Elliptic curve data - 288.d2

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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': '288d', 'Clabel': '288d3', 'Cnumber': 3, 'abc_quality': 1.172456969504371, 'absD': 373248, 'ainvs': [0, 0, 0, -99, 378], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 4, 'class_size': 4, 'cm': -16, 'conductor': 288, 'degree': 32, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.068079601017509363137420343384', 'prec': 110}, 'faltings_index': 2, 'faltings_ratio': 2, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4], 'jinv': [287496, 1], 'lmfdb_iso': '288.d', 'lmfdb_label': '288.d2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -11, -14], 'min_quad_twist_disc': -3, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 6, 32]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1372461307715231908979670529', 'prec': 103}, 'szpiro_ratio': 4.485103272788107, '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, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, 2, 0, 0, 6, -2, 0, 0, 10, 0, -2, -10, 0, 0, -14, 0, -10, 0, 0, -6, 0, 0, -10, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 288, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '288.d', 'trace_hash': 2083241323606420378}
• 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': '1.1458643030033954712483492966', 'prec': 100}, 'conductor': 288, 'gens': [], 'heights': [], 'lmfdb_label': '288.d2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.0276912696024942909434725134', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5138456348012471454717362566780873986', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[6, 0, 1]], 'xcoord_integral_points': [6]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a'}, 'iwp0': 3, 'lmfdb_label': '288.d2'}
• ec_torsion_growth •

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

  
  
  • id: 12105
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [4]}
  • id: 12106
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [4]}
  • id: 12104
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [2, 2]}
  • id: 12107
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [2, 4]}
  • id: 12111
    {'degree': 8, 'field': [-3, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [12]}
  • id: 12109
    {'degree': 8, 'field': [1, 0, -16, 0, 20, 0, -8, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [2, 8]}
  • id: 12110
    {'degree': 8, 'field': [4, 0, -4, 0, 2, 0, -2, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [8]}
  • id: 12108
    {'degree': 8, 'field': [4, 0, 0, 0, 2, 0, 0, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [2, 4]}
  • id: 12112
    {'degree': 8, 'field': [34, -76, 48, 8, -12, -4, 2, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [10]}
  • id: 12116
    {'degree': 16, 'field': [-1844, 4632, -5456, 2560, 3672, -9344, 8824, -3728, 182, 700, -604, 272, -40, -8, 6, -4, 1], 'lmfdb_label': '288.d2', 'torsion': [10]}
  • id: 12115
    {'degree': 16, 'field': [1, -8, 26, -48, 80, -172, 328, -444, 451, -372, 256, -152, 80, -36, 14, -4, 1], 'lmfdb_label': '288.d2', 'torsion': [3, 12]}
  • id: 12113
    {'degree': 16, 'field': [1, 0, -4, 0, 8, 0, -24, 0, 47, 0, -24, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [4, 4]}
  • id: 12114
    {'degree': 16, 'field': [1, 0, 0, 0, -6, 0, 0, 0, 35, 0, 0, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [2, 8]}
  • id: 12119
    {'degree': 16, 'field': [1, 4, 4, 32, 46, -384, 768, -976, 1036, -948, 700, -424, 226, -104, 36, -8, 1], 'lmfdb_label': '288.d2', 'torsion': [20]}
  • id: 12117
    {'degree': 16, 'field': [4, 0, -16, 0, 16, 0, 8, 0, -20, 0, -16, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [2, 12]}
  • id: 12120
    {'degree': 16, 'field': [25, 0, 0, 0, 10, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1], 'lmfdb_label': '288.d2', 'torsion': [20]}
  • id: 12118
    {'degree': 16, 'field': [34, -232, 964, -2592, 5036, -7240, 8260, -7720, 6076, -4060, 2332, -1136, 474, -160, 44, -8, 1], 'lmfdb_label': '288.d2', 'torsion': [2, 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: 2631
    {'conductor': 288, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '288.d2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2632
    {'conductor': 288, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '288.d2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 288.d2 does not appear in ec_galrep
• lmfdb_iso 288.d does not appear in ec_padic