245509
    {'degree': 16, 'field': [20820969, 0, 10143549, 0, -419796, 0, 237445, 0, 98189, 0, -1313, 0, 403, 0, 26, 0, 1], 'lmfdb_label': '4719.k1', 'torsion': [12]}
  • id: 245505
    {'degree': 16, 'field': [381381841, 0, -151946360, 0, 16438330, 0, 1612260, 0, 236043, 0, -3900, 0, -386, 0, -20, 0, 1], 'lmfdb_label': '4719.k1', 'torsion': [2, 8]}
  • id: 245507
    {'degree': 16, 'field': [11322593649, 2483369910, -4298522598, -929137356, 776399745, 149022930, -83929158, -13946298, 6145840, 850504, -313696, -36374, 11605, 656, -184, -4, 1], 'lmfdb_label': '4719.k1', 'torsion': [2, 16]}
  • id: 245508
    {'degree': 16, 'field': [11334946913, 3329903216, -3221419749, -250522482, 208666590, -98574606, 29859961, 3541768, -2133411, 883540, -228221, 28020, -4579, -70, 30, -8, 1], 'lmfdb_label': '4719.k1', 'torsion': [2, 6]}
  • id: 245506
    {'degree': 16, 'field': [15178486401, 0, 0, 0, 168169365, 0, 0, 0, 766584, 0, 0, 0, 1365, 0, 0, 0, 1], 'lmfdb_label': '4719.k1', 'torsion': [16]}
  • id: 245504
    {'degree': 16, 'field': [2714061848481, 0, -126044135640, 0, -6262691670, 0, 161818020, 0, 10927867, 0, -26780, 0, -4962, 0, -20, 0, 1], 'lmfdb_label': '4719.k1', 'torsion': [4, 4]}
• 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: 90368
    {'conductor': 4719, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4719.k1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 90369
    {'conductor': 4719, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '4719.k1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 90370
    {'conductor': 4719, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4719.k1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1694693
    {'adelic_gens': [[4589, 16, 2032, 6549], [1, 16, 1724, 1845], [4298, 5159, 2491, 3318], [6849, 16, 6848, 17], [1, 16, 0, 1], [15, 2, 6766, 6851], [5, 4, 6860, 6861], [536, 1, 2719, 10], [1, 0, 16, 1], [5600, 6859, 4413, 14]], 'adelic_image': '6864.192.1.?', 'conductor': 4719, 'lmfdb_label': '4719.k1', 'prime': 0}
  • id: 23348
    {'conductor': 4719, 'elladic_image': '16.24.0.3', 'lmfdb_label': '4719.k1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 171501
    {'lmfdb_iso': '4719.k', 'p': 5, 'prec': 20, 'unit': 742792485376, 'val': 1}
  • id: 171492
    {'lmfdb_iso': '4719.k', 'p': 17, 'prec': 20, 'unit': 167747349772048937989442, 'val': 1}
  • id: 171484
    {'lmfdb_iso': '4719.k', 'p': 19, 'prec': 20, 'unit': 361572533176156245374551, 'val': 1}
  • id: 171497
    {'lmfdb_iso': '4719.k', 'p': 23, 'prec': 20, 'unit': 766620561591255482979232, 'val': 1}
  • id: 171490
    {'lmfdb_iso': '4719.k', 'p': 29, 'prec': 20, 'unit': 2620779449757387275758613131, 'val': 1}
  • id: 171487
    {'lmfdb_iso': '4719.k', 'p': 37, 'prec': 20, 'unit': 6878422962412513594009459885, 'val': 2}
  • id: 171488
    {'lmfdb_iso': '4719.k', 'p': 41, 'prec': 20, 'unit': 3186340724563978299196351190170, 'val': 1}
  • id: 171489
    {'lmfdb_iso': '4719.k', 'p': 43, 'prec': 20, 'unit': 5330973967931442074548474562300, 'val': 1}
  • id: 171499
    {'lmfdb_iso': '4719.k', 'p': 47, 'prec': 20, 'unit': 44564685393837090230289855356657, 'val': 1}
  • id: 171494
    {'lmfdb_iso': '4719.k', 'p': 53, 'prec': 20, 'unit': 349528728002746683299528243785551, 'val': 1}
  • id: 171495
    {'lmfdb_iso': '4719.k', 'p': 59, 'prec': 20, 'unit': 1055295318150835112560012409242345, 'val': 1}
  • id: 171500
    {'lmfdb_iso': '4719.k', 'p': 61, 'prec': 20, 'unit': 1280807151151372366946115011862646, 'val': 1}
  • id: 171486
    {'lmfdb_iso': '4719.k', 'p': 67, 'prec': 20, 'unit': 34337456980664284194317093940565703, 'val': 1}
  • id: 171496
    {'lmfdb_iso': '4719.k', 'p': 73, 'prec': 20, 'unit': 93490783076897516849584059697004465, 'val': 1}
  • id: 171491
    {'lmfdb_iso': '4719.k', 'p': 79, 'prec': 20, 'unit': 13292785715240895354501152418547523, 'val': 1}
  • id: 171493
    {'lmfdb_iso': '4719.k', 'p': 83, 'prec': 20, 'unit': 2447792631941917451962196781707786989, 'val': 1}
  • id: 171498
    {'lmfdb_iso': '4719.k', 'p': 89, 'prec': 20, 'unit': 4968717094116823419987768344306938405, 'val': 1}
  • id: 171485
    {'lmfdb_iso': '4719.k', 'p': 97, 'prec': 20, 'unit': 46481452340786538727310128949855069374, 'val': 1}