Elliptic curve data - 119952.bx5

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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': '119952gs', 'Clabel': '119952gs1', 'Cnumber': 1, 'abc_quality': 1.0214246831520672, 'absD': 19485955778292453224742912, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 5712, 'ainvs': [0, 0, 0, -495641811, -4241860146286], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 119952, 'degree': 35389440, 'elladic_images': ['16.48.0.102'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7548165979047566060764900506', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 49, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [38331145780597164097, 55468445663232], 'lmfdb_iso': '119952.bx', 'lmfdb_label': '119952.bx5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -70244, 7127525], 'min_quad_twist_disc': -84, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '16.48.0.z.1', '34.6.0.a.1', '68.12.0.g.1', '84.12.0.?', '136.48.0.?', '168.48.0.?', '272.96.1.?', '336.96.0.?', '1428.24.0.?', '2856.96.0.?', '5712.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '56.790984329630032872421113022', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 7497], [3, 8, 13328], [7, 32, 2448], [17, 18, 7056]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5394081984830997984089589390', 'prec': 100}, 'szpiro_ratio': 6.12899814725959, '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, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 1, 0, 4, 0], 'aplist': [0, 0, -2, 0, 4, 2, 1, 4, 8, -6, 0, -2, 10, 4, 0, -6, 4, -6, 12, -8, 6, 0, 12, -6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 119952, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '119952.bx', 'trace_hash': 777727554865656218}
• 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': '0.00054778198059383685885438451507', 'prec': 113}, 'conductor': 119952, 'gens': [[-79280229889948206500749879, 13402836570688640595309510708376846331, 77519056280]], 'heights': [{'__RealLiteral__': 0, 'data': '56.790984329630032872421113022', 'prec': 100}], 'lmfdb_label': '119952.bx5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.031999656259619934355882764974', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.2691679087744931314027336456092740545', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-13223, 0, 1]], 'xcoord_integral_points': [-13223]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [4, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '119952.bx5'}
• ec_torsion_growth •

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

  
  
  • id: 5486077
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '119952.bx5', 'torsion': [2, 2]}
  • id: 5486079
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '119952.bx5', 'torsion': [8]}
  • id: 5486078
    {'degree': 2, 'field': [357, 0, 1], 'lmfdb_label': '119952.bx5', 'torsion': [4]}
  • id: 5486080
    {'degree': 4, 'field': [646, -34, 35, -2, 1], 'lmfdb_label': '119952.bx5', 'torsion': [2, 8]}
  • id: 5486084
    {'degree': 8, 'field': [-84672, 0, -2268, 0, 2961, 0, -98, 0, 1], 'lmfdb_label': '119952.bx5', 'torsion': [6]}
  • id: 5486081
    {'degree': 8, 'field': [-293, 1588, -1472, -212, 57, 56, -14, -4, 1], 'lmfdb_label': '119952.bx5', 'torsion': [2, 4]}
  • id: 5486083
    {'degree': 8, 'field': [238, 420, 22, 48, 303, -12, 34, 0, 1], 'lmfdb_label': '119952.bx5', 'torsion': [16]}
  • id: 5486082
    {'degree': 8, 'field': [7413, 3570, 268, -646, 193, -34, -4, 0, 1], 'lmfdb_label': '119952.bx5', 'torsion': [8]}
  • id: 5486086
    {'degree': 16, 'field': [648958, 1192380, 1183490, 532596, 487819, 720308, 687170, 297588, 59505, -1436, -3034, 284, 485, 44, -10, -4, 1], 'lmfdb_label': '119952.bx5', 'torsion': [2, 16]}
  • id: 5486085
    {'degree': 16, 'field': [1212201, 0, -1141980, 0, 593170, 0, -148060, 0, 41907, 0, -7460, 0, 738, 0, -40, 0, 1], 'lmfdb_label': '119952.bx5', 'torsion': [4, 8]}
  • id: 5486088
    {'degree': 16, 'field': [23686441, -32028950, 33311026, -11270358, 1821320, 1085620, 130416, -135034, 61657, 15820, -3096, -1666, 536, 66, -26, -4, 1], 'lmfdb_label': '119952.bx5', 'torsion': [16]}
  • id: 5486091
    {'degree': 16, 'field': [152473104, 0, 30163077, 0, 1581426, 0, 4372515, 0, 555219, 0, 4431, 0, 567, 0, 42, 0, 1], 'lmfdb_label': '119952.bx5', 'torsion': [24]}
  • id: 5486087
    {'degree': 16, 'field': [270207844, 0, -37003784, 0, 53805880, 0, 15892492, 0, 3227365, 0, 243880, 0, 8674, 0, 148, 0, 1], 'lmfdb_label': '119952.bx5', 'torsion': [2, 16]}
  • id: 5486089
    {'degree': 16, 'field': [448084224, 0, -3250611, 0, -143945928, 0, 11385738, 0, -4012659, 0, 299481, 0, -6678, 0, 0, 0, 1], 'lmfdb_label': '119952.bx5', 'torsion': [2, 6]}
  • id: 5486090
    {'degree': 16, 'field': [2778391282321, -27862707022, 217533603491, 24282590934, 50968388585, -1623366992, 264638210, -43774012, -2005962, 11108, -83162, -81464, 5589, 538, -49, -2, 1], 'lmfdb_label': '119952.bx5', '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: 2952737
    {'conductor': 119952, 'conductor_valuation': 4, 'discriminant_valuation': 36, 'j_denominator_valuation': 24, 'kodaira_symbol': -32, 'lmfdb_label': '119952.bx5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2952738
    {'conductor': 119952, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '119952.bx5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2952739
    {'conductor': 119952, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '119952.bx5', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2952740
    {'conductor': 119952, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '119952.bx5', '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: 2447056
    {'adelic_gens': [[1903, 0, 0, 5711], [568, 273, 5439, 2458], [3695, 1344, 2478, 4241], [1, 16, 0, 1], [5697, 16, 5696, 17], [1, 4368, 1428, 1429], [2447, 0, 0, 5711], [1, 0, 16, 1], [15, 2, 5614, 5699], [5, 4, 5708, 5709]], 'adelic_image': '5712.192.1.?', 'conductor': 119952, 'lmfdb_label': '119952.bx5', 'prime': 0}
  • id: 471447
    {'conductor': 119952, 'elladic_image': '16.48.0.102', 'lmfdb_label': '119952.bx5', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 6269983
    {'lmfdb_iso': '119952.bx', 'p': 5, 'prec': 20, 'unit': 8124719341959, 'val': 1}
  • id: 6269989
    {'lmfdb_iso': '119952.bx', 'p': 11, 'prec': 20, 'unit': 10641412975759558417, 'val': 1}
  • id: 6269987
    {'lmfdb_iso': '119952.bx', 'p': 13, 'prec': 20, 'unit': 1206281286607851929454, 'val': 1}
  • id: 6269990
    {'lmfdb_iso': '119952.bx', 'p': 19, 'prec': 20, 'unit': 763352270582781770449186, 'val': 1}
  • id: 6269993
    {'lmfdb_iso': '119952.bx', 'p': 23, 'prec': 20, 'unit': 66016405342046055367567909, 'val': 1}
  • id: 6269988
    {'lmfdb_iso': '119952.bx', 'p': 29, 'prec': 20, 'unit': 1408969820756135299224462057, 'val': 1}
  • id: 6269997
    {'lmfdb_iso': '119952.bx', 'p': 37, 'prec': 20, 'unit': 586613683561783530376947774293, 'val': 1}
  • id: 6269985
    {'lmfdb_iso': '119952.bx', 'p': 41, 'prec': 20, 'unit': 3655924756477255056162337540035, 'val': 1}
  • id: 6269986
    {'lmfdb_iso': '119952.bx', 'p': 43, 'prec': 20, 'unit': 5164911611246249340017400249191, 'val': 1}
  • id: 6269991
    {'lmfdb_iso': '119952.bx', 'p': 53, 'prec': 20, 'unit': 58350388188919975343522054929949, 'val': 1}
  • id: 6269995
    {'lmfdb_iso': '119952.bx', 'p': 59, 'prec': 20, 'unit': 3658045368875657108071825074038754, 'val': 1}
  • id: 6269996
    {'lmfdb_iso': '119952.bx', 'p': 61, 'prec': 20, 'unit': 7110999496677421534583240272016299, 'val': 1}
  • id: 6269982
    {'lmfdb_iso': '119952.bx', 'p': 67, 'prec': 20, 'unit': 9355659966709892152959743078929765, 'val': 1}
  • id: 6269984
    {'lmfdb_iso': '119952.bx', 'p': 71, 'prec': 20, 'unit': 67275744286095954244751261163508844, 'val': 1}
  • id: 6269992
    {'lmfdb_iso': '119952.bx', 'p': 73, 'prec': 20, 'unit': 37798637582404244654105805444440009, 'val': 1}
  • id: 6269981
    {'lmfdb_iso': '119952.bx', 'p': 83, 'prec': 20, 'unit': 222092178103959026777014454410963777, 'val': 1}
  • id: 6269994
    {'lmfdb_iso': '119952.bx', 'p': 89, 'prec': 20, 'unit': 9362485569204983998328832933629519125, 'val': 1}
  • id: 6269980
    {'lmfdb_iso': '119952.bx', 'p': 97, 'prec': 20, 'unit': 31397010655869202509708452646140009643, 'val': 1}