Elliptic curve data - 9680.f1

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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': '9680q', 'Clabel': '9680q2', 'Cnumber': 2, 'abc_quality': 0.8833424252798248, 'absD': 3872000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 660, 'ainvs': [0, -1, 0, -436, -3364], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 9680, 'degree': 1728, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.22525057340964914372020472738', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 5, 'isogeny_degrees': [1, 3], 'jinv': [-296587984, 125], 'lmfdb_iso': '9680.f', 'lmfdb_label': '9680.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -436, 3364], 'min_quad_twist_disc': -4, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '20.2.0.a.1', '60.8.0.a.1', '132.8.0.?', '330.8.0.?', '660.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.6373843227590505354189502182', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 605], [3, 2, 1936], [5, 6, 1936], [11, 32, 80]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.63649675909670948656827394992', 'prec': 107}, 'szpiro_ratio': 3.252358365406462, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 0, -1, 0, -2, 0, 0, 0, -2, 0, 1, 0, 0, 0, 2, 0], 'aplist': [0, -1, -1, -1, 0, -2, 0, 2, 0, 6, 4, -4, -9, -1, 3, -6, 0, 1, 13, 12, 16, -10, 12, -3, -10], 'class_deg': 3, 'class_size': 2, 'conductor': 9680, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '9680.f', 'trace_hash': 261627380190417128}
• 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': '0.63730868635787952568278868177', 'prec': 103}, 'conductor': 9680, 'gens': [[269, 4390, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.6373843227590505354189502182', 'prec': 100}], 'lmfdb_label': '9680.f1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.52228070505347809800557293637', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9442970587480210500768257093589661118', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': [269]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1], '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '9680.f1'}
• ec_torsion_growth •

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

  
  
  • id: 502372
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '9680.f1', 'torsion': [3]}
  • id: 502373
    {'degree': 3, 'field': [-20, 4, -1, 1], 'lmfdb_label': '9680.f1', 'torsion': [2]}
  • id: 502375
    {'degree': 6, 'field': [-176, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '9680.f1', 'torsion': [3]}
  • id: 502374
    {'degree': 6, 'field': [5, 0, 71, 0, -13, 0, 1], 'lmfdb_label': '9680.f1', 'torsion': [2, 2]}
  • id: 502376
    {'degree': 6, 'field': [37, -94, 144, -48, 20, -2, 1], 'lmfdb_label': '9680.f1', 'torsion': [6]}
  • id: 502379
    {'degree': 12, 'field': [3364, 2900, -4038, 310, 1627, -1792, 1413, -688, 338, -102, 35, -4, 1], 'lmfdb_label': '9680.f1', 'torsion': [2, 6]}
  • id: 502378
    {'degree': 12, 'field': [30625, 1050, 2661, -7090, 2730, 930, -211, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '9680.f1', 'torsion': [3, 3]}
  • id: 502377
    {'degree': 12, 'field': [45149, 80338, 12461, 10166, 5931, -2144, 3636, -1432, 679, -170, 45, -6, 1], 'lmfdb_label': '9680.f1', 'torsion': [4]}
  • id: 502381
    {'degree': 18, 'field': [-206338, 609840, -940368, 779394, -247962, -292908, 548937, -503322, 335034, -173894, 71973, -23106, 4788, -216, -231, 58, 6, -6, 1], 'lmfdb_label': '9680.f1', 'torsion': [6]}
  • id: 502380
    {'degree': 18, 'field': [2842131213, -4168710360, 1725585876, -64308510, 4979475, 8455320, -26499053, 990600, 880851, -92600, 97674, 91230, 8492, -540, 951, -10, -21, 0, 1], 'lmfdb_label': '9680.f1', 'torsion': [9]}
• 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: 203812
    {'conductor': 9680, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '9680.f1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 203813
    {'conductor': 9680, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '9680.f1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 203814
    {'conductor': 9680, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '9680.f1', 'prime': 11, 'reduction_type': 0, '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: 1727917
    {'adelic_gens': [[397, 6, 531, 19], [3, 4, 8, 11], [4, 3, 9, 7], [1, 0, 6, 1], [655, 6, 654, 7], [329, 654, 327, 641], [303, 2, 130, 7], [278, 387, 175, 7], [1, 6, 0, 1]], 'adelic_image': '660.16.0.?', 'conductor': 9680, 'lmfdb_label': '9680.f1', 'prime': 0}
  • id: 46779
    {'conductor': 9680, 'elladic_image': '3.4.0.1', 'lmfdb_label': '9680.f1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 406266
    {'lmfdb_iso': '9680.f', 'p': 7, 'prec': 20, 'unit': 3552452157437045, 'val': 1}
  • id: 406270
    {'lmfdb_iso': '9680.f', 'p': 13, 'prec': 20, 'unit': 189691553604665906087, 'val': 1}
  • id: 406272
    {'lmfdb_iso': '9680.f', 'p': 19, 'prec': 20, 'unit': 492124833733038872044809, 'val': 1}
  • id: 406269
    {'lmfdb_iso': '9680.f', 'p': 29, 'prec': 20, 'unit': 5426023958656404593102684016, 'val': 1}
  • id: 406279
    {'lmfdb_iso': '9680.f', 'p': 31, 'prec': 20, 'unit': 1453349314805532999521122305, 'val': 1}
  • id: 406265
    {'lmfdb_iso': '9680.f', 'p': 37, 'prec': 20, 'unit': 411213425222036324156876895372, 'val': 1}
  • id: 406267
    {'lmfdb_iso': '9680.f', 'p': 41, 'prec': 20, 'unit': 2604203794385065180421309210968, 'val': 1}
  • id: 406268
    {'lmfdb_iso': '9680.f', 'p': 43, 'prec': 20, 'unit': 4632015375415292399017183962807, 'val': 1}
  • id: 406271
    {'lmfdb_iso': '9680.f', 'p': 47, 'prec': 20, 'unit': 4416420157143702369473181747039, 'val': 1}
  • id: 406273
    {'lmfdb_iso': '9680.f', 'p': 53, 'prec': 20, 'unit': 142521225454955509278250125818331, 'val': 1}
  • id: 406278
    {'lmfdb_iso': '9680.f', 'p': 61, 'prec': 20, 'unit': 272243268767467631834073558390637694, 'val': -1}
  • id: 406264
    {'lmfdb_iso': '9680.f', 'p': 67, 'prec': 20, 'unit': 36061834940740489522576072925416426, 'val': 1}
  • id: 406276
    {'lmfdb_iso': '9680.f', 'p': 71, 'prec': 20, 'unit': 90094220969929058220972040724655209, 'val': 1}
  • id: 406274
    {'lmfdb_iso': '9680.f', 'p': 73, 'prec': 20, 'unit': 139547966545157075663724799098088785, 'val': 1}
  • id: 406277
    {'lmfdb_iso': '9680.f', 'p': 79, 'prec': 20, 'unit': 31061004088811451717907338344643674, 'val': 1}
  • id: 406263
    {'lmfdb_iso': '9680.f', 'p': 83, 'prec': 20, 'unit': 2500821767132384964665503934078235207, 'val': 1}
  • id: 406275
    {'lmfdb_iso': '9680.f', 'p': 89, 'prec': 20, 'unit': 489066923237980937426258756905337817, 'val': 1}
  • id: 406262
    {'lmfdb_iso': '9680.f', 'p': 97, 'prec': 20, 'unit': 13279935551400870200049170385053898617, 'val': 1}