Elliptic curve data - 82.a1

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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': '82a', 'Clabel': '82a2', 'Cnumber': 2, 'abc_quality': 0.8904800315898436, 'absD': 3362, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 328, 'ainvs': [1, 0, 1, -12, -16], 'analytic_rank': 1, 'bad_primes': [2, 41], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 82, 'degree': 8, 'elladic_images': ['8.6.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.53158001088427622742284127210', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [169112377, 3362], 'lmfdb_iso': '82.a', 'lmfdb_label': '82.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -12, -16], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.b.1', '164.6.0.?', '328.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.44941384983775616445759072027', 'prec': 103}, 'semistable': True, 'serre_invariants': [[2, 4, 1], [41, 42, 2]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.53158001088427622742284127210', 'prec': 107}, 'szpiro_ratio': 4.299360349840523, '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, -1, -2, 1, -2, 2, -4, -1, 1, 2, -2, -2, 4, 4, 4, 1, -2, -1, 6, -2], 'aplist': [-1, -2, -2, -4, -2, 4, -2, 6, -8, 0, -8, 2, -1, -12, 4, -4, 8, -14, -2, 8, 10, 4, 12, -14, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 82, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '82.a', 'trace_hash': 1061891762443100711}
• 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': '2.8955064108897658705100762196', 'prec': 100}, 'conductor': 82, 'gens': [[-2, 1, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.44941384983775616445759072027', 'prec': 103}], 'lmfdb_label': '82.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.5944975201858040037948471824', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.58300155947060683185532129854168781740', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[-9, 5, 2]], 'xcoord_integral_points': [-2, 4, 8]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': [1, 0], '5': [5, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '82.a1'}
• ec_torsion_growth •

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

  
  
  • id: 2971
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '82.a1', 'torsion': [2, 2]}
  • id: 2972
    {'degree': 4, 'field': [2, 0, 7, 0, 1], 'lmfdb_label': '82.a1', 'torsion': [4]}
  • id: 2975
    {'degree': 8, 'field': [-12, -27, 42, -31, 19, -7, 7, -4, 1], 'lmfdb_label': '82.a1', 'torsion': [6]}
  • id: 2973
    {'degree': 8, 'field': [4, 0, 16, 0, -30, 0, 8, 0, 1], 'lmfdb_label': '82.a1', 'torsion': [2, 4]}
  • id: 2974
    {'degree': 8, 'field': [46, -68, 30, -16, 55, -20, 18, 0, 1], 'lmfdb_label': '82.a1', 'torsion': [2, 4]}
  • id: 2977
    {'degree': 16, 'field': [1024, 0, -16456, 0, 20836, 0, -12712, 0, 2620, 0, 164, 0, -56, 0, -4, 0, 1], 'lmfdb_label': '82.a1', 'torsion': [2, 6]}
  • id: 2976
    {'degree': 16, 'field': [160000, 0, 297600, 0, 469668, 0, 17552, 0, 5256, 0, -1648, 0, 93, 0, -12, 0, 1], 'lmfdb_label': '82.a1', 'torsion': [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: 473
    {'conductor': 82, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '82.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 474
    {'conductor': 82, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82.a1', 'prime': 41, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1666105
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [289, 42, 40, 287], [325, 4, 324, 5], [1, 2, 2, 5], [1, 4, 0, 1], [129, 4, 258, 9], [2, 1, 163, 0]], 'adelic_image': '328.12.0.?', 'conductor': 82, 'lmfdb_label': '82.a1', 'prime': 0}
  • id: 264
    {'conductor': 82, 'elladic_image': '8.6.0.6', 'lmfdb_label': '82.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 124
    {'lmfdb_iso': '82.a', 'p': 5, 'prec': 20, 'unit': 1557823528814, 'val': 2}
  • id: 125
    {'lmfdb_iso': '82.a', 'p': 7, 'prec': 20, 'unit': 278749504730014, 'val': 1}
  • id: 123
    {'lmfdb_iso': '82.a', 'p': 11, 'prec': 20, 'unit': 16080308325287567142, 'val': 1}
  • id: 129
    {'lmfdb_iso': '82.a', 'p': 13, 'prec': 20, 'unit': 523466972352260118876, 'val': 1}
  • id: 131
    {'lmfdb_iso': '82.a', 'p': 17, 'prec': 20, 'unit': 38682907241074376976713, 'val': 1}
  • id: 132
    {'lmfdb_iso': '82.a', 'p': 19, 'prec': 20, 'unit': 1914840288692219052081053, 'val': 1}
  • id: 135
    {'lmfdb_iso': '82.a', 'p': 23, 'prec': 20, 'unit': 45766032623407409179411856, 'val': 1}
  • id: 126
    {'lmfdb_iso': '82.a', 'p': 31, 'prec': 20, 'unit': 19344611287025876708285665126, 'val': 1}
  • id: 141
    {'lmfdb_iso': '82.a', 'p': 37, 'prec': 20, 'unit': 302012133112911736322392393862, 'val': 1}
  • id: 128
    {'lmfdb_iso': '82.a', 'p': 43, 'prec': 20, 'unit': 4486262108992341938187431171639, 'val': 1}
  • id: 139
    {'lmfdb_iso': '82.a', 'p': 47, 'prec': 20, 'unit': 48291084567076718782411621424617, 'val': 1}
  • id: 133
    {'lmfdb_iso': '82.a', 'p': 53, 'prec': 20, 'unit': 244454590848262200125537110812876, 'val': 1}
  • id: 134
    {'lmfdb_iso': '82.a', 'p': 59, 'prec': 20, 'unit': 3521454946209581029537396491332181, 'val': 1}
  • id: 140
    {'lmfdb_iso': '82.a', 'p': 61, 'prec': 20, 'unit': 6451010161647420626889856136037596, 'val': 1}
  • id: 122
    {'lmfdb_iso': '82.a', 'p': 67, 'prec': 20, 'unit': 26320851178523032850196281015108905, 'val': 1}
  • id: 138
    {'lmfdb_iso': '82.a', 'p': 71, 'prec': 20, 'unit': 2759730248698633469456865339487754, 'val': 1}
  • id: 127
    {'lmfdb_iso': '82.a', 'p': 73, 'prec': 20, 'unit': 188143547221186521938811723852775909, 'val': 1}
  • id: 130
    {'lmfdb_iso': '82.a', 'p': 79, 'prec': 20, 'unit': 502788761236757579470218089318191126, 'val': 1}
  • id: 136
    {'lmfdb_iso': '82.a', 'p': 83, 'prec': 20, 'unit': 369410702025806069167894632987743640, 'val': 1}
  • id: 137
    {'lmfdb_iso': '82.a', 'p': 89, 'prec': 20, 'unit': 6085783516224973521261376890545622628, 'val': 1}
  • id: 121
    {'lmfdb_iso': '82.a', 'p': 97, 'prec': 20, 'unit': 26790686947235431071765108652090142479, 'val': 1}