Elliptic curve data - 9680.j1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '9680s', 'Clabel': '9680s1', 'Cnumber': 1, 'abc_quality': 0.9395996129829801, 'absD': 6181218395095040, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 1320, 'ainvs': [0, -1, 0, -171376, 27624896], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 9680, 'degree': 80640, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8449036494758781137489191028', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 3], 'jinv': [-76711450249, 851840], 'lmfdb_iso': '9680.j', 'lmfdb_label': '9680.j1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -89, 316], 'min_quad_twist_disc': 44, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '120.8.0.?', '132.8.0.?', '440.2.0.?', '1320.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.1112718399738617671903022558', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 605], [5, 6, 1936], [11, 72, 80]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.047191167483252467699284807641', 'prec': 110}, 'szpiro_ratio': 5.206843896688738, '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, 5, 0, -2, 0, 0, 0, -2, 0, 1, 0, -3, 0, -7, 0], 'aplist': [0, -1, -1, 5, 0, -2, -3, -7, 6, 3, 7, -7, -6, 8, -6, -3, 6, 1, -8, -3, -2, -10, -6, 9, -4], 'class_deg': 3, 'class_size': 2, 'conductor': 9680, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '9680.j', 'trace_hash': 374108331104003918}
• 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': '0.024976814636927570670977419593', 'prec': 107}, 'conductor': 9680, 'gens': [[488, 7744, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.1112718399738617671903022558', 'prec': 100}], 'lmfdb_label': '9680.j1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.42606174622576868272052625012', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.7877633653662921467764792856311301336', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [250, 488]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [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.j1'}
• ec_torsion_growth •

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

  
  
  • id: 502402
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '9680.j1', 'torsion': [3]}
  • id: 502403
    {'degree': 3, 'field': [-8, 2, 0, 1], 'lmfdb_label': '9680.j1', 'torsion': [2]}
  • id: 502406
    {'degree': 6, 'field': [-2, -4, -24, -16, -5, 0, 1], 'lmfdb_label': '9680.j1', 'torsion': [6]}
  • id: 502404
    {'degree': 6, 'field': [16, -32, 118, 16, -7, -2, 1], 'lmfdb_label': '9680.j1', 'torsion': [2, 2]}
  • id: 502405
    {'degree': 6, 'field': [3993, 0, 847, 0, 11, 0, 1], 'lmfdb_label': '9680.j1', 'torsion': [3]}
  • id: 502407
    {'degree': 12, 'field': [-1760, 0, -868, 0, -108, 0, -4, 0, -12, 0, -1, 0, 1], 'lmfdb_label': '9680.j1', 'torsion': [4]}
  • id: 502409
    {'degree': 12, 'field': [1016, -2640, 4032, -4400, 3474, -1980, 766, -220, 59, 0, 2, 0, 1], 'lmfdb_label': '9680.j1', 'torsion': [2, 6]}
  • id: 502408
    {'degree': 12, 'field': [1526677, 899796, -688933, -396690, 137466, 68328, -15089, -6210, 1086, 300, -49, -6, 1], 'lmfdb_label': '9680.j1', 'torsion': [3, 3]}
  • id: 502410
    {'degree': 18, 'field': [-26672, -206976, -471312, -373488, -41520, -522312, -382356, 41880, 14652, 68640, 6798, 10770, -363, -948, -306, -24, 15, -6, 1], 'lmfdb_label': '9680.j1', 'torsion': [9]}
  • id: 502411
    {'degree': 18, 'field': [7268116, -14243936, 15866420, -13146624, 9018544, -5835328, 3532224, -1922496, 947372, -417156, 163492, -57696, 18389, -4928, 1159, -254, 45, -6, 1], 'lmfdb_label': '9680.j1', 'torsion': [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: 203821
    {'conductor': 9680, 'conductor_valuation': 4, 'discriminant_valuation': 19, 'j_denominator_valuation': 7, 'kodaira_symbol': -15, 'lmfdb_label': '9680.j1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 203822
    {'conductor': 9680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9680.j1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 203823
    {'conductor': 9680, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '9680.j1', '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: 1727924
    {'adelic_gens': [[4, 3, 9, 7], [1057, 6, 531, 19], [606, 721, 385, 771], [329, 1314, 0, 1319], [1315, 6, 1314, 7], [661, 6, 663, 19], [1, 6, 0, 1], [3, 4, 8, 11], [119, 1314, 357, 1301], [1, 0, 6, 1]], 'adelic_image': '1320.16.0.?', 'conductor': 9680, 'lmfdb_label': '9680.j1', 'prime': 0}
  • id: 46785
    {'conductor': 9680, 'elladic_image': '3.4.0.1', 'lmfdb_label': '9680.j1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 406341
    {'lmfdb_iso': '9680.j', 'p': 7, 'prec': 20, 'unit': 913544334991394, 'val': 1}
  • id: 406345
    {'lmfdb_iso': '9680.j', 'p': 13, 'prec': 20, 'unit': 1327564752594816326446, 'val': 1}
  • id: 406347
    {'lmfdb_iso': '9680.j', 'p': 17, 'prec': 20, 'unit': 128353540241270347096261, 'val': 1}
  • id: 406348
    {'lmfdb_iso': '9680.j', 'p': 19, 'prec': 20, 'unit': 1036788085990262789560764, 'val': 1}
  • id: 406352
    {'lmfdb_iso': '9680.j', 'p': 23, 'prec': 20, 'unit': 54178320016775461287193110, 'val': 1}
  • id: 406344
    {'lmfdb_iso': '9680.j', 'p': 29, 'prec': 20, 'unit': 2981570222745842029971928477, 'val': 1}
  • id: 406357
    {'lmfdb_iso': '9680.j', 'p': 31, 'prec': 20, 'unit': 2116505264648206180063494051, 'val': 1}
  • id: 406340
    {'lmfdb_iso': '9680.j', 'p': 37, 'prec': 20, 'unit': 23726832897708017100742746419, 'val': 1}
  • id: 406342
    {'lmfdb_iso': '9680.j', 'p': 41, 'prec': 20, 'unit': 2893558419266204396066587460618, 'val': 1}
  • id: 406343
    {'lmfdb_iso': '9680.j', 'p': 43, 'prec': 20, 'unit': 8371125725682968722237419234275, 'val': 1}
  • id: 406355
    {'lmfdb_iso': '9680.j', 'p': 47, 'prec': 20, 'unit': 41001256052396815887478366671490, 'val': 1}
  • id: 406349
    {'lmfdb_iso': '9680.j', 'p': 53, 'prec': 20, 'unit': 51522154376141412436914559167221, 'val': 1}
  • id: 406350
    {'lmfdb_iso': '9680.j', 'p': 59, 'prec': 20, 'unit': 3464180942739588530697911952392395, 'val': 1}
  • id: 406356
    {'lmfdb_iso': '9680.j', 'p': 61, 'prec': 20, 'unit': 298044097181123043396453776599833146, 'val': -1}
  • id: 406339
    {'lmfdb_iso': '9680.j', 'p': 67, 'prec': 20, 'unit': 19012383507032714661711716850200256, 'val': 1}
  • id: 406354
    {'lmfdb_iso': '9680.j', 'p': 71, 'prec': 20, 'unit': 11650994556740478730337704709940551, 'val': 1}
  • id: 406351
    {'lmfdb_iso': '9680.j', 'p': 73, 'prec': 20, 'unit': 141570243236317231469216867547035742, 'val': 1}
  • id: 406346
    {'lmfdb_iso': '9680.j', 'p': 79, 'prec': 20, 'unit': 882661256362583546530091685591737476, 'val': 1}
  • id: 406338
    {'lmfdb_iso': '9680.j', 'p': 83, 'prec': 20, 'unit': 1825344394740357986283884539785214525, 'val': 1}
  • id: 406353
    {'lmfdb_iso': '9680.j', 'p': 89, 'prec': 20, 'unit': 10250922933842821741787955008686532853, 'val': 1}
  • id: 406337
    {'lmfdb_iso': '9680.j', 'p': 97, 'prec': 20, 'unit': 50682552154824341590425272657458108320, 'val': 1}