Elliptic curve data - 8640.s2

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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': '8640bu', 'Clabel': '8640bu2', 'Cnumber': 2, 'abc_quality': 1.0691763773828689, 'absD': 62208000000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 24, 'ainvs': [0, 0, 0, 672, 9952], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 8640, 'degree': 6912, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.75584209175696868620050572877', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 18, 'isogeny_degrees': [1, 3], 'jinv': [8429568, 15625], 'lmfdb_iso': '8640.s', 'lmfdb_label': '8640.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 1512, 33588], 'min_quad_twist_disc': 24, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0.b.1', '24.16.0-6.b.1.2'], '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': '2.9668228717149674353922453372', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 27], [3, 8, 32], [5, 6, 1728]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.51058473917467987953428392832', 'prec': 107}, 'szpiro_ratio': 3.5231296337143765, '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, 0, 0, -1, 0, 1, 0, 0, 0, 6, 0, 1, 0, 0, 0, 0, 0, -1, 0], 'aplist': [0, 0, -1, 1, 6, 1, 0, -1, -6, -6, -8, 7, -6, -4, -12, 6, 0, -11, -7, 6, 11, 1, 6, -12, -13], 'class_deg': 3, 'class_size': 2, 'conductor': 8640, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '8640.s', 'trace_hash': 53244205641635296}
• 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': '0.22053823814333875871933222872', 'prec': 103}, 'conductor': 8640, 'gens': [[201, 2875, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9668228717149674353922453372', 'prec': 100}], 'lmfdb_label': '8640.s2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.76137963204046247692725648459', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.5177570127911402336899104511592601891', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [201]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [3, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [3, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '8640.s2'}
• ec_torsion_growth •

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

  
  
  • id: 451482
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '8640.s2', 'torsion': [3]}
  • id: 451483
    {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '8640.s2', 'torsion': [2]}
  • id: 451485
    {'degree': 6, 'field': [-6, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '8640.s2', 'torsion': [3]}
  • id: 451484
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '8640.s2', 'torsion': [2, 2]}
  • id: 451486
    {'degree': 6, 'field': [2, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '8640.s2', 'torsion': [6]}
  • id: 451487
    {'degree': 12, 'field': [-3, 0, 0, 0, 3, 0, -60, 0, 51, 0, -12, 0, 1], 'lmfdb_label': '8640.s2', 'torsion': [4]}
  • id: 451489
    {'degree': 12, 'field': [4, 0, -24, 0, 60, 0, -44, 0, 0, 0, 6, 0, 1], 'lmfdb_label': '8640.s2', 'torsion': [2, 6]}
  • id: 451488
    {'degree': 12, 'field': [25, 30, 111, -290, 180, -90, 129, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '8640.s2', 'torsion': [3, 3]}
  • id: 451491
    {'degree': 18, 'field': [-216, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, -90, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '8640.s2', 'torsion': [6]}
  • id: 451490
    {'degree': 18, 'field': [60747, -48870, 125931, 158630, 44109, 132090, 72280, 24690, 57246, -3940, 12003, 1020, 625, -30, 27, -10, 12, 0, 1], 'lmfdb_label': '8640.s2', '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: 180396
    {'conductor': 8640, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '8640.s2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 180397
    {'conductor': 8640, 'conductor_valuation': 3, 'discriminant_valuation': 5, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '8640.s2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 180398
    {'conductor': 8640, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '8640.s2', 'prime': 5, 'reduction_type': -1, '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: 1721136
    {'adelic_gens': [[19, 6, 18, 7], [1, 0, 6, 1], [4, 3, 9, 7], [17, 0, 0, 23], [3, 4, 8, 11], [21, 20, 22, 19], [4, 3, 3, 1], [0, 23, 23, 0], [1, 6, 0, 1], [11, 0, 0, 23]], 'adelic_image': '24.16.0.?', 'conductor': 8640, 'lmfdb_label': '8640.s2', 'prime': 0}
  • id: 42304
    {'conductor': 8640, 'elladic_image': '3.4.0.1', 'lmfdb_label': '8640.s2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 358167
    {'lmfdb_iso': '8640.s', 'p': 7, 'prec': 20, 'unit': 51643364383457527, 'val': -1}
  • id: 358165
    {'lmfdb_iso': '8640.s', 'p': 11, 'prec': 20, 'unit': 1492626131546248220, 'val': 2}
  • id: 358171
    {'lmfdb_iso': '8640.s', 'p': 13, 'prec': 20, 'unit': 10232411763901229870282, 'val': -1}
  • id: 358173
    {'lmfdb_iso': '8640.s', 'p': 19, 'prec': 20, 'unit': 766462546579030765198078, 'val': 1}
  • id: 358176
    {'lmfdb_iso': '8640.s', 'p': 23, 'prec': 20, 'unit': 33631760317318479898156727, 'val': 1}
  • id: 358170
    {'lmfdb_iso': '8640.s', 'p': 29, 'prec': 20, 'unit': 125573271722248346002724630, 'val': 2}
  • id: 358182
    {'lmfdb_iso': '8640.s', 'p': 31, 'prec': 20, 'unit': 2347360049956821906224820990, 'val': 1}
  • id: 358166
    {'lmfdb_iso': '8640.s', 'p': 37, 'prec': 20, 'unit': 81554263173130597657990388155, 'val': 1}
  • id: 358168
    {'lmfdb_iso': '8640.s', 'p': 41, 'prec': 20, 'unit': 25600162615155290270124776889, 'val': 1}
  • id: 358169
    {'lmfdb_iso': '8640.s', 'p': 43, 'prec': 20, 'unit': 7527426669164833086972174132996, 'val': 1}
  • id: 358172
    {'lmfdb_iso': '8640.s', 'p': 47, 'prec': 20, 'unit': 24806997190505998481650086802540, 'val': 1}
  • id: 358174
    {'lmfdb_iso': '8640.s', 'p': 53, 'prec': 20, 'unit': 346241650363160395775179728325846, 'val': 1}
  • id: 358180
    {'lmfdb_iso': '8640.s', 'p': 61, 'prec': 20, 'unit': 5649229513963317989034260140673775, 'val': 1}
  • id: 358164
    {'lmfdb_iso': '8640.s', 'p': 67, 'prec': 20, 'unit': 49331676138326041289751965984431588, 'val': 1}
  • id: 358178
    {'lmfdb_iso': '8640.s', 'p': 71, 'prec': 20, 'unit': 32120882464528054293038349894695006, 'val': 1}
  • id: 358175
    {'lmfdb_iso': '8640.s', 'p': 73, 'prec': 20, 'unit': 41434356736810623380510022899409468, 'val': 1}
  • id: 358179
    {'lmfdb_iso': '8640.s', 'p': 79, 'prec': 20, 'unit': 39834615922673144901149888348410964865, 'val': -1}
  • id: 358181
    {'lmfdb_iso': '8640.s', 'p': 83, 'prec': 20, 'unit': 1312685754171787108558137415805656845, 'val': 1}
  • id: 358177
    {'lmfdb_iso': '8640.s', 'p': 89, 'prec': 20, 'unit': 3713784339276343966611484791439794259, 'val': 1}
  • id: 358163
    {'lmfdb_iso': '8640.s', 'p': 97, 'prec': 20, 'unit': 51643498010960759166542961337220566748, 'val': 1}