Elliptic curve data - 8976.ba4

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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': '8976x', 'Clabel': '8976x4', 'Cnumber': 4, 'abc_quality': 1.0924697760886544, 'absD': 212416063475457245184, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 4488, 'ainvs': [0, 1, 0, 819528, -640164780], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 8976, 'degree': 368640, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5834131697006351293232752776', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2, 4], 'jinv': [14861225463775641287, 51859390496937804], 'lmfdb_iso': '8976.ba', 'lmfdb_label': '8976.ba4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 51221, 10028185], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0-4.c.1.2', '68.12.0-4.c.1.2', '88.12.0.?', '102.6.0.?', '204.24.0.?', '264.24.0.?', '1496.24.0.?', '4488.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.9632380310128935041066394261', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 51], [3, 4, 272], [5, 2, 2992], [11, 12, 816], [17, 18, 528]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8902659891406898199060431561', 'prec': 100}, 'szpiro_ratio': 5.9411812344319, '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, 2, 0, -4, 0, 1, 0, -1, 0, 6, 0, 2, 0, -1, 0, -4, 0], 'aplist': [0, 1, 2, -4, -1, 6, -1, -4, 0, 2, 0, -10, -10, 4, -4, -2, 0, 2, -12, 0, -10, -4, 12, -14, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 8976, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '8976.ba', 'trace_hash': 1580043496378457475}
• 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': '0.0057026383694451567261025475723', 'prec': 110}, 'conductor': 8976, 'gens': [[1188, 44850, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.9632380310128935041066394261', 'prec': 100}], 'lmfdb_label': '8976.ba4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.090504972877005162535609518247', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.3970269625594759685514402691420119813', 'prec': 130}, 'tamagawa_product': 40, 'torsion_generators': [[563, 0, 1]], 'xcoord_integral_points': [563, 1188]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [3, 0], '17': [1, 0], '19': [3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '8976.ba4'}
• ec_torsion_growth •

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

  
  
  • id: 467574
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '8976.ba4', 'torsion': [4]}
  • id: 467575
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '8976.ba4', 'torsion': [4]}
  • id: 467573
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '8976.ba4', 'torsion': [2, 2]}
  • id: 467576
    {'degree': 4, 'field': [16, 4, 5, -1, 1], 'lmfdb_label': '8976.ba4', 'torsion': [2, 4]}
  • id: 467580
    {'degree': 8, 'field': [-192, 0, 80, 0, 48, 0, 0, 0, 1], 'lmfdb_label': '8976.ba4', 'torsion': [6]}
  • id: 467577
    {'degree': 8, 'field': [2601, 0, 0, 0, 714, 0, 0, 0, 1], 'lmfdb_label': '8976.ba4', 'torsion': [2, 4]}
  • id: 467578
    {'degree': 8, 'field': [10404, 0, 34680, 0, -1751, 0, -34, 0, 1], 'lmfdb_label': '8976.ba4', 'torsion': [8]}
  • id: 467579
    {'degree': 8, 'field': [41616, 0, 7344, 0, 1500, 0, -36, 0, 1], 'lmfdb_label': '8976.ba4', 'torsion': [8]}
  • id: 467585
    {'degree': 16, 'field': [144, 0, -3708, 0, -4472, 0, 648, 0, -339, 0, -660, 0, -78, 0, 0, 0, 1], 'lmfdb_label': '8976.ba4', 'torsion': [12]}
  • id: 467586
    {'degree': 16, 'field': [11664, 0, 0, 0, -3888, 0, -1080, 0, 1404, 0, 180, 0, 61, 0, -5, 0, 1], 'lmfdb_label': '8976.ba4', 'torsion': [12]}
  • id: 467584
    {'degree': 16, 'field': [5322249, 0, 3239484, 0, 1251250, 0, -178872, 0, 23223, 0, -728, 0, 330, 0, 0, 0, 1], 'lmfdb_label': '8976.ba4', 'torsion': [2, 6]}
  • id: 467581
    {'degree': 16, 'field': [7038409, 0, -1506952, 0, -185630, 0, 47924, 0, 21235, 0, -220, 0, -194, 0, -4, 0, 1], 'lmfdb_label': '8976.ba4', 'torsion': [4, 4]}
  • id: 467583
    {'degree': 16, 'field': [18974736, 0, 173072592, 0, 405225612, 0, -43471560, 0, -1020791, 0, 115000, 0, 5562, 0, 112, 0, 1], 'lmfdb_label': '8976.ba4', 'torsion': [2, 8]}
  • id: 467582
    {'degree': 16, 'field': [607525983, -70467228, 317173788, -31286736, 61147155, -4690236, 7203342, -809988, 737806, -105844, 55168, -6952, 2527, -244, 70, -4, 1], 'lmfdb_label': '8976.ba4', 'torsion': [2, 8]}
• 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: 187858
    {'conductor': 8976, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '8976.ba4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 187859
    {'conductor': 8976, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '8976.ba4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 187860
    {'conductor': 8976, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '8976.ba4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 187861
    {'conductor': 8976, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8976.ba4', 'prime': 17, '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

  
  
  • id: 1723257
    {'adelic_gens': [[1504, 3, 1501, 2], [1, 0, 8, 1], [7, 6, 4482, 4483], [1, 8, 0, 1], [1, 4, 4, 17], [3931, 3930, 2818, 571], [409, 8, 1636, 33], [4228, 1, 1871, 6], [4481, 8, 4480, 9], [2797, 2804, 2758, 555]], 'adelic_image': '4488.48.0.?', 'conductor': 8976, 'lmfdb_label': '8976.ba4', 'prime': 0}
  • id: 43671
    {'conductor': 8976, 'elladic_image': '4.6.0.1', 'lmfdb_label': '8976.ba4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 374146
    {'lmfdb_iso': '8976.ba', 'p': 5, 'prec': 20, 'unit': 18786188427686, 'val': 0}
  • id: 374134
    {'lmfdb_iso': '8976.ba', 'p': 7, 'prec': 20, 'unit': 10010283079116259, 'val': 1}
  • id: 374138
    {'lmfdb_iso': '8976.ba', 'p': 13, 'prec': 20, 'unit': 20311205456292922118, 'val': 2}
  • id: 374140
    {'lmfdb_iso': '8976.ba', 'p': 19, 'prec': 20, 'unit': 75883658906258714309239, 'val': 2}
  • id: 374137
    {'lmfdb_iso': '8976.ba', 'p': 29, 'prec': 20, 'unit': 1039303621329489949326806272, 'val': 1}
  • id: 374133
    {'lmfdb_iso': '8976.ba', 'p': 37, 'prec': 20, 'unit': 245185214628550767430019822024, 'val': 1}
  • id: 374135
    {'lmfdb_iso': '8976.ba', 'p': 41, 'prec': 20, 'unit': 2383956699368892932815858823277, 'val': 1}
  • id: 374136
    {'lmfdb_iso': '8976.ba', 'p': 43, 'prec': 20, 'unit': 3542576161604048955413700809033, 'val': 1}
  • id: 374139
    {'lmfdb_iso': '8976.ba', 'p': 47, 'prec': 20, 'unit': 747023607833261634082458267272, 'val': 1}
  • id: 374141
    {'lmfdb_iso': '8976.ba', 'p': 53, 'prec': 20, 'unit': 348730350972065963966434524091769, 'val': 1}
  • id: 374145
    {'lmfdb_iso': '8976.ba', 'p': 61, 'prec': 20, 'unit': 3852449708869690124604853986993409, 'val': 1}
  • id: 374132
    {'lmfdb_iso': '8976.ba', 'p': 67, 'prec': 20, 'unit': 15426432178073176264605463730946926, 'val': 1}
  • id: 374142
    {'lmfdb_iso': '8976.ba', 'p': 73, 'prec': 20, 'unit': 103176770210218337217219274165327687, 'val': 1}
  • id: 374144
    {'lmfdb_iso': '8976.ba', 'p': 79, 'prec': 20, 'unit': 709425273322462564140742528508832688, 'val': 1}
  • id: 374131
    {'lmfdb_iso': '8976.ba', 'p': 83, 'prec': 20, 'unit': 2896888454222135357813338527241929955, 'val': 1}
  • id: 374143
    {'lmfdb_iso': '8976.ba', 'p': 89, 'prec': 20, 'unit': 4293559292905127882237908500454082928, 'val': 1}
  • id: 374130
    {'lmfdb_iso': '8976.ba', 'p': 97, 'prec': 20, 'unit': 25839406728339457195118407610802608077, 'val': 1}