Elliptic curve data - 8976.h1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '8976m', 'Clabel': '8976m3', 'Cnumber': 3, 'abc_quality': 1.1764898982289331, 'absD': 3340929972830208, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 264, 'ainvs': [0, -1, 0, -265513088, 1665329197056], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 8976, 'degree': 829440, 'elladic_images': ['8.6.0.4', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1340920652190196062270612315', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [505384091400037554067434625, 815656731648], 'lmfdb_iso': '8976.h', 'lmfdb_label': '8976.h1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -16594568, -26020768704], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.d.1', '12.24.0-6.a.1.9', '24.48.0-24.bx.1.1', '66.24.0.b.1', '132.48.0.?', '264.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4409448846590742968098291100', 'prec': 100}, 'szpiro_ratio': 7.668946670730743, '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, 0, 0, -2, 0, 1, 0, -1, 0, -4, 0, 0, 0, -1, 0, -8, 0], 'aplist': [0, -1, 0, -2, -1, -4, -1, -8, -6, 6, 4, 2, -6, 4, -6, -12, 0, -4, 4, -6, 2, 10, -12, 18, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 8976, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '8976.h', 'trace_hash': 495552068481473179}
• 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': '0.0018956677450881293810363244634', 'prec': 110}, 'conductor': 8976, 'gens': [], 'heights': [], 'lmfdb_label': '8976.h1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20274219346730625014329454643', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.40548438693461250028658909286230748495', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[9408, 0, 1]], 'xcoord_integral_points': [9408]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '11': [0, 0], '17': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '8976.h1'}
• ec_torsion_growth •

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

  
  
  • id: 467327
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '8976.h1', 'torsion': [2, 2]}
  • id: 467328
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [6]}
  • id: 467330
    {'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [2, 6]}
  • id: 467329
    {'degree': 4, 'field': [9, -8, 0, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [4]}
  • id: 467331
    {'degree': 6, 'field': [4356, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [6]}
  • id: 467334
    {'degree': 8, 'field': [4, -8, 12, 0, -2, 0, 6, -4, 1], 'lmfdb_label': '8976.h1', 'torsion': [12]}
  • id: 467333
    {'degree': 8, 'field': [36, 0, 204, 0, 13, 0, 10, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [2, 4]}
  • id: 467332
    {'degree': 8, 'field': [5683456, 669904, -311110, -16409, -2663, -280, -142, -1, 1], 'lmfdb_label': '8976.h1', 'torsion': [2, 4]}
  • id: 467336
    {'degree': 12, 'field': [4356, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [2, 6]}
  • id: 467335
    {'degree': 12, 'field': [18983449, -1725372, 143745, -1151436, 39210, 2772, 26129, 0, 6, -264, -3, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [3, 6]}
  • id: 467339
    {'degree': 16, 'field': [1, 0, 12, 0, -47, 0, 108, 0, 336, 0, 108, 0, -47, 0, 12, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [2, 12]}
  • id: 467337
    {'degree': 16, 'field': [432972864, 0, -64255104, 0, -496400, 0, -462032, 0, 41305, 0, 3548, 0, 298, 0, 4, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [8]}
  • id: 467338
    {'degree': 16, 'field': [75524933124, 0, -4660462296, 0, -949267119, 0, 12769476, 0, 3025348, 0, -3626, 0, -3216, 0, -8, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [2, 12]}
  • id: 467340
    {'degree': 18, 'field': [-726865211952, 0, 549887849280, 0, -164771432496, 0, 22497115212, 0, -1582391052, 0, 64194768, 0, -1627719, 0, 25569, 0, -234, 0, 1], 'lmfdb_label': '8976.h1', 'torsion': [18]}
• 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: 187754
    {'conductor': 8976, 'conductor_valuation': 4, 'discriminant_valuation': 22, 'j_denominator_valuation': 10, 'kodaira_symbol': -18, 'lmfdb_label': '8976.h1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 187755
    {'conductor': 8976, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8976.h1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 187756
    {'conductor': 8976, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8976.h1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 187757
    {'conductor': 8976, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '8976.h1', 'prime': 17, 'reduction_type': -1, '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: 1723277
    {'adelic_gens': [[11, 2, 214, 255], [130, 3, 45, 256], [230, 3, 61, 256], [1, 12, 0, 1], [1, 6, 6, 37], [1, 0, 12, 1], [253, 12, 252, 13], [249, 206, 34, 259], [133, 12, 6, 73]], 'adelic_image': '264.96.1.?', 'conductor': 8976, 'lmfdb_label': '8976.h1', 'prime': 0}
  • id: 43688
    {'conductor': 8976, 'elladic_image': '8.6.0.4', 'lmfdb_label': '8976.h1', 'modell_image': '2B', 'prime': 2}
  • id: 43689
    {'conductor': 8976, 'elladic_image': '3.4.0.1', 'lmfdb_label': '8976.h1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 8976.h does not appear in ec_padic