Elliptic curve data - 7968.a2

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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': '7968e', 'Clabel': '7968e1', 'Cnumber': 1, 'abc_quality': 1.005667872837618, 'absD': 2057977637568, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 996, 'ainvs': [0, -1, 0, -6450, 213156], 'analytic_rank': 0, 'bad_primes': [2, 3, 83], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 7968, 'degree': 27360, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1135900531481313342232811540', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [-463756716835264, 32155900587], 'lmfdb_iso': '7968.a', 'lmfdb_label': '7968.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -6450, 213156], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.b.1', '166.6.0.?', '996.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 83], [3, 4, 2656], [83, 84, 96]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.76701646286815867951466509327', 'prec': 103}, 'szpiro_ratio': 4.2348468212941, '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, 6, 0, 4, 0, 6, 0, -6, 0], 'aplist': [0, -1, -4, 0, -4, 6, 6, -6, 8, 6, -4, -10, 2, -10, 4, -12, 4, 2, 10, -8, -2, -10, -1, -8, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 7968, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '7968.a', 'trace_hash': 522862443764530535}
• 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': '0.10783207680335920101863701569', 'prec': 103}, 'conductor': 7968, 'gens': [], 'heights': [], 'lmfdb_label': '7968.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.81289842584117480290668117429', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.81289842584117480290668117429039004474', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-93, 0, 1]], 'xcoord_integral_points': [-93]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '83': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '7968.a2'}
• ec_torsion_growth •

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

  
  
  • id: 417313
    {'degree': 2, 'field': [21, -1, 1], 'lmfdb_label': '7968.a2', 'torsion': [2, 2]}
  • id: 417314
    {'degree': 4, 'field': [-23, 14, 8, -2, 1], 'lmfdb_label': '7968.a2', 'torsion': [4]}
  • id: 417317
    {'degree': 8, 'field': [-2187, 0, 1120, 0, -162, 0, 0, 0, 1], 'lmfdb_label': '7968.a2', 'torsion': [6]}
  • id: 417315
    {'degree': 8, 'field': [441, 0, 534, 0, 163, 0, -22, 0, 1], 'lmfdb_label': '7968.a2', 'torsion': [2, 4]}
  • id: 417316
    {'degree': 8, 'field': [275625, 0, -11350, 0, -253, 0, 10, 0, 1], 'lmfdb_label': '7968.a2', 'torsion': [2, 4]}
  • id: 417318
    {'degree': 16, 'field': [1164897, -9992088, -8550504, 8064216, 3771624, 2118312, 714648, 132504, 134866, -40184, 22552, -7496, 2056, -440, 88, -8, 1], 'lmfdb_label': '7968.a2', 'torsion': [8]}
  • id: 417319
    {'degree': 16, 'field': [4782969, 0, 1206600, 0, 921670, 0, 254640, 0, 28095, 0, 2240, 0, 174, 0, 0, 0, 1], 'lmfdb_label': '7968.a2', '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: 165181
    {'conductor': 7968, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '7968.a2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 165182
    {'conductor': 7968, 'conductor_valuation': 1, 'discriminant_valuation': 18, 'j_denominator_valuation': 18, 'kodaira_symbol': 22, 'lmfdb_label': '7968.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 165183
    {'conductor': 7968, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7968.a2', 'prime': 83, '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: 1716654
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [993, 4, 992, 5], [665, 4, 334, 9], [170, 1, 911, 0], [253, 748, 248, 747]], 'adelic_image': '996.12.0.?', 'conductor': 7968, 'lmfdb_label': '7968.a2', 'prime': 0}
  • id: 39084
    {'conductor': 7968, 'elladic_image': '2.3.0.1', 'lmfdb_label': '7968.a2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 7968.a does not appear in ec_padic