Elliptic curve data - 81120.bd1

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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': '81120t', 'Clabel': '81120t4', 'Cnumber': 4, 'abc_quality': 1.0109039721020272, 'absD': 111209679360, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 3120, 'ainvs': [0, 1, 0, -81176, -8929140], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 81120, 'degree': 294912, 'elladic_images': ['8.12.0.10'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3747941196655699299944040385', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 29, 'isogeny_degrees': [1, 2, 4], 'jinv': [23937672968, 45], 'lmfdb_iso': '81120.bd', 'lmfdb_label': '81120.bd1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -480, 4212], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.o.1', '40.24.0.by.1', '48.24.0.j.1', '52.12.0-4.c.1.1', '80.48.0.?', '104.24.0.?', '240.96.3.?', '520.48.0.?', '624.48.0.?', '1040.96.0.?', '3120.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '19.638682034644086209457215009', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 845], [3, 4, 27040], [5, 6, 16224], [13, 86, 480]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.42754094448515742009526377338', 'prec': 107}, 'szpiro_ratio': 4.0276016917658115, '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, -1, 0, -4, 0, 1, 0, 0, 0, 0, 0, -1, 0, -6, 0, 0, 0], 'aplist': [0, 1, -1, -4, 0, 0, -6, 0, 4, -2, -8, -6, 6, -12, -12, -10, 8, -10, -12, 8, -10, -16, 12, 6, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 81120, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '81120.bd', 'trace_hash': 870410044602946298}
• 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': '0.063954189605724447990457315889', 'prec': 107}, 'conductor': 81120, 'gens': [[511, 9126, 1], [619, 13356, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.4016842922703696055580723563', 'prec': 100}, {'__RealLiteral__': 0, 'data': '6.1148844906393245070382507026', 'prec': 100}], 'lmfdb_label': '81120.bd1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.28284092311146208234731799982', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.109245910742439428225487526941840971', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-165, 0, 1]], 'xcoord_integral_points': [-165, 511, 619]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [2, 0], '7': [2, 0], '11': [2, 2, 0], '13': 'a', '17': [2, 0], '19': [2, 2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '81120.bd1'}
• ec_torsion_growth •

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

  
  
  • id: 3814060
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '81120.bd1', 'torsion': [2, 2]}
  • id: 3814061
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '81120.bd1', 'torsion': [4]}
  • id: 3814062
    {'degree': 2, 'field': [130, 0, 1], 'lmfdb_label': '81120.bd1', 'torsion': [4]}
  • id: 3814063
    {'degree': 4, 'field': [529, 0, 6, 0, 1], 'lmfdb_label': '81120.bd1', 'torsion': [2, 4]}
  • id: 3814067
    {'degree': 8, 'field': [-85683, 0, 333944, 0, -1014, 0, 0, 0, 1], 'lmfdb_label': '81120.bd1', 'torsion': [6]}
  • id: 3814064
    {'degree': 8, 'field': [5391, 3708, -3834, 264, -161, 32, -6, -4, 1], 'lmfdb_label': '81120.bd1', 'torsion': [2, 4]}
  • id: 3814065
    {'degree': 8, 'field': [26361, -72, -4464, 288, 445, -12, -22, 0, 1], 'lmfdb_label': '81120.bd1', 'torsion': [8]}
  • id: 3814066
    {'degree': 8, 'field': [269361, 0, 8308, 0, 1074, 0, 12, 0, 1], 'lmfdb_label': '81120.bd1', 'torsion': [2, 8]}
  • id: 3814070
    {'degree': 16, 'field': [-5434879239, 13503564, 5425505424, 3599073528, 930279366, -21592848, -76106576, -11983032, 1190476, 395972, 46816, 9536, -506, -352, -44, 0, 1], 'lmfdb_label': '81120.bd1', 'torsion': [2, 6]}
  • id: 3814069
    {'degree': 16, 'field': [7955089, -3815628, 5649008, -4119436, 3292208, -1774272, 1124084, -542028, 252481, -94248, 35992, -10484, 2718, -476, 88, -8, 1], 'lmfdb_label': '81120.bd1', 'torsion': [2, 8]}
  • id: 3814071
    {'degree': 16, 'field': [27632484, -34947648, 12374496, 2399352, 992820, -1895856, 535108, 50300, 2597, -26828, 6676, -372, -98, -28, 32, -8, 1], 'lmfdb_label': '81120.bd1', 'torsion': [12]}
  • id: 3814068
    {'degree': 16, 'field': [29062881, 0, 55087452, 0, 11005830, 0, -862848, 0, 95479, 0, 4648, 0, -30, 0, 28, 0, 1], 'lmfdb_label': '81120.bd1', 'torsion': [4, 4]}
  • id: 3814072
    {'degree': 16, 'field': [2073760210726, -423310253376, 390394871324, -77242133072, 33342046096, -5485046368, 1779696044, -216117032, 63329476, -5043868, 1533056, -65504, 24694, -352, 236, 0, 1], 'lmfdb_label': '81120.bd1', '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: 1973774
    {'conductor': 81120, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '81120.bd1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1973775
    {'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '81120.bd1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1973776
    {'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '81120.bd1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1973777
    {'conductor': 81120, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '81120.bd1', 'prime': 13, '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: 2198641
    {'adelic_gens': [[2081, 1456, 1768, 2289], [1, 16, 0, 1], [638, 1443, 2301, 2900], [15, 166, 2834, 3075], [1, 8, 8, 65], [2573, 2210, 1976, 3067], [479, 0, 0, 3119], [1, 0, 16, 1], [2588, 429, 143, 1106], [3105, 16, 3104, 17]], 'adelic_image': '3120.192.3.?', 'conductor': 81120, 'lmfdb_label': '81120.bd1', 'prime': 0}
  • id: 332636
    {'conductor': 81120, 'elladic_image': '8.12.0.10', 'lmfdb_label': '81120.bd1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4180095
    {'lmfdb_iso': '81120.bd', 'p': 7, 'prec': 20, 'unit': 10685413354291070, 'val': 2}
  • id: 4180100
    {'lmfdb_iso': '81120.bd', 'p': 17, 'prec': 20, 'unit': 163665206326186597916982, 'val': 2}
  • id: 4180105
    {'lmfdb_iso': '81120.bd', 'p': 23, 'prec': 20, 'unit': 15481329216516367678701096, 'val': 2}
  • id: 4180098
    {'lmfdb_iso': '81120.bd', 'p': 29, 'prec': 20, 'unit': 3918499039544424287221202022, 'val': 2}
  • id: 4180110
    {'lmfdb_iso': '81120.bd', 'p': 31, 'prec': 20, 'unit': 3511958841097462738461231350, 'val': 2}
  • id: 4180094
    {'lmfdb_iso': '81120.bd', 'p': 37, 'prec': 20, 'unit': 527694187790173461793078399050, 'val': 2}
  • id: 4180096
    {'lmfdb_iso': '81120.bd', 'p': 41, 'prec': 20, 'unit': 2301649563427959144389984911506, 'val': 2}
  • id: 4180097
    {'lmfdb_iso': '81120.bd', 'p': 43, 'prec': 20, 'unit': 3977350144244029266619339259293, 'val': 2}
  • id: 4180108
    {'lmfdb_iso': '81120.bd', 'p': 47, 'prec': 20, 'unit': 34759102504408565246689931481908, 'val': 2}
  • id: 4180102
    {'lmfdb_iso': '81120.bd', 'p': 53, 'prec': 20, 'unit': 312146210867714413428941738104361, 'val': 2}
  • id: 4180103
    {'lmfdb_iso': '81120.bd', 'p': 59, 'prec': 20, 'unit': 4199615169177674302906879398089199, 'val': 2}
  • id: 4180109
    {'lmfdb_iso': '81120.bd', 'p': 61, 'prec': 20, 'unit': 4644766029425856848359589537785754, 'val': 2}
  • id: 4180093
    {'lmfdb_iso': '81120.bd', 'p': 67, 'prec': 20, 'unit': 15272985021435975428084586994428440, 'val': 2}
  • id: 4180107
    {'lmfdb_iso': '81120.bd', 'p': 71, 'prec': 20, 'unit': 96927840928473278802484709405027162, 'val': 2}
  • id: 4180104
    {'lmfdb_iso': '81120.bd', 'p': 73, 'prec': 20, 'unit': 38484801016986320377870140418845116, 'val': 2}
  • id: 4180099
    {'lmfdb_iso': '81120.bd', 'p': 79, 'prec': 20, 'unit': 806127323834305884124597600033862192, 'val': 2}
  • id: 4180101
    {'lmfdb_iso': '81120.bd', 'p': 83, 'prec': 20, 'unit': 2525585634077129848739888507783847514, 'val': 2}
  • id: 4180106
    {'lmfdb_iso': '81120.bd', 'p': 89, 'prec': 20, 'unit': 463464594889288276030794360597976530, 'val': 2}
  • id: 4180092
    {'lmfdb_iso': '81120.bd', 'p': 97, 'prec': 20, 'unit': 50554149393635136701930087925031442154, 'val': 2}