Elliptic curve data - 394944.k4

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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': '394944k', 'Clabel': '394944k1', 'Cnumber': 1, 'abc_quality': 0.9867709317256699, 'absD': 2307877284672795995799552, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1496, 'ainvs': [0, -1, 0, -45279329, 91724697825], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 394944, 'degree': 61931520, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3877889408850080629615445665', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [22106889268753393, 4969545596928], 'lmfdb_iso': '394944.k', 'lmfdb_label': '394944.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -5847, -135063], 'min_quad_twist_disc': -88, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '34.6.0.a.1', '68.12.0.g.1', '88.24.0.?', '136.24.0.?', '1496.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 2057], [3, 4, 131648], [11, 72, 3264], [17, 18, 23232]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1491205336459048268047245953', 'prec': 100}, 'szpiro_ratio': 5.00513640389026, '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, 0, -1, 0, -2, 0, -4, 0, 1, 0, 0, 0, -2, 0, 2, 0, -1, 0, -4, 0], 'aplist': [0, -1, -2, -4, 0, -2, -1, -4, -4, 2, -4, 6, 6, -4, 0, -6, -4, -6, 4, 4, -10, -4, 12, -6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 394944, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '394944.k', 'trace_hash': 1479757911635522481}
• 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': '0.0011413107666580715472213437305', 'prec': 110}, 'conductor': 394944, 'gens': [], 'heights': [], 'lmfdb_label': '394944.k4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.077198093213810226303500342113', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.30879237285524090521400136845036446347', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-7575, 0, 1]], 'xcoord_integral_points': [-7575]}
• lmfdb_label 394944.k4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16302474
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '394944.k4', 'torsion': [2, 2]}
  • id: 16302475
    {'degree': 2, 'field': [22, 0, 1], 'lmfdb_label': '394944.k4', 'torsion': [4]}
  • id: 16302476
    {'degree': 2, 'field': [374, 0, 1], 'lmfdb_label': '394944.k4', 'torsion': [4]}
  • id: 16302477
    {'degree': 4, 'field': [698, -36, 37, -2, 1], 'lmfdb_label': '394944.k4', 'torsion': [2, 4]}
  • id: 16302481
    {'degree': 8, 'field': [-9763248, 0, 51040, 0, -10824, 0, 0, 0, 1], 'lmfdb_label': '394944.k4', 'torsion': [6]}
  • id: 16302478
    {'degree': 8, 'field': [64, 0, -3190, 0, 105, 0, -22, 0, 1], 'lmfdb_label': '394944.k4', 'torsion': [2, 4]}
  • id: 16302479
    {'degree': 8, 'field': [262, -212, 506, -620, 391, -100, 38, -4, 1], 'lmfdb_label': '394944.k4', 'torsion': [8]}
  • id: 16302480
    {'degree': 8, 'field': [1296, 0, 3752, 0, 889, 0, 62, 0, 1], 'lmfdb_label': '394944.k4', 'torsion': [8]}
  • id: 16302483
    {'degree': 16, 'field': [35344, 0, -3824, 0, 60076, 0, 34308, 0, 33417, 0, 8808, 0, 1018, 0, 52, 0, 1], 'lmfdb_label': '394944.k4', 'torsion': [2, 8]}
  • id: 16302484
    {'degree': 16, 'field': [713542, -275964, -547582, 668764, 922443, -465060, 282858, -308108, 131349, -52884, 24046, -5100, 1937, -236, 70, -4, 1], 'lmfdb_label': '394944.k4', 'torsion': [2, 8]}
  • id: 16302482
    {'degree': 16, 'field': [9253764, 0, 19602648, 0, 9572112, 0, 75348, 0, 86413, 0, 13936, 0, 942, 0, 52, 0, 1], 'lmfdb_label': '394944.k4', 'torsion': [4, 4]}
  • id: 16302486
    {'degree': 16, 'field': [18664149416, -40101665648, 45592664572, -11408498280, 6790479730, -1360057384, 549581161, -86379272, 26562672, -3462566, 845741, -86860, 17237, -1302, 206, -8, 1], 'lmfdb_label': '394944.k4', 'torsion': [12]}
  • id: 16302485
    {'degree': 16, 'field': [95988142586576, -4415470056320, 4618066324768, -399809727232, 186557654360, 15709287360, -4724531360, -437952544, 108316841, 1014584, -437076, 128264, -21802, 168, -4, -8, 1], 'lmfdb_label': '394944.k4', 'torsion': [2, 6]}
  • id: 16302487
    {'degree': 16, 'field': [349204865976576, 0, 37702105053696, 0, 795502828800, 0, -12348218880, 0, 179079072, 0, 1922848, 0, 3648, 0, 0, 0, 1], 'lmfdb_label': '394944.k4', 'torsion': [12]}
• 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: 9767650
    {'conductor': 394944, 'conductor_valuation': 6, 'discriminant_valuation': 46, 'j_denominator_valuation': 28, 'kodaira_symbol': -40, 'lmfdb_label': '394944.k4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 9767651
    {'conductor': 394944, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '394944.k4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9767652
    {'conductor': 394944, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '394944.k4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9767653
    {'conductor': 394944, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '394944.k4', 'prime': 17, '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: 4114795
    {'adelic_gens': [[1087, 0, 0, 1495], [1165, 1034, 726, 1341], [1, 0, 8, 1], [89, 88, 1254, 639], [1489, 8, 1488, 9], [7, 6, 1490, 1491], [12, 1089, 1463, 958], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '1496.48.0.?', 'conductor': 394944, 'lmfdb_label': '394944.k4', 'prime': 0}
  • id: 1344883
    {'conductor': 394944, 'elladic_image': '8.12.0.11', 'lmfdb_label': '394944.k4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 394944.k does not appear in ec_padic