Elliptic curve data - 64320.b2

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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': '64320bw', 'Clabel': '64320bw1', 'Cnumber': 1, 'abc_quality': 1.082811567459726, 'absD': 5269094400, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 8040, 'ainvs': [0, -1, 0, -481, -1919], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 67], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 64320, 'degree': 30720, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.56196354713015585351671975023', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [47045881, 20100], 'lmfdb_iso': '64320.b', 'lmfdb_label': '64320.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -7, 1], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '40.6.0.c.1', '402.6.0.?', '8040.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5985625490212067492326016329', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 201], [3, 4, 21440], [5, 6, 12864], [67, 68, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.47775722370976211060912843196', 'prec': 107}, 'szpiro_ratio': 2.7225705950368146, '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, -2, 0, 1, 0, 0, 0, -2, 0, 1, 0, -4, 0, -8, 0], 'aplist': [0, -1, -1, -2, 0, -2, -4, -8, 6, 4, 4, -2, -2, 8, 2, -2, -6, 8, 1, 0, 10, 4, -12, -2, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 64320, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '64320.b', 'trace_hash': 2028179627747082622}
• 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': '0.32500097577889338910530113952', 'prec': 103}, 'conductor': 64320, 'gens': [[-9, 40, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5985625490212067492326016329', 'prec': 100}], 'lmfdb_label': '64320.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0592781602401802105559931872', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3866447919120735518350605753657379481', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-19, 0, 1]], 'xcoord_integral_points': [-19, -9, 45]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 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], '67': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '64320.b2'}
• ec_torsion_growth •

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

  
  
  • id: 3073132
    {'degree': 2, 'field': [-50, -1, 1], 'lmfdb_label': '64320.b2', 'torsion': [2, 2]}
  • id: 3073133
    {'degree': 4, 'field': [129, -80, 24, 0, 1], 'lmfdb_label': '64320.b2', 'torsion': [4]}
  • id: 3073134
    {'degree': 8, 'field': [-968018, -422684, 142441, -12194, -3131, 1072, -77, -2, 1], 'lmfdb_label': '64320.b2', 'torsion': [2, 4]}
  • id: 3073136
    {'degree': 8, 'field': [-187500, 0, 36250, 0, -1500, 0, 0, 0, 1], 'lmfdb_label': '64320.b2', 'torsion': [6]}
  • id: 3073135
    {'degree': 8, 'field': [57066, -14100, 3130, -480, 2307, -100, 90, 0, 1], 'lmfdb_label': '64320.b2', 'torsion': [2, 4]}
  • id: 3073137
    {'degree': 16, 'field': [3846627681, 1661776800, 1102030304, 337197440, 218219812, 20968800, 11566112, 940800, 1807910, 172000, 71328, -16000, 612, -480, 96, 0, 1], 'lmfdb_label': '64320.b2', 'torsion': [8]}
  • id: 3073138
    {'degree': 16, 'field': [7885440000, 0, 4021235400, 0, -948700700, 0, -23969640, 0, 5265012, 0, -60196, 0, -3324, 0, 0, 0, 1], 'lmfdb_label': '64320.b2', '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: 1552885
    {'conductor': 64320, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '64320.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1552886
    {'conductor': 64320, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '64320.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1552887
    {'conductor': 64320, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '64320.b2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1552888
    {'conductor': 64320, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '64320.b2', 'prime': 67, '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: 2089998
    {'adelic_gens': [[1, 2, 2, 5], [3017, 5026, 5024, 3015], [4021, 4, 2, 9], [1, 4, 0, 1], [5362, 1, 5359, 0], [1, 0, 4, 1], [2282, 1, 2879, 0], [3, 4, 8, 11], [3217, 4, 6434, 9], [8037, 4, 8036, 5]], 'adelic_image': '8040.12.0.?', 'conductor': 64320, 'lmfdb_label': '64320.b2', 'prime': 0}
  • id: 269817
    {'conductor': 64320, 'elladic_image': '2.3.0.1', 'lmfdb_label': '64320.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3278339
    {'lmfdb_iso': '64320.b', 'p': 7, 'prec': 20, 'unit': 9209989186299176, 'val': 1}
  • id: 3278343
    {'lmfdb_iso': '64320.b', 'p': 13, 'prec': 20, 'unit': 264645599978772156039, 'val': 1}
  • id: 3278345
    {'lmfdb_iso': '64320.b', 'p': 17, 'prec': 20, 'unit': 158636902995276286954971, 'val': 1}
  • id: 3278346
    {'lmfdb_iso': '64320.b', 'p': 19, 'prec': 20, 'unit': 462939977884346656701931, 'val': 1}
  • id: 3278349
    {'lmfdb_iso': '64320.b', 'p': 23, 'prec': 20, 'unit': 22850256577340780026146281, 'val': 1}
  • id: 3278342
    {'lmfdb_iso': '64320.b', 'p': 29, 'prec': 20, 'unit': 681320646600451656734924414, 'val': 1}
  • id: 3278353
    {'lmfdb_iso': '64320.b', 'p': 31, 'prec': 20, 'unit': 1034188422368705119627885189, 'val': 1}
  • id: 3278338
    {'lmfdb_iso': '64320.b', 'p': 37, 'prec': 20, 'unit': 550522943334542090465085646505, 'val': 1}
  • id: 3278340
    {'lmfdb_iso': '64320.b', 'p': 41, 'prec': 20, 'unit': 800979588298092134143729306567, 'val': 1}
  • id: 3278341
    {'lmfdb_iso': '64320.b', 'p': 43, 'prec': 20, 'unit': 2550223197821771716763288718201, 'val': 1}
  • id: 3278351
    {'lmfdb_iso': '64320.b', 'p': 47, 'prec': 20, 'unit': 8748829651182050301737780645188, 'val': 1}
  • id: 3278347
    {'lmfdb_iso': '64320.b', 'p': 53, 'prec': 20, 'unit': 500361883191514531138661519462329, 'val': 1}
  • id: 3278337
    {'lmfdb_iso': '64320.b', 'p': 59, 'prec': 20, 'unit': 2368453738961402864412078532059486, 'val': 1}
  • id: 3278352
    {'lmfdb_iso': '64320.b', 'p': 61, 'prec': 20, 'unit': 1570687587177290234636136503461643, 'val': 1}
  • id: 3278348
    {'lmfdb_iso': '64320.b', 'p': 73, 'prec': 20, 'unit': 63092742002994418446003897995516490, 'val': 1}
  • id: 3278344
    {'lmfdb_iso': '64320.b', 'p': 79, 'prec': 20, 'unit': 792384173497578663703375277148781812, 'val': 1}
  • id: 3278336
    {'lmfdb_iso': '64320.b', 'p': 83, 'prec': 20, 'unit': 185667616432653190573581023284752181, 'val': 1}
  • id: 3278350
    {'lmfdb_iso': '64320.b', 'p': 89, 'prec': 20, 'unit': 6426224372318925005221965835822001348, 'val': 1}
  • id: 3278335
    {'lmfdb_iso': '64320.b', 'p': 97, 'prec': 20, 'unit': 5295009790623949741224782652454491437, 'val': 1}