Elliptic curve data - 82368.bb1

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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': '82368bv', 'Clabel': '82368bv4', 'Cnumber': 4, 'abc_quality': 1.059433311036222, 'absD': 1475697180672, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3432, 'ainvs': [0, 0, 0, -23721996, -44470801424], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 82368, 'degree': 1769472, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5232927106348381855389436523', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 27, 'isogeny_degrees': [1, 2, 4], 'jinv': [7725203825376001537, 7722], 'lmfdb_iso': '82368.bb', 'lmfdb_label': '82368.bb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -41184, 3199767], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.6', '88.12.0.?', '104.12.0.?', '132.12.0.?', '264.24.0.?', '312.24.0.?', '1144.24.0.?', '3432.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '16.617281587659313774931641905', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1287], [3, 6, 9152], [11, 12, 7488], [13, 14, 6336]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.93426579546086537571547285165', 'prec': 103}, 'szpiro_ratio': 5.526955256588992, '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, 1, 0, -1, 0, 0, 0, -6, 0, 0, 0], 'aplist': [0, 0, -2, 0, 1, -1, -6, 0, -4, 6, 4, -2, -10, 4, -8, -6, 4, 2, 4, 8, 14, -8, 4, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 82368, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '82368.bb', 'trace_hash': 478137534167936897}
• 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': '0.0064312560268059045078079122362', 'prec': 110}, 'conductor': 82368, 'gens': [[23811412, 77542773560, 57]], 'heights': [{'__RealLiteral__': 0, 'data': '16.617281587659313774931641905', 'prec': 100}], 'lmfdb_label': '82368.bb1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.068408764609586409826824049981', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.5470708183256013301355026746874139876', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-2812, 0, 1]], 'xcoord_integral_points': [-2812]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 3, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [3, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '82368.bb1'}
• ec_torsion_growth •

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

  
  
  • id: 3869518
    {'degree': 2, 'field': [-858, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [2, 2]}
  • id: 3869519
    {'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [4]}
  • id: 3869520
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [4]}
  • id: 3869521
    {'degree': 4, 'field': [49, 0, 118, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [2, 4]}
  • id: 3869525
    {'degree': 8, 'field': [-8112, 0, -954, 0, -120, 0, 2, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [6]}
  • id: 3869523
    {'degree': 8, 'field': [8238, 2616, -732, -408, 181, 94, -3, -2, 1], 'lmfdb_label': '82368.bb1', 'torsion': [8]}
  • id: 3869524
    {'degree': 8, 'field': [1002001, 0, -69212, 0, 2640, 0, -44, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [8]}
  • id: 3869522
    {'degree': 8, 'field': [11230168, 345248, -351728, 12992, -6575, 92, -26, -4, 1], 'lmfdb_label': '82368.bb1', 'torsion': [2, 4]}
  • id: 3869530
    {'degree': 16, 'field': [216178209, 0, 443723696, 0, -11064092, 0, 3948516, 0, 40898, 0, 7072, 0, 576, 0, -4, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [12]}
  • id: 3869528
    {'degree': 16, 'field': [1184591593, 349246108, -119827596, -80014516, 25295907, 13540680, -881870, -861940, -137616, 45436, 12640, -3156, 675, -32, 42, -4, 1], 'lmfdb_label': '82368.bb1', 'torsion': [2, 8]}
  • id: 3869531
    {'degree': 16, 'field': [4545995776, 0, 2085465088, 0, 199205632, 0, -58181632, 0, 2812736, 0, -51712, 0, 1876, 0, 4, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [12]}
  • id: 3869529
    {'degree': 16, 'field': [23711072256, 0, 1473398784, 0, -22765824, 0, -8881056, 0, -400416, 0, -11112, 0, 628, 0, 28, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [2, 6]}
  • id: 3869526
    {'degree': 16, 'field': [771583046404, 0, -143810052688, 0, 10194785212, 0, -296627968, 0, 1409413, 0, -25636, 0, 5422, 0, 68, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [4, 4]}
  • id: 3869527
    {'degree': 16, 'field': [3046928432068, -387336903360, -367198868640, 19146320160, 23693196280, -758140944, -805036656, 27274368, 20355000, -1364880, -360384, 19536, 5332, -264, -24, 0, 1], 'lmfdb_label': '82368.bb1', 'torsion': [2, 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: 2005928
    {'conductor': 82368, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '82368.bb1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2005929
    {'conductor': 82368, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '82368.bb1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2005930
    {'conductor': 82368, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '82368.bb1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2005931
    {'conductor': 82368, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '82368.bb1', '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: 2206724
    {'adelic_gens': [[7, 6, 3426, 3427], [536, 3, 2909, 2], [3425, 8, 3424, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [3011, 3004, 3050, 1293], [1136, 3429, 1139, 3430], [3000, 1279, 437, 450], [316, 1, 959, 6]], 'adelic_image': '3432.48.0.?', 'conductor': 82368, 'lmfdb_label': '82368.bb1', 'prime': 0}
  • id: 337094
    {'conductor': 82368, 'elladic_image': '4.6.0.1', 'lmfdb_label': '82368.bb1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4248551
    {'lmfdb_iso': '82368.bb', 'p': 5, 'prec': 20, 'unit': 3461012599516, 'val': 1}
  • id: 4248542
    {'lmfdb_iso': '82368.bb', 'p': 17, 'prec': 20, 'unit': 161464970127082831002777, 'val': 1}
  • id: 4248547
    {'lmfdb_iso': '82368.bb', 'p': 23, 'prec': 20, 'unit': 2915074969903840605206216, 'val': 2}
  • id: 4248540
    {'lmfdb_iso': '82368.bb', 'p': 29, 'prec': 20, 'unit': 1752643532304156507388776779, 'val': 1}
  • id: 4248537
    {'lmfdb_iso': '82368.bb', 'p': 31, 'prec': 20, 'unit': 17463511576899440559637950339, 'val': 1}
  • id: 4248535
    {'lmfdb_iso': '82368.bb', 'p': 37, 'prec': 20, 'unit': 489317396002578547697929717468, 'val': 1}
  • id: 4248538
    {'lmfdb_iso': '82368.bb', 'p': 41, 'prec': 20, 'unit': 3081531190240624874767031320978, 'val': 1}
  • id: 4248539
    {'lmfdb_iso': '82368.bb', 'p': 43, 'prec': 20, 'unit': 1924817813061954246898511154351, 'val': 1}
  • id: 4248549
    {'lmfdb_iso': '82368.bb', 'p': 47, 'prec': 20, 'unit': 51182103697737624332480754391339, 'val': 1}
  • id: 4248544
    {'lmfdb_iso': '82368.bb', 'p': 53, 'prec': 20, 'unit': 358190571095794763052089000286063, 'val': 1}
  • id: 4248545
    {'lmfdb_iso': '82368.bb', 'p': 59, 'prec': 20, 'unit': 4278433381693823959662345122474360, 'val': 1}
  • id: 4248550
    {'lmfdb_iso': '82368.bb', 'p': 61, 'prec': 20, 'unit': 6445427468418412960174637337083417, 'val': 1}
  • id: 4248534
    {'lmfdb_iso': '82368.bb', 'p': 67, 'prec': 20, 'unit': 32110755237867395814413373796940651, 'val': 1}
  • id: 4248536
    {'lmfdb_iso': '82368.bb', 'p': 71, 'prec': 20, 'unit': 67270066069801969175098111870548181, 'val': 1}
  • id: 4248546
    {'lmfdb_iso': '82368.bb', 'p': 73, 'prec': 20, 'unit': 220418345311623074772019118478054075, 'val': 1}
  • id: 4248541
    {'lmfdb_iso': '82368.bb', 'p': 79, 'prec': 20, 'unit': 423058435150053848872060130387864413, 'val': 1}
  • id: 4248543
    {'lmfdb_iso': '82368.bb', 'p': 83, 'prec': 20, 'unit': 557431399242544561706618052892913913, 'val': 1}
  • id: 4248548
    {'lmfdb_iso': '82368.bb', 'p': 89, 'prec': 20, 'unit': 8997323114208024410304075524972962618, 'val': 1}
  • id: 4248533
    {'lmfdb_iso': '82368.bb', 'p': 97, 'prec': 20, 'unit': 20938030829314697571227860839569245041, 'val': 1}