Elliptic curve data - 81312.bf4

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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': '81312bv', 'Clabel': '81312bv2', 'Cnumber': 2, 'abc_quality': 0.9620157606942951, 'absD': 4269361509146055168, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 88, 'ainvs': [0, 1, 0, -332064, -123833448], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 81312, 'degree': 1228800, 'elladic_images': ['8.24.0.106'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2699706333167514787302788365', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4], 'jinv': [-4464412682696, 4706920449], 'lmfdb_iso': '81312.bf', 'lmfdb_label': '81312.bf4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -2744, -92040], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.d.1.3', '44.12.0-4.c.1.2', '88.48.0.?'], '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': '2.3000724769840831553412974989', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 121], [3, 4, 27104], [7, 8, 11616], [11, 72, 672]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.55116261149760722463638295642', 'prec': 103}, 'szpiro_ratio': 4.492307938514742, '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, 1, 0, 1, 0, 0, 0, -2, 0, -2, 0, -2, 0, 4, 0], 'aplist': [0, 1, -2, 1, 0, -2, -2, 4, 4, 6, -4, -2, 6, -12, -4, 6, 4, -2, -12, -12, -2, 8, -12, -6, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 81312, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '81312.bf', 'trace_hash': 107256030793049498}
• 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': '0.010674033457031702263862521580', 'prec': 107}, 'conductor': 81312, 'gens': [[1602, 58806, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3000724769840831553412974989', 'prec': 100}], 'lmfdb_label': '81312.bf4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.095441556444740262545915517877', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.0247199084502374677663524519425270266', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[711, 0, 1]], 'xcoord_integral_points': [711, 1602, 2042]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [5, 0], '7': [2, 0], '11': 'a', '13': [5, 0], '17': [1, 0], '19': [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': '81312.bf4'}
• ec_torsion_growth •

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

  
  
  • id: 3823367
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [4]}
  • id: 3823366
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [2, 2]}
  • id: 3823368
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '81312.bf4', 'torsion': [4]}
  • id: 3823370
    {'degree': 4, 'field': [-882, 0, -28, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [8]}
  • id: 3823369
    {'degree': 4, 'field': [3, -10, 11, -2, 1], 'lmfdb_label': '81312.bf4', 'torsion': [2, 4]}
  • id: 3823374
    {'degree': 8, 'field': [-29403, 0, 39600, 0, -594, 0, 0, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [6]}
  • id: 3823372
    {'degree': 8, 'field': [100, 0, -76, 0, 38, 0, -10, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [8]}
  • id: 3823371
    {'degree': 8, 'field': [19441, -728, -4888, 560, 390, -56, 24, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [2, 4]}
  • id: 3823373
    {'degree': 8, 'field': [86436, 0, 35672, 0, 4410, 0, 84, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [2, 8]}
  • id: 3823376
    {'degree': 16, 'field': [9, -84, 500, -1740, 4064, -6920, 9096, -9580, 8225, -5808, 3388, -1620, 634, -196, 48, -8, 1], 'lmfdb_label': '81312.bf4', 'torsion': [2, 8]}
  • id: 3823375
    {'degree': 16, 'field': [266121, 2126184, 3800240, -13783224, 12084128, -7299656, 4343640, -1904752, 829697, -266568, 85372, -18984, 4438, -616, 108, -8, 1], 'lmfdb_label': '81312.bf4', 'torsion': [4, 4]}
  • id: 3823379
    {'degree': 16, 'field': [3814209, 0, 3026484, 0, -54324, 0, -463372, 0, 93770, 0, -8956, 0, 844, 0, -44, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [12]}
  • id: 3823380
    {'degree': 16, 'field': [47320641, 0, -21374688, 0, -1149854, 0, 769728, 0, 71463, 0, 1984, 0, 546, 0, 0, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [12]}
  • id: 3823377
    {'degree': 16, 'field': [94128804, 0, 753030432, 0, 760636800, 0, 7606368, 0, 134260, 0, 229712, 0, 75264, 0, -784, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [16]}
  • id: 3823378
    {'degree': 16, 'field': [1584358416, 0, 1401398208, 0, 352276704, 0, -6750976, 0, -950248, 0, 39344, 0, -152, 0, 16, 0, 1], 'lmfdb_label': '81312.bf4', 'torsion': [2, 6]}
• 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: 1979113
    {'conductor': 81312, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '81312.bf4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1979114
    {'conductor': 81312, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '81312.bf4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 1979115
    {'conductor': 81312, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '81312.bf4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1979116
    {'conductor': 81312, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '81312.bf4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2199969
    {'adelic_gens': [[81, 8, 80, 9], [1, 0, 8, 1], [31, 80, 36, 55], [80, 41, 25, 12], [1, 4, 4, 17], [7, 6, 82, 83], [80, 41, 3, 78], [1, 8, 0, 1]], 'adelic_image': '88.48.0.?', 'conductor': 81312, 'lmfdb_label': '81312.bf4', 'prime': 0}
  • id: 333302
    {'conductor': 81312, 'elladic_image': '8.24.0.106', 'lmfdb_label': '81312.bf4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4192229
    {'lmfdb_iso': '81312.bf', 'p': 5, 'prec': 20, 'unit': 1936490621598, 'val': 2}
  • id: 4192235
    {'lmfdb_iso': '81312.bf', 'p': 13, 'prec': 20, 'unit': 108754255717191163336, 'val': 2}
  • id: 4192237
    {'lmfdb_iso': '81312.bf', 'p': 17, 'prec': 20, 'unit': 19097182650869945329656, 'val': 1}
  • id: 4192238
    {'lmfdb_iso': '81312.bf', 'p': 19, 'prec': 20, 'unit': 684195614262614152123029, 'val': 1}
  • id: 4192242
    {'lmfdb_iso': '81312.bf', 'p': 23, 'prec': 20, 'unit': 41617445654653099744931385, 'val': 1}
  • id: 4192234
    {'lmfdb_iso': '81312.bf', 'p': 29, 'prec': 20, 'unit': 439851150304921579060142500, 'val': 1}
  • id: 4192231
    {'lmfdb_iso': '81312.bf', 'p': 31, 'prec': 20, 'unit': 7762547227927236321913316270, 'val': 1}
  • id: 4192246
    {'lmfdb_iso': '81312.bf', 'p': 37, 'prec': 20, 'unit': 353892463019905417290765636730, 'val': 1}
  • id: 4192232
    {'lmfdb_iso': '81312.bf', 'p': 41, 'prec': 20, 'unit': 885107633614380287105324790842, 'val': 1}
  • id: 4192233
    {'lmfdb_iso': '81312.bf', 'p': 43, 'prec': 20, 'unit': 6390459496474605275373347874954, 'val': 1}
  • id: 4192244
    {'lmfdb_iso': '81312.bf', 'p': 47, 'prec': 20, 'unit': 28848599511214268740906505737335, 'val': 1}
  • id: 4192239
    {'lmfdb_iso': '81312.bf', 'p': 53, 'prec': 20, 'unit': 178890641676194547028162739020830, 'val': 1}
  • id: 4192240
    {'lmfdb_iso': '81312.bf', 'p': 59, 'prec': 20, 'unit': 2283786941161825453287014279746459, 'val': 1}
  • id: 4192245
    {'lmfdb_iso': '81312.bf', 'p': 61, 'prec': 20, 'unit': 2228050461657317394064068885884837, 'val': 1}
  • id: 4192228
    {'lmfdb_iso': '81312.bf', 'p': 67, 'prec': 20, 'unit': 13027654788452538361856524381313198, 'val': 1}
  • id: 4192230
    {'lmfdb_iso': '81312.bf', 'p': 71, 'prec': 20, 'unit': 100408426273134038041351648138888236, 'val': 1}
  • id: 4192241
    {'lmfdb_iso': '81312.bf', 'p': 73, 'prec': 20, 'unit': 250449389726866227739367795846859811, 'val': 1}
  • id: 4192236
    {'lmfdb_iso': '81312.bf', 'p': 79, 'prec': 20, 'unit': 201357008597425833562797509983351629, 'val': 1}
  • id: 4192227
    {'lmfdb_iso': '81312.bf', 'p': 83, 'prec': 20, 'unit': 1795382788700326399752528308274048501, 'val': 1}
  • id: 4192243
    {'lmfdb_iso': '81312.bf', 'p': 89, 'prec': 20, 'unit': 6302863619958418809737146326257778254, 'val': 1}
  • id: 4192226
    {'lmfdb_iso': '81312.bf', 'p': 97, 'prec': 20, 'unit': 17804327285643202255902476774097091079, 'val': 1}