Elliptic curve data - 988.b1

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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': '988c', 'Clabel': '988c1', 'Cnumber': 1, 'abc_quality': 1.1058997720349297, 'absD': 822016, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 38, 'ainvs': [0, 0, 0, 16, 36], 'analytic_rank': 1, 'bad_primes': [2, 13, 19], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 988, 'degree': 120, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.18027739816412565870145332759', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [1769472, 3211], 'lmfdb_iso': '988.b', 'lmfdb_label': '988.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 16, 36], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['38.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.19338157133963465991308156272', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 19], [13, 14, 76], [19, 20, 52]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.64237551853742253164627474189', 'prec': 107}, 'szpiro_ratio': 3.0004546788786777, '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, 0, 0, -3, 0, 3, 0, -3, 0, 3, 0, -1, 0, 0, 0, -7, 0, 1, 0], 'aplist': [0, 0, -3, 3, 3, -1, -7, 1, 0, -8, 2, -8, 2, 1, -7, -4, -12, -9, 2, 4, -13, 6, 4, -6, 4], 'class_deg': 1, 'class_size': 1, 'conductor': 988, 'isogeny_matrix': [[1]], 'lmfdb_iso': '988.b', 'trace_hash': 1366818698804460812}
• 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': '1.4341248410861682847235899287', 'prec': 100}, 'conductor': 988, 'gens': [[8, 26, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.19338157133963465991308156272', 'prec': 103}], 'lmfdb_label': '988.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.9393544816600979715406634193', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2502125022879546014799083900358842149', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [0, 8]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '988.b1'}
• ec_torsion_growth •

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

  
  
  • id: 47914
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '988.b1', 'torsion': [2]}
  • id: 47915
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '988.b1', 'torsion': [2, 2]}
  • id: 47916
    {'degree': 8, 'field': [-1587, 0, 924, 0, -138, 0, 0, 0, 1], 'lmfdb_label': '988.b1', 'torsion': [3]}
  • id: 47917
    {'degree': 12, 'field': [-1482, 532, 3268, 2204, -376, -832, -180, 140, 68, -10, -12, 0, 1], 'lmfdb_label': '988.b1', '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: 13678
    {'conductor': 988, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '988.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 13679
    {'conductor': 988, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '988.b1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 13680
    {'conductor': 988, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '988.b1', 'prime': 19, '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': [[37, 2, 36, 3], [1, 2, 0, 1], [1, 0, 2, 1], [21, 2, 21, 3], [1, 1, 37, 0]], 'adelic_image': '38.2.0.?', 'conductor': 988, 'lmfdb_label': '988.b1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 22195
    {'lmfdb_iso': '988.b', 'p': 5, 'prec': 20, 'unit': 2490048120393, 'val': 2}
  • id: 22196
    {'lmfdb_iso': '988.b', 'p': 7, 'prec': 20, 'unit': 4152980389542797, 'val': 1}
  • id: 22194
    {'lmfdb_iso': '988.b', 'p': 11, 'prec': 20, 'unit': 40685180921358649306, 'val': 1}
  • id: 22202
    {'lmfdb_iso': '988.b', 'p': 17, 'prec': 20, 'unit': 103899756682240156926811, 'val': 1}
  • id: 22200
    {'lmfdb_iso': '988.b', 'p': 29, 'prec': 20, 'unit': 3641584413990581702723271252, 'val': 1}
  • id: 22197
    {'lmfdb_iso': '988.b', 'p': 31, 'prec': 20, 'unit': 573710638019518925598234003, 'val': 2}
  • id: 22211
    {'lmfdb_iso': '988.b', 'p': 37, 'prec': 20, 'unit': 469693757058892145612644887297, 'val': 1}
  • id: 22198
    {'lmfdb_iso': '988.b', 'p': 41, 'prec': 20, 'unit': 44045517852765924250302491814, 'val': 2}
  • id: 22199
    {'lmfdb_iso': '988.b', 'p': 43, 'prec': 20, 'unit': 456919310568704662816148662699129, 'val': -1}
  • id: 22209
    {'lmfdb_iso': '988.b', 'p': 47, 'prec': 20, 'unit': 18721144368099474276343656464132, 'val': 1}
  • id: 22204
    {'lmfdb_iso': '988.b', 'p': 53, 'prec': 20, 'unit': 213671803244429444272046564817247, 'val': 1}
  • id: 22205
    {'lmfdb_iso': '988.b', 'p': 59, 'prec': 20, 'unit': 599259845620288335123400652974632, 'val': 1}
  • id: 22210
    {'lmfdb_iso': '988.b', 'p': 61, 'prec': 20, 'unit': 3446241938167830947718495436108638, 'val': 1}
  • id: 22193
    {'lmfdb_iso': '988.b', 'p': 67, 'prec': 20, 'unit': 7459675214936365382671895969300592, 'val': 1}
  • id: 22208
    {'lmfdb_iso': '988.b', 'p': 71, 'prec': 20, 'unit': 50988630474325398725463554491820557, 'val': 1}
  • id: 22206
    {'lmfdb_iso': '988.b', 'p': 73, 'prec': 20, 'unit': 31316701999472242803261406870393605, 'val': 1}
  • id: 22201
    {'lmfdb_iso': '988.b', 'p': 79, 'prec': 20, 'unit': 160064496332404841196269455859024238, 'val': 1}
  • id: 22203
    {'lmfdb_iso': '988.b', 'p': 83, 'prec': 20, 'unit': 2671562263117993471757708482275469419, 'val': 1}
  • id: 22207
    {'lmfdb_iso': '988.b', 'p': 89, 'prec': 20, 'unit': 5555830445634923814062926398675950932, 'val': 1}
  • id: 22192
    {'lmfdb_iso': '988.b', 'p': 97, 'prec': 20, 'unit': 9014955571425951582135785722929433494, 'val': 1}