Elliptic curve data - 9408.b2

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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': '9408ch', 'Clabel': '9408ch1', 'Cnumber': 1, 'abc_quality': 1.1327926724636421, 'absD': 13709678915616768, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 56, 'ainvs': [0, -1, 0, 7775, 5624641], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 9408, 'degree': 86016, 'elladic_images': ['8.48.0.203'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7755833047251611573793236903', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [4913, 1296], 'lmfdb_iso': '9408.b', 'lmfdb_label': '9408.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 2, 32], 'min_quad_twist_disc': 56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.f.1', '8.48.0.q.1', '14.6.0.b.1', '28.24.0.g.1', '56.96.1.co.2'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7699289568482357412839756096', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 7], [3, 4, 3136], [7, 20, 192]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.72357007790624178557553904947', 'prec': 107}, 'szpiro_ratio': 4.8757091580653915, '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, -1, 0, -4, 0, 0, 0, 1, 0, -4, 0, -4, 0, 4, 0, 0, 0, 4, 0], 'aplist': [0, -1, -4, 0, -4, -4, 0, 4, 0, -2, -8, 6, 0, 4, 8, 10, 4, 4, 4, -8, -16, 8, -12, 8, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 9408, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '9408.b', 'trace_hash': 1925021392247864911}
• 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': '0.028691148757358454164756798841', 'prec': 107}, 'conductor': 9408, 'gens': [[-35, 2304, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7699289568482357412839756096', 'prec': 100}], 'lmfdb_label': '9408.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.30742016307851792720036808049', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1764473942067030033263152115708025266', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-163, 0, 1]], 'xcoord_integral_points': [-163, -35, 523]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [5, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 3, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '9408.b2'}
• ec_torsion_growth •

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

  
  
  • id: 490214
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '9408.b2', 'torsion': [2, 2]}
  • id: 490215
    {'degree': 4, 'field': [-7, 0, 0, 0, 1], 'lmfdb_label': '9408.b2', 'torsion': [8]}
  • id: 490216
    {'degree': 4, 'field': [28, 0, 0, 0, 1], 'lmfdb_label': '9408.b2', 'torsion': [2, 4]}
  • id: 490218
    {'degree': 8, 'field': [-37632, 0, 7840, 0, -672, 0, 0, 0, 1], 'lmfdb_label': '9408.b2', 'torsion': [6]}
  • id: 490217
    {'degree': 8, 'field': [36, 0, 88, 0, -8, 0, 4, 0, 1], 'lmfdb_label': '9408.b2', 'torsion': [4, 8]}
  • id: 490221
    {'degree': 16, 'field': [-16358, 19064, -3412, -13864, 26278, -36608, 28392, -4268, -7141, 3924, -472, 28, -130, 44, 12, -8, 1], 'lmfdb_label': '9408.b2', 'torsion': [16]}
  • id: 490220
    {'degree': 16, 'field': [16, 64, 248, 304, 464, 320, 498, 368, 3, -2, -7, 38, -24, -14, 15, -6, 1], 'lmfdb_label': '9408.b2', 'torsion': [2, 8]}
  • id: 490219
    {'degree': 16, 'field': [396, -1944, 4278, -6060, 6049, -4194, 2077, -594, 236, -294, 247, -150, 80, -42, 19, -6, 1], 'lmfdb_label': '9408.b2', 'torsion': [2, 8]}
  • id: 490222
    {'degree': 16, 'field': [5531904, 0, -10372320, 0, 4170880, 0, 740880, 0, 23520, 0, 4410, 0, 336, 0, 0, 0, 1], 'lmfdb_label': '9408.b2', 'torsion': [2, 6]}
• 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: 198070
    {'conductor': 9408, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '9408.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 198071
    {'conductor': 9408, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '9408.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 198072
    {'conductor': 9408, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '9408.b2', 'prime': 7, 'reduction_type': 0, '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: 1726113
    {'adelic_gens': [[3, 4, 52, 51], [49, 8, 48, 9], [1, 8, 28, 29], [1, 0, 8, 1], [5, 4, 52, 53], [1, 8, 0, 15], [24, 5, 27, 32], [1, 8, 0, 1]], 'adelic_image': '56.96.1.?', 'conductor': 9408, 'lmfdb_label': '9408.b2', 'prime': 0}
  • id: 45582
    {'conductor': 9408, 'elladic_image': '8.48.0.203', 'lmfdb_label': '9408.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 394658
    {'lmfdb_iso': '9408.b', 'p': 5, 'prec': 20, 'unit': 28042570305951, 'val': -1}
  • id: 394657
    {'lmfdb_iso': '9408.b', 'p': 11, 'prec': 20, 'unit': 52142397834854514423, 'val': 1}
  • id: 394664
    {'lmfdb_iso': '9408.b', 'p': 13, 'prec': 20, 'unit': 173790710814341593910, 'val': 1}
  • id: 394667
    {'lmfdb_iso': '9408.b', 'p': 19, 'prec': 20, 'unit': 1759485211890472983400590, 'val': 1}
  • id: 394663
    {'lmfdb_iso': '9408.b', 'p': 29, 'prec': 20, 'unit': 3926404414947823110151072066, 'val': 1}
  • id: 394660
    {'lmfdb_iso': '9408.b', 'p': 31, 'prec': 20, 'unit': 2582054871769757481613211744, 'val': 1}
  • id: 394673
    {'lmfdb_iso': '9408.b', 'p': 37, 'prec': 20, 'unit': 232279047469306856188725100678, 'val': 1}
  • id: 394662
    {'lmfdb_iso': '9408.b', 'p': 43, 'prec': 20, 'unit': 3148577162035242794163027283235, 'val': 1}
  • id: 394671
    {'lmfdb_iso': '9408.b', 'p': 47, 'prec': 20, 'unit': 31800955176191311323159469981891, 'val': 1}
  • id: 394668
    {'lmfdb_iso': '9408.b', 'p': 53, 'prec': 20, 'unit': 43137006905765642246929055565191, 'val': 1}
  • id: 394666
    {'lmfdb_iso': '9408.b', 'p': 59, 'prec': 20, 'unit': 2465569776969879581554263378625650, 'val': 1}
  • id: 394672
    {'lmfdb_iso': '9408.b', 'p': 61, 'prec': 20, 'unit': 2944118100003037529534751080754842, 'val': 1}
  • id: 394656
    {'lmfdb_iso': '9408.b', 'p': 67, 'prec': 20, 'unit': 47051703518835021129145157253487515, 'val': 1}
  • id: 394659
    {'lmfdb_iso': '9408.b', 'p': 71, 'prec': 20, 'unit': 28076910041287690738270462997470922, 'val': 1}
  • id: 394661
    {'lmfdb_iso': '9408.b', 'p': 73, 'prec': 20, 'unit': 44152128924599809839908441714423534, 'val': 1}
  • id: 394665
    {'lmfdb_iso': '9408.b', 'p': 79, 'prec': 20, 'unit': 512821552261651648182996320845254112, 'val': 1}
  • id: 394669
    {'lmfdb_iso': '9408.b', 'p': 83, 'prec': 20, 'unit': 1744670968347270703613949027151048845, 'val': 1}
  • id: 394670
    {'lmfdb_iso': '9408.b', 'p': 89, 'prec': 20, 'unit': 10606291000451224401071130270218297333, 'val': 1}
  • id: 394655
    {'lmfdb_iso': '9408.b', 'p': 97, 'prec': 20, 'unit': 18798279088657694108764068858932383833, 'val': 1}