Elliptic curve data - 52416.fj1

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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': '52416gn', 'Clabel': '52416gn4', 'Cnumber': 4, 'abc_quality': 1.087583326356874, 'absD': 1711032926733437239296, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 0, 0, -34061004, 76486945680], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 52416, 'degree': 4423680, 'elladic_images': ['8.12.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0390336823068597837859127139', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 139, 'isogeny_degrees': [1, 2, 4], 'jinv': [22868021811807457713, 8953460393696], 'lmfdb_iso': '52416.fj', 'lmfdb_label': '52416.fj1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -59134, 5547693], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.p.1', '12.12.0-4.c.1.1', '24.24.0-8.p.1.6', '56.24.0.bp.1', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.0926004791404120838951671152', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 63], [3, 6, 832], [7, 8, 7488], [13, 14, 4032]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4500067671328869739624419133', 'prec': 100}, 'szpiro_ratio': 5.856702535664275, '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, 0, 0, 2, 0, 1, 0, 0, 0, -4, 0, 1, 0, 0, 0, 6, 0, 0, 0], 'aplist': [0, 0, 2, 1, -4, 1, 6, 0, 8, -10, 8, -6, 6, 4, -8, 6, -8, -10, 4, -8, 2, -8, 0, -18, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 52416, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '52416.fj', 'trace_hash': 1327000886824306728}
• 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': '0.0022926031401067791985890482692', 'prec': 110}, 'conductor': 52416, 'gens': [[2770, 58240, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0926004791404120838951671152', 'prec': 100}], 'lmfdb_label': '52416.fj1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14673829753571117148421137935', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.6956640413967860342489007192238342348', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[3420, 0, 1]], 'xcoord_integral_points': [2770, 3420, 41445]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [2, 0], '11': [3, 0], '13': [2, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '52416.fj1'}
• ec_torsion_growth •

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

  
  
  • id: 2540046
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [4]}
  • id: 2540044
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [2, 2]}
  • id: 2540045
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [4]}
  • id: 2540047
    {'degree': 4, 'field': [49, 0, -28, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [2, 4]}
  • id: 2540051
    {'degree': 8, 'field': [-432, 0, -54, 0, 0, 0, 6, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [6]}
  • id: 2540050
    {'degree': 8, 'field': [4, 0, 10, 0, 89, 0, -16, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [8]}
  • id: 2540049
    {'degree': 8, 'field': [49, 0, -196, 0, 116, 0, -20, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [8]}
  • id: 2540048
    {'degree': 8, 'field': [196, 0, 0, 0, 14, 0, 0, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [2, 4]}
  • id: 2540056
    {'degree': 16, 'field': [9, 0, 2016, 0, 504, 0, -612, 0, -294, 0, 192, 0, 12, 0, -12, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [12]}
  • id: 2540054
    {'degree': 16, 'field': [81, 0, -756, 0, 2448, 0, -3696, 0, 2911, 0, -1232, 0, 272, 0, -28, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [2, 8]}
  • id: 2540053
    {'degree': 16, 'field': [625, 0, 488, 0, 1242, 0, 164, 0, 363, 0, 68, 0, 62, 0, 12, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [2, 8]}
  • id: 2540055
    {'degree': 16, 'field': [3136, 0, -12376, 0, 53764, 0, -72280, 0, 35596, 0, -8476, 0, 976, 0, -52, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [2, 6]}
  • id: 2540052
    {'degree': 16, 'field': [44521, 0, -43168, 0, 33656, 0, -10920, 0, 182, 0, 0, 0, 56, 0, 8, 0, 1], 'lmfdb_label': '52416.fj1', 'torsion': [4, 4]}
  • id: 2540057
    {'degree': 16, 'field': [7706176, 0, -9567040, 0, 4099696, 0, -770272, 0, 88972, 0, -6148, 0, 517, 0, -40, 0, 1], 'lmfdb_label': '52416.fj1', '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: 1256712
    {'conductor': 52416, 'conductor_valuation': 6, 'discriminant_valuation': 23, 'j_denominator_valuation': 5, 'kodaira_symbol': -17, 'lmfdb_label': '52416.fj1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1256713
    {'conductor': 52416, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '52416.fj1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1256714
    {'conductor': 52416, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '52416.fj1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1256715
    {'conductor': 52416, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '52416.fj1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

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

  
  
  • id: 2012474
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [7, 6, 162, 163], [161, 8, 160, 9], [124, 57, 111, 118], [104, 69, 87, 2], [1, 4, 4, 17], [32, 111, 63, 128], [55, 0, 0, 167]], 'adelic_image': '168.48.0.?', 'conductor': 52416, 'lmfdb_label': '52416.fj1', 'prime': 0}
  • id: 224313
    {'conductor': 52416, 'elladic_image': '8.12.0.9', 'lmfdb_label': '52416.fj1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2641499
    {'lmfdb_iso': '52416.fj', 'p': 5, 'prec': 20, 'unit': 6404272776156, 'val': 1}
  • id: 2641498
    {'lmfdb_iso': '52416.fj', 'p': 11, 'prec': 20, 'unit': 5134108310262019494, 'val': 2}
  • id: 2641506
    {'lmfdb_iso': '52416.fj', 'p': 17, 'prec': 20, 'unit': 233889892094359644776625, 'val': 1}
  • id: 2641511
    {'lmfdb_iso': '52416.fj', 'p': 23, 'prec': 20, 'unit': 68789469566725889230226658, 'val': 1}
  • id: 2641504
    {'lmfdb_iso': '52416.fj', 'p': 29, 'prec': 20, 'unit': 3909753788986551515938603363, 'val': 1}
  • id: 2641501
    {'lmfdb_iso': '52416.fj', 'p': 31, 'prec': 20, 'unit': 21524244251114226086491739672, 'val': 1}
  • id: 2641515
    {'lmfdb_iso': '52416.fj', 'p': 37, 'prec': 20, 'unit': 196934342428742846698809779115, 'val': 1}
  • id: 2641502
    {'lmfdb_iso': '52416.fj', 'p': 41, 'prec': 20, 'unit': 764588018355457900046174462818, 'val': 1}
  • id: 2641503
    {'lmfdb_iso': '52416.fj', 'p': 43, 'prec': 20, 'unit': 4614612224124059217393376306347, 'val': 1}
  • id: 2641513
    {'lmfdb_iso': '52416.fj', 'p': 47, 'prec': 20, 'unit': 55441437810887221543168913819590, 'val': 1}
  • id: 2641508
    {'lmfdb_iso': '52416.fj', 'p': 53, 'prec': 20, 'unit': 316080562255718933604851025796905, 'val': 1}
  • id: 2641509
    {'lmfdb_iso': '52416.fj', 'p': 59, 'prec': 20, 'unit': 3187099604904108160510181463229914, 'val': 1}
  • id: 2641514
    {'lmfdb_iso': '52416.fj', 'p': 61, 'prec': 20, 'unit': 3167446872745886890691141945687049, 'val': 1}
  • id: 2641507
    {'lmfdb_iso': '52416.fj', 'p': 67, 'prec': 20, 'unit': 23925798674135815176920043283331368, 'val': 1}
  • id: 2641500
    {'lmfdb_iso': '52416.fj', 'p': 71, 'prec': 20, 'unit': 55446231760507714118889280684441239, 'val': 1}
  • id: 2641510
    {'lmfdb_iso': '52416.fj', 'p': 73, 'prec': 20, 'unit': 56658542529289114594276411856802780, 'val': 1}
  • id: 2641505
    {'lmfdb_iso': '52416.fj', 'p': 79, 'prec': 20, 'unit': 595975591591771579056763573850420364, 'val': 1}
  • id: 2641512
    {'lmfdb_iso': '52416.fj', 'p': 89, 'prec': 20, 'unit': 9374171552025243047390954520143035782, 'val': 1}
  • id: 2641497
    {'lmfdb_iso': '52416.fj', 'p': 97, 'prec': 20, 'unit': 42752528621138560753720118283718113, 'val': 2}