Elliptic curve data - 9680.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
  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': '9680m', 'Clabel': '9680m1', 'Cnumber': 1, 'abc_quality': 1.0570730436530982, 'absD': 4944974716076032000, 'adelic_genus': 5, 'adelic_index': 144, 'adelic_level': 660, 'ainvs': [0, 1, 0, -398856, -144518156], 'analytic_rank': 0, 'bad_primes': [2, 5, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 9680, 'degree': 190080, 'elladic_images': ['2.3.0.1', '3.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2870826510830802091754222120', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [-726572699, 512000], 'lmfdb_iso': '9680.b', 'lmfdb_label': '9680.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -206, -1781], 'min_quad_twist_disc': 44, 'modell_images': ['2B', '3Ns'], 'modm_images': ['2.3.0.a.1', '3.6.0.b.1', '6.18.0.b.1', '12.36.0.c.1', '20.6.0.e.1', '30.36.0.d.1', '33.12.0.a.1', '44.6.0.b.1', '60.72.1.eu.1', '66.36.0.a.1', '110.6.0.?', '132.72.1.?', '220.12.0.?', '330.72.1.?', '660.144.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 55], [3, 2, 1936], [5, 6, 1936], [11, 42, 80]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.20448598407564300828826759293', 'prec': 107}, 'szpiro_ratio': 5.567678584187435, '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, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, -6, 0, 2, 0, -6, 0, 0, 0], 'aplist': [0, -2, -1, 0, 0, -6, -6, 0, 6, 0, -4, -2, -12, -12, -6, 6, 0, 0, 14, 0, -6, -12, -12, 6, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 9680, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '9680.b', 'trace_hash': 151459061480105839}
• 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': '0.010314905414903494234437217534', 'prec': 107}, 'conductor': 9680, 'gens': [], 'heights': [], 'lmfdb_label': '9680.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.092122976191415143007747298430', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.18424595238283028601549459685954147521', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[766, 0, 1]], 'xcoord_integral_points': [766]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '5': [0, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '9680.b2'}
• ec_torsion_growth •

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

  
  
  • id: 502308
    {'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '9680.b2', 'torsion': [2, 2]}
  • id: 502310
    {'degree': 4, 'field': [-44, 0, -11, 0, 1], 'lmfdb_label': '9680.b2', 'torsion': [6]}
  • id: 502309
    {'degree': 4, 'field': [-2, -6, 7, -2, 1], 'lmfdb_label': '9680.b2', 'torsion': [4]}
  • id: 502311
    {'degree': 4, 'field': [33, 0, 11, 0, 1], 'lmfdb_label': '9680.b2', 'torsion': [6]}
  • id: 502313
    {'degree': 8, 'field': [71, -220, 298, -220, 79, 0, -8, 0, 1], 'lmfdb_label': '9680.b2', 'torsion': [2, 4]}
  • id: 502312
    {'degree': 8, 'field': [784, 344, 390, -110, -39, 22, 12, -4, 1], 'lmfdb_label': '9680.b2', 'torsion': [2, 4]}
  • id: 502314
    {'degree': 8, 'field': [1089, 0, -363, 0, 88, 0, -11, 0, 1], 'lmfdb_label': '9680.b2', 'torsion': [3, 6]}
  • id: 502315
    {'degree': 8, 'field': [1224, -4392, 4422, -54, 13, 14, 0, -4, 1], 'lmfdb_label': '9680.b2', 'torsion': [2, 6]}
  • id: 502316
    {'degree': 8, 'field': [2564, -964, 1146, -382, 237, -58, 24, -4, 1], 'lmfdb_label': '9680.b2', 'torsion': [2, 6]}
  • id: 502320
    {'degree': 16, 'field': [5, -30, 523, -1992, 3913, -4526, 3090, -1070, 58, 6, 122, -146, 109, -60, 23, -6, 1], 'lmfdb_label': '9680.b2', 'torsion': [12]}
  • id: 502317
    {'degree': 16, 'field': [25, 0, -7248, 0, -7828, 0, 1488, 0, -1010, 0, -240, 0, 124, 0, -16, 0, 1], 'lmfdb_label': '9680.b2', 'torsion': [8]}
  • id: 502319
    {'degree': 16, 'field': [64, -32, -88, 48, -78, 350, 53, -356, -130, 154, 77, -80, -5, 16, 2, -4, 1], 'lmfdb_label': '9680.b2', 'torsion': [12]}
  • id: 502318
    {'degree': 16, 'field': [569284, -890468, 1443610, -1220030, 1115573, -680186, 451860, -200210, 109832, -33694, 15930, -3310, 1328, -178, 58, -4, 1], 'lmfdb_label': '9680.b2', 'torsion': [6, 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: 203791
    {'conductor': 9680, 'conductor_valuation': 4, 'discriminant_valuation': 24, 'j_denominator_valuation': 12, 'kodaira_symbol': -20, 'lmfdb_label': '9680.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 203792
    {'conductor': 9680, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '9680.b2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 203793
    {'conductor': 9680, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '9680.b2', 'prime': 11, '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: 1727899
    {'adelic_gens': [[7, 12, 144, 247], [389, 498, 186, 71], [1, 0, 12, 1], [649, 12, 648, 13], [1, 6, 6, 37], [5, 12, 612, 545], [1, 12, 0, 1], [552, 5, 127, 588], [3, 442, 22, 15], [10, 3, 501, 652]], 'adelic_image': '660.144.5.?', 'conductor': 9680, 'lmfdb_label': '9680.b2', 'prime': 0}
  • id: 46755
    {'conductor': 9680, 'elladic_image': '2.3.0.1', 'lmfdb_label': '9680.b2', 'modell_image': '2B', 'prime': 2}
  • id: 46756
    {'conductor': 9680, 'elladic_image': '3.6.0.1', 'lmfdb_label': '9680.b2', 'modell_image': '3Ns', 'prime': 3}
• lmfdb_iso 9680.b does not appear in ec_padic