Elliptic curve data - 88.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': '88a', 'Clabel': '88a1', 'Cnumber': 1, 'abc_quality': 0.7866607319557362, 'absD': 2816, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 22, 'ainvs': [0, 0, 0, -4, 4], 'analytic_rank': 1, 'bad_primes': [2, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 88, 'degree': 8, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.62921188472456407340791357381', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [-27648, 11], 'lmfdb_iso': '88.a', 'lmfdb_label': '88.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -4, 4], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['22.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 14, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.040264364336880642943215152248', 'prec': 107}, 'semistable': False, 'serre_invariants': [[2, 2, 11], [11, 12, 8]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0913100050978609463527349881', 'prec': 103}, 'szpiro_ratio': 3.6396042860016586, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -3, 0, -3, 0, -2, 0, 6, 0, -1, 0, 0, 0, 9, 0, -6, 0, 4, 0], 'aplist': [0, -3, -3, -2, -1, 0, -6, 4, 1, -8, -7, -1, 4, 6, -8, 2, -1, 4, -5, 3, 16, 2, -2, 15, -7], 'class_deg': 1, 'class_size': 1, 'conductor': 88, 'isogeny_matrix': [[1]], 'lmfdb_iso': '88.a', 'trace_hash': 1435130181846567800}
• 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': '3.5198689874718797429894327063', 'prec': 100}, 'conductor': 88, 'gens': [[2, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.040264364336880642943215152248', 'prec': 107}], 'lmfdb_label': '88.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '4.2525295331483600253449531458', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.68490159390412206930227406663676327994', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-2, 0, 1, 2, 6, 8, 310]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [5, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '88.a1'}
• ec_torsion_growth •

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

  
  
  • id: 3053
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '88.a1', 'torsion': [2]}
  • id: 3054
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '88.a1', 'torsion': [2, 2]}
  • id: 3055
    {'degree': 8, 'field': [-2, -8, -14, -14, -14, -14, -8, -2, 1], 'lmfdb_label': '88.a1', 'torsion': [3]}
  • id: 3056
    {'degree': 12, 'field': [-2, 4, 4, -12, 0, 4, 12, -4, -14, 6, 4, -4, 1], 'lmfdb_label': '88.a1', 'torsion': [4]}
• 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: 498
    {'conductor': 88, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '88.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 499
    {'conductor': 88, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '88.a1', 'prime': 11, '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

  
  {'adelic_gens': [[1, 1, 21, 0], [1, 2, 0, 1], [1, 0, 2, 1], [21, 2, 20, 3], [13, 2, 13, 3]], 'adelic_image': '22.2.0.?', 'conductor': 88, 'lmfdb_label': '88.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 306
    {'lmfdb_iso': '88.a', 'p': 5, 'prec': 20, 'unit': 3060858510511, 'val': 1}
  • id: 307
    {'lmfdb_iso': '88.a', 'p': 7, 'prec': 20, 'unit': 10313537940972053, 'val': 1}
  • id: 313
    {'lmfdb_iso': '88.a', 'p': 17, 'prec': 20, 'unit': 13537423672075093832584, 'val': 1}
  • id: 303
    {'lmfdb_iso': '88.a', 'p': 19, 'prec': 20, 'unit': 601484357867997167443526, 'val': 1}
  • id: 318
    {'lmfdb_iso': '88.a', 'p': 23, 'prec': 20, 'unit': 310560452506704646008397739, 'val': -1}
  • id: 311
    {'lmfdb_iso': '88.a', 'p': 29, 'prec': 20, 'unit': 188381051036379709127190911, 'val': 2}
  • id: 308
    {'lmfdb_iso': '88.a', 'p': 31, 'prec': 20, 'unit': 14357448870186945310328602916, 'val': 1}
  • id: 323
    {'lmfdb_iso': '88.a', 'p': 37, 'prec': 20, 'unit': 194745958267817272710923410209, 'val': 1}
  • id: 309
    {'lmfdb_iso': '88.a', 'p': 41, 'prec': 20, 'unit': 101062001489567861736972546241, 'val': 2}
  • id: 310
    {'lmfdb_iso': '88.a', 'p': 43, 'prec': 20, 'unit': 5074682944158245463971729086461, 'val': 1}
  • id: 321
    {'lmfdb_iso': '88.a', 'p': 47, 'prec': 20, 'unit': 29814576271444614519470011199263, 'val': 1}
  • id: 315
    {'lmfdb_iso': '88.a', 'p': 53, 'prec': 20, 'unit': 477039213445580360969899496427871, 'val': 1}
  • id: 316
    {'lmfdb_iso': '88.a', 'p': 59, 'prec': 20, 'unit': 861251239713034788688827833116281, 'val': 1}
  • id: 322
    {'lmfdb_iso': '88.a', 'p': 61, 'prec': 20, 'unit': 8269993296871493699255755532620881, 'val': 1}
  • id: 305
    {'lmfdb_iso': '88.a', 'p': 67, 'prec': 20, 'unit': 18649807941817280335072814483671613, 'val': 1}
  • id: 320
    {'lmfdb_iso': '88.a', 'p': 71, 'prec': 20, 'unit': 40598523838613687411698582802473759, 'val': 1}
  • id: 317
    {'lmfdb_iso': '88.a', 'p': 73, 'prec': 20, 'unit': 152605128355563308522849930189978760, 'val': 1}
  • id: 312
    {'lmfdb_iso': '88.a', 'p': 79, 'prec': 20, 'unit': 1105750303768539801785666725246167379, 'val': 1}
  • id: 314
    {'lmfdb_iso': '88.a', 'p': 83, 'prec': 20, 'unit': 2246944977445601130531934601963466395, 'val': 1}
  • id: 319
    {'lmfdb_iso': '88.a', 'p': 89, 'prec': 20, 'unit': 6332354775092741182136488195467149134, 'val': 1}
  • id: 304
    {'lmfdb_iso': '88.a', 'p': 97, 'prec': 20, 'unit': 26277779288747130988047844066929188369, 'val': 1}