Elliptic curve data - 288.a2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '288a', 'Clabel': '288a1', 'Cnumber': 1, 'absD': 1728, 'ainvs': [0, 0, 0, 3, 0], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 2, 'class_size': 2, 'cm': -4, 'conductor': 288, 'degree': 16, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.68930626346450944069484771334', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [1728, 1], 'lmfdb_iso': '288.a', 'lmfdb_label': '288.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 3, 0], 'min_quad_twist_disc': 1, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.50118239204717836371111998437', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 6, 32]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3105329259115095182522750833', 'prec': 103}, 'szpiro_ratio': 2.632799566768314, '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, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -8, 0, 0, 0], 'aplist': [0, 0, -4, 0, 0, -6, -8, 0, 0, 4, 0, -2, 8, 0, 0, 4, 0, -10, 0, 0, 6, 0, 0, -16, -18], 'class_deg': 2, 'class_size': 2, 'conductor': 288, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '288.a', 'trace_hash': 851919934628461349}
• 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': '3.9693903827627596663162680333', 'prec': 100}, 'conductor': 288, 'gens': [[1, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.50118239204717836371111998437', 'prec': 103}], 'lmfdb_label': '288.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.8175842073530862500159992852', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4121235928355727678865401697777185079', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0, 1, 3, 12]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [1, 1, 0], '11': [1, 1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '288.a2'}
• ec_torsion_growth •

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

  
  
  • id: 11956
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '288.a2', 'torsion': [2, 2]}
  • id: 11957
    {'degree': 4, 'field': [1, -2, 0, -2, 1], 'lmfdb_label': '288.a2', 'torsion': [4]}
  • id: 11960
    {'degree': 8, 'field': [-3, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '288.a2', 'torsion': [12]}
  • id: 11958
    {'degree': 8, 'field': [1, -4, 8, -10, 7, -2, 2, -2, 1], 'lmfdb_label': '288.a2', 'torsion': [2, 4]}
  • id: 11959
    {'degree': 8, 'field': [1, 0, 4, 0, 3, 0, -2, 0, 1], 'lmfdb_label': '288.a2', 'torsion': [2, 4]}
  • id: 11961
    {'degree': 8, 'field': [130, -68, -4, -68, 52, -4, 2, -4, 1], 'lmfdb_label': '288.a2', 'torsion': [10]}
  • id: 11962
    {'degree': 16, 'field': [1, -12, 68, -232, 488, -564, 194, 396, -665, 444, -62, -152, 162, -92, 34, -8, 1], 'lmfdb_label': '288.a2', 'torsion': [4, 4]}
  • id: 11964
    {'degree': 16, 'field': [1, -8, 26, -48, 80, -172, 328, -444, 451, -372, 256, -152, 80, -36, 14, -4, 1], 'lmfdb_label': '288.a2', 'torsion': [6, 12]}
  • id: 11966
    {'degree': 16, 'field': [1, -4, 124, -328, 260, 128, -242, 16, 79, 36, -50, 0, 22, -4, -2, 0, 1], 'lmfdb_label': '288.a2', 'torsion': [2, 10]}
  • id: 11963
    {'degree': 16, 'field': [4, 0, 16, 0, -16, 0, -104, 0, -116, 0, -40, 0, -4, 0, -4, 0, 1], 'lmfdb_label': '288.a2', 'torsion': [8]}
  • id: 11965
    {'degree': 16, 'field': [81, 0, 0, 0, -54, 0, 0, 0, -369, 0, 0, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '288.a2', 'torsion': [10]}
• 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: 2607
    {'conductor': 288, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '288.a2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2608
    {'conductor': 288, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '288.a2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• lmfdb_label 288.a2 does not appear in ec_galrep
• ec_padic •

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

  
  
  • id: 2864
    {'lmfdb_iso': '288.a', 'p': 5, 'prec': 20, 'unit': 7640432806881, 'val': 0}
  • id: 2857
    {'lmfdb_iso': '288.a', 'p': 13, 'prec': 20, 'unit': 102038231423300165688, 'val': 2}
  • id: 2859
    {'lmfdb_iso': '288.a', 'p': 17, 'prec': 20, 'unit': 69246037717185445586758, 'val': 1}
  • id: 2858
    {'lmfdb_iso': '288.a', 'p': 29, 'prec': 20, 'unit': 798713391996569919103079092, 'val': 1}
  • id: 2855
    {'lmfdb_iso': '288.a', 'p': 37, 'prec': 20, 'unit': 592619856111202582125979448808, 'val': 1}
  • id: 2856
    {'lmfdb_iso': '288.a', 'p': 41, 'prec': 20, 'unit': 1954062407884422172076014922548, 'val': 1}
  • id: 2860
    {'lmfdb_iso': '288.a', 'p': 53, 'prec': 20, 'unit': 566148829173454245717073710393419, 'val': 1}
  • id: 2863
    {'lmfdb_iso': '288.a', 'p': 61, 'prec': 20, 'unit': 7635849659047664007694093548161465, 'val': 1}
  • id: 2861
    {'lmfdb_iso': '288.a', 'p': 73, 'prec': 20, 'unit': 164720197785288767903993420419081940, 'val': 1}
  • id: 2862
    {'lmfdb_iso': '288.a', 'p': 89, 'prec': 20, 'unit': 8286545421112635956876988804803313351, 'val': 1}
  • id: 2854
    {'lmfdb_iso': '288.a', 'p': 97, 'prec': 20, 'unit': 38623986116752999508741170377566431167, 'val': 1}