Elliptic curve data - 8976.z4

Formats: - HTML - YAML - JSON - 2024-05-02T08:45:19.920755

• 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': '8976bc', 'Clabel': '8976bc4', 'Cnumber': 4, 'abc_quality': 0.9733322416401273, 'absD': 543176581128192, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 136, 'ainvs': [0, 1, 0, 12848, -966892], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 8976, 'degree': 36864, 'elladic_images': ['8.24.0.48'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5114065370924891744701722806', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 4], 'jinv': [57258048889007, 132611470002], 'lmfdb_iso': '8976.z', 'lmfdb_label': '8976.z4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 803, 15509], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.d.1.2', '136.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.81825935653254386505294015914', 'prec': 103}, 'szpiro_ratio': 4.514861644397981, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, -2, 0, 2, 0, 1, 0, -4, 0], 'aplist': [0, 1, 2, -4, -1, -2, 1, -4, 4, -6, 4, 2, 10, -4, 8, 6, 4, -6, -12, 12, 2, -4, 4, 10, 10], '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.z', 'trace_hash': 1991056980437603553}
• 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': '0.048664129824958480244746372362', 'prec': 107}, 'conductor': 8976, 'gens': [], 'heights': [], 'lmfdb_label': '8976.z4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.26909596232231362653052152229', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1527676985785090122441721783292315840', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[212, 3366, 1]], 'xcoord_integral_points': [59, 212]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '11': [0, 0], '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '8976.z4'}
• ec_torsion_growth •

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

  
  
  • id: 467708
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '8976.z4', 'torsion': [2, 4]}
  • id: 467709
    {'degree': 4, 'field': [-242, 0, -33, 0, 1], 'lmfdb_label': '8976.z4', 'torsion': [8]}
  • id: 467713
    {'degree': 8, 'field': [-48, 0, 548, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '8976.z4', 'torsion': [12]}
  • id: 467711
    {'degree': 8, 'field': [81, 0, -28, 0, 120, 0, -12, 0, 1], 'lmfdb_label': '8976.z4', 'torsion': [2, 8]}
  • id: 467712
    {'degree': 8, 'field': [13689, 0, 1818, 0, 394, 0, 42, 0, 1], 'lmfdb_label': '8976.z4', 'torsion': [2, 8]}
  • id: 467710
    {'degree': 8, 'field': [14641, 0, -5324, 0, 968, 0, -44, 0, 1], 'lmfdb_label': '8976.z4', 'torsion': [4, 4]}
  • id: 467715
    {'degree': 16, 'field': [1498176, 0, 1498176, 0, 374544, 0, -65152, 0, -23632, 0, 1736, 0, 64, 0, 16, 0, 1], 'lmfdb_label': '8976.z4', 'torsion': [2, 12]}
  • id: 467714
    {'degree': 16, 'field': [98365031424, 0, -60111963648, 0, 27282220416, 0, 1944239616, 0, -225150992, 0, -1361976, 0, 7634, 0, 198, 0, 1], 'lmfdb_label': '8976.z4', 'torsion': [16]}
• 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: 187910
    {'conductor': 8976, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '8976.z4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 187911
    {'conductor': 8976, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '8976.z4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 187912
    {'conductor': 8976, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8976.z4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 187913
    {'conductor': 8976, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '8976.z4', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1723326
    {'adelic_gens': [[120, 59, 89, 118], [48, 111, 23, 112], [1, 0, 8, 1], [1, 4, 4, 17], [7, 6, 130, 131], [105, 8, 12, 33], [129, 8, 128, 9], [1, 8, 0, 1]], 'adelic_image': '136.48.0.?', 'conductor': 8976, 'lmfdb_label': '8976.z4', 'prime': 0}
  • id: 43737
    {'conductor': 8976, 'elladic_image': '8.24.0.48', 'lmfdb_label': '8976.z4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 8976.z does not appear in ec_padic