Elliptic curve data - 4560.w4

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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': '4560bd', 'Clabel': '4560bd1', 'Cnumber': 1, 'abc_quality': 0.9487490541305785, 'absD': 63825408000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 760, 'ainvs': [0, 1, 0, 360, 11988], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4560, 'degree': 4608, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.75413885482685399943231616098', 'prec': 97}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 22, 'isogeny_degrees': [1, 2, 4], 'jinv': [1256216039, 15582375], 'lmfdb_iso': '4560.w', 'lmfdb_label': '4560.w4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 23, -176], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '20.12.0-4.c.1.1', '40.24.0-40.z.1.2', '76.12.0.?', '152.24.0.?', '190.6.0.?', '380.24.0.?', '760.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 15, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.21337998219511602845504834113', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 2, 95], [3, 4, 304], [5, 6, 912], [19, 20, 240]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.060991674266908690015084039522', 'prec': 97}, 'szpiro_ratio': 3.832173465573506, '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, 1, 0, -4, 0, 1, 0, -4, 0, 2, 0, 1, 0, 2, 0, 1, 0], 'aplist': [0, 1, 1, -4, -4, 2, 2, 1, 4, -2, 0, -6, -6, -8, 12, -14, -4, 14, 4, 0, -14, -16, 0, -6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 4560, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '4560.w', 'trace_hash': 837783030744650886}
• 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': '0.22129077691086640779232670755', 'prec': 97}, 'conductor': 4560, 'gens': [[6, 120, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.21337998219511602845504834113', 'prec': 97}], 'lmfdb_label': '4560.w4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.81614517334448583304444730401', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1795770213650305212802935111334701082', 'prec': 127}, 'tamagawa_product': 96, 'torsion_generators': [[-18, 0, 1]], 'xcoord_integral_points': [-18, -12, -9, 6, 36, 126, 198, 3156]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [2, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4560.w4'}
• ec_torsion_growth •

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

  
  
  • id: 238285
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [4]}
  • id: 238286
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [4]}
  • id: 238284
    {'degree': 2, 'field': [24, -1, 1], 'lmfdb_label': '4560.w4', 'torsion': [2, 2]}
  • id: 238288
    {'degree': 4, 'field': [-51, -10, 11, -2, 1], 'lmfdb_label': '4560.w4', 'torsion': [8]}
  • id: 238287
    {'degree': 4, 'field': [36, 0, -7, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [2, 4]}
  • id: 238292
    {'degree': 8, 'field': [-147, 0, -163, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [6]}
  • id: 238290
    {'degree': 8, 'field': [16, 0, 44, 0, -19, 0, -1, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [8]}
  • id: 238291
    {'degree': 8, 'field': [676, 0, -148, 0, 213, 0, -13, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [2, 8]}
  • id: 238289
    {'degree': 8, 'field': [9691, -1516, 1712, -388, 185, 8, 2, -4, 1], 'lmfdb_label': '4560.w4', 'torsion': [2, 4]}
  • id: 238298
    {'degree': 16, 'field': [2025, 0, 3240, 0, 1296, 0, 875, 0, 80, 0, 197, 0, 25, 0, 10, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [12]}
  • id: 238294
    {'degree': 16, 'field': [6400, 0, 2800, 0, -215, 0, 405, 0, 126, 0, -111, 0, 46, 0, -11, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [2, 8]}
  • id: 238293
    {'degree': 16, 'field': [6561, 0, 0, 0, 18306, 0, 0, 0, -749, 0, 0, 0, 226, 0, 0, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [4, 4]}
  • id: 238297
    {'degree': 16, 'field': [149769, 0, -330804, 0, 413856, 0, -208549, 0, 45416, 0, -6139, 0, 613, 0, -38, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [12]}
  • id: 238296
    {'degree': 16, 'field': [15116544, 0, -28276992, 0, 13393440, 0, 845856, 0, 52845, 0, -4771, 0, 138, 0, 0, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [2, 6]}
  • id: 238295
    {'degree': 16, 'field': [191850201, 511600536, 511600536, 255800268, 89740629, 37545444, 14035680, 2768148, 261459, 41040, -10944, -14136, -3743, -456, -38, 0, 1], 'lmfdb_label': '4560.w4', 'torsion': [16]}
• 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: 87160
    {'conductor': 4560, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '4560.w4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 87161
    {'conductor': 4560, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '4560.w4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 87162
    {'conductor': 4560, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '4560.w4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 87163
    {'conductor': 4560, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4560.w4', 'prime': 19, '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: 1693711
    {'adelic_gens': [[99, 98, 298, 675], [308, 1, 631, 6], [1, 0, 8, 1], [753, 8, 752, 9], [7, 6, 754, 755], [168, 3, 485, 2], [1, 8, 0, 1], [1, 4, 4, 17], [471, 472, 82, 465]], 'adelic_image': '760.48.0.?', 'conductor': 4560, 'lmfdb_label': '4560.w4', 'prime': 0}
  • id: 22702
    {'conductor': 4560, 'elladic_image': '8.12.0.6', 'lmfdb_label': '4560.w4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 164333
    {'lmfdb_iso': '4560.w', 'p': 7, 'prec': 20, 'unit': 4907117923867463, 'val': 1}
  • id: 164331
    {'lmfdb_iso': '4560.w', 'p': 11, 'prec': 20, 'unit': 5510842613807474773, 'val': 1}
  • id: 164337
    {'lmfdb_iso': '4560.w', 'p': 13, 'prec': 20, 'unit': 836393831055301168398, 'val': 1}
  • id: 164339
    {'lmfdb_iso': '4560.w', 'p': 17, 'prec': 20, 'unit': 58950458427014630671754, 'val': 1}
  • id: 164344
    {'lmfdb_iso': '4560.w', 'p': 23, 'prec': 20, 'unit': 46625110565406426731218312, 'val': 1}
  • id: 164336
    {'lmfdb_iso': '4560.w', 'p': 29, 'prec': 20, 'unit': 4613013535063145023011250346, 'val': 1}
  • id: 164332
    {'lmfdb_iso': '4560.w', 'p': 37, 'prec': 20, 'unit': 440812269812118616430446957671, 'val': 1}
  • id: 164334
    {'lmfdb_iso': '4560.w', 'p': 41, 'prec': 20, 'unit': 1078161947818976744129127678359, 'val': 1}
  • id: 164335
    {'lmfdb_iso': '4560.w', 'p': 43, 'prec': 20, 'unit': 500130516978313236800315490513, 'val': 1}
  • id: 164346
    {'lmfdb_iso': '4560.w', 'p': 47, 'prec': 20, 'unit': 1579539631319096273951582654035, 'val': 1}
  • id: 164341
    {'lmfdb_iso': '4560.w', 'p': 53, 'prec': 20, 'unit': 457332617184166741004930000881743, 'val': 1}
  • id: 164342
    {'lmfdb_iso': '4560.w', 'p': 59, 'prec': 20, 'unit': 1095929321968385393898997384175288, 'val': 1}
  • id: 164347
    {'lmfdb_iso': '4560.w', 'p': 61, 'prec': 20, 'unit': 100980023806603366208468679661910, 'val': 1}
  • id: 164340
    {'lmfdb_iso': '4560.w', 'p': 67, 'prec': 20, 'unit': 38953652214652852400945221266597893, 'val': 1}
  • id: 164343
    {'lmfdb_iso': '4560.w', 'p': 73, 'prec': 20, 'unit': 192331965680599296087794244477987205, 'val': 1}
  • id: 164338
    {'lmfdb_iso': '4560.w', 'p': 79, 'prec': 20, 'unit': 560077261108627607490869793076131580, 'val': 1}
  • id: 164345
    {'lmfdb_iso': '4560.w', 'p': 89, 'prec': 20, 'unit': 2525031413602421130744263256805033187, 'val': 1}
  • id: 164330
    {'lmfdb_iso': '4560.w', 'p': 97, 'prec': 20, 'unit': 51782364531250054179892023643237724058, 'val': 1}