Elliptic curve data - 19600.dl1

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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': '19600cp', 'Clabel': '19600cp6', 'Cnumber': 6, 'abc_quality': 1.0648884149541868, 'absD': 188900999168000000, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 2520, 'ainvs': [0, -1, 0, -53518208, -150677721088], 'analytic_rank': 1, 'bad_primes': [2, 5, 7], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 19600, 'degree': 995328, 'elladic_images': ['8.6.0.6', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8839221917277366068510705146', 'prec': 97}, 'faltings_index': 5, 'faltings_ratio': 18, 'intrinsic_torsion': 1, 'iso_nlabel': 89, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [2251439055699625, 25088], 'lmfdb_iso': '19600.dl', 'lmfdb_label': '19600.dl1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -2731, -55146], 'min_quad_twist_disc': 140, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.b.1', '9.12.0.a.1', '18.36.0.a.1', '24.24.0.y.1', '28.6.0.c.1', '56.12.0.k.1', '60.24.0-6.a.1.8', '63.36.0.d.1', '72.72.1.?', '84.24.0.?', '120.48.0.?', '126.108.2.?', '168.48.1.?', '180.72.0.?', '252.216.7.?', '360.144.1.?', '420.48.0.?', '504.432.21.?', '840.96.1.?', '1260.432.7.?', '2520.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '16.194506149016274216152360081', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 1225], [5, 14, 784], [7, 32, 400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.41310098042308445758078235480', 'prec': 97}, 'szpiro_ratio': 6.576781054134611, '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, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, 6, 0, 2, 0], 'aplist': [0, 2, 0, 0, 0, -4, 6, 2, 0, -6, -4, -2, -6, 8, 12, -6, -6, -8, -4, 0, 2, -8, 6, 6, -10], 'class_deg': 18, 'class_size': 6, 'conductor': 19600, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '19600.dl', 'trace_hash': 13194813727399451}
• 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': '0.0031264897685500192696403035344', 'prec': 97}, 'conductor': 19600, 'gens': [[4793695168, 13987637372800, 753]], 'heights': [{'__RealLiteral__': 0, 'data': '16.194506149016274216152360081', 'prec': 97}], 'lmfdb_label': '19600.dl1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.055817986141401597819658333012', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '7.2315577583410668267242918085745484295', 'prec': 127}, 'tamagawa_product': 32, 'torsion_generators': [[-4223, 0, 1]], 'xcoord_integral_points': [-4223]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 2], '5': 'a', '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [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': '19600.dl1'}
• ec_torsion_growth •

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

  
  
  • id: 1002067
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [2, 2]}
  • id: 1002068
    {'degree': 2, 'field': [105, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [6]}
  • id: 1002069
    {'degree': 4, 'field': [14, 7, -5, -1, 1], 'lmfdb_label': '19600.dl1', 'torsion': [4]}
  • id: 1002070
    {'degree': 4, 'field': [2809, 0, 104, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [2, 6]}
  • id: 1002071
    {'degree': 6, 'field': [-875, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [6]}
  • id: 1002072
    {'degree': 6, 'field': [168000, 0, 11025, 0, 210, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [18]}
  • id: 1002073
    {'degree': 8, 'field': [14, -28, 43, -50, 53, -24, 9, -2, 1], 'lmfdb_label': '19600.dl1', 'torsion': [2, 4]}
  • id: 1002075
    {'degree': 8, 'field': [196, 28, -6, 20, -10, -10, 9, -2, 1], 'lmfdb_label': '19600.dl1', 'torsion': [12]}
  • id: 1002074
    {'degree': 8, 'field': [3656, 3232, -2096, -112, 204, -32, -28, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [2, 4]}
  • id: 1002078
    {'degree': 12, 'field': [49, 0, 0, 0, 0, 0, -11844, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [2, 6]}
  • id: 1002076
    {'degree': 12, 'field': [763876, 5244, 13146, -35050, 13215, 5124, -1609, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '19600.dl1', 'torsion': [3, 6]}
  • id: 1002077
    {'degree': 12, 'field': [37515625, 0, 0, 0, 0, 0, -1750, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [18]}
  • id: 1002079
    {'degree': 12, 'field': [2124103744, 0, 230385456, 0, 12296697, 0, 446936, 0, 12474, 0, 168, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [2, 18]}
  • id: 1002081
    {'degree': 16, 'field': [3136, -1792, 3168, -9888, 14680, -11648, 12432, -15120, 13278, -7188, 2994, -980, 343, -84, 18, -4, 1], 'lmfdb_label': '19600.dl1', 'torsion': [2, 12]}
  • id: 1002080
    {'degree': 16, 'field': [3584, -5824, 7728, -4480, 7688, -8144, 4888, -736, -1308, 1168, -526, 88, 45, -42, 20, -6, 1], 'lmfdb_label': '19600.dl1', 'torsion': [8]}
  • id: 1002082
    {'degree': 16, 'field': [5364256, 3332352, 5263872, 324032, 1042032, -101888, 149072, 18432, 38444, 13264, 6712, 2016, 292, -88, -40, 0, 1], 'lmfdb_label': '19600.dl1', 'torsion': [2, 12]}
• 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: 443702
    {'conductor': 19600, 'conductor_valuation': 4, 'discriminant_valuation': 21, 'j_denominator_valuation': 9, 'kodaira_symbol': -17, 'lmfdb_label': '19600.dl1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 443703
    {'conductor': 19600, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '19600.dl1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 443704
    {'conductor': 19600, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '19600.dl1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1795084
    {'adelic_gens': [[1, 36, 0, 1], [1889, 1980, 1250, 2159], [1, 0, 36, 1], [1769, 1980, 1270, 2009], [19, 36, 720, 1099], [2485, 36, 2484, 37], [503, 0, 0, 2519], [1036, 1035, 1065, 1306], [901, 540, 1600, 1541], [1, 18, 14, 253]], 'adelic_image': '2520.864.21.?', 'conductor': 19600, 'lmfdb_label': '19600.dl1', 'prime': 0}
  • id: 91576
    {'conductor': 19600, 'elladic_image': '8.6.0.6', 'lmfdb_label': '19600.dl1', 'modell_image': '2B', 'prime': 2}
  • id: 91577
    {'conductor': 19600, 'elladic_image': '9.12.0.1', 'lmfdb_label': '19600.dl1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 909303
    {'lmfdb_iso': '19600.dl', 'p': 13, 'prec': 20, 'unit': 1223216308584065834815, 'val': 1}
  • id: 909305
    {'lmfdb_iso': '19600.dl', 'p': 17, 'prec': 20, 'unit': 56087602494692020965518, 'val': 1}
  • id: 909306
    {'lmfdb_iso': '19600.dl', 'p': 19, 'prec': 20, 'unit': 904235768008582880632810, 'val': 1}
  • id: 909302
    {'lmfdb_iso': '19600.dl', 'p': 29, 'prec': 20, 'unit': 4816161341641916291961454337, 'val': 1}
  • id: 909313
    {'lmfdb_iso': '19600.dl', 'p': 31, 'prec': 20, 'unit': 10043536546127731926296239816, 'val': 1}
  • id: 909299
    {'lmfdb_iso': '19600.dl', 'p': 37, 'prec': 20, 'unit': 522306027524229416452136939262, 'val': 1}
  • id: 909300
    {'lmfdb_iso': '19600.dl', 'p': 41, 'prec': 20, 'unit': 1981486242951229891783525333258, 'val': 1}
  • id: 909301
    {'lmfdb_iso': '19600.dl', 'p': 43, 'prec': 20, 'unit': 9753841990613848274743852393665, 'val': 1}
  • id: 909311
    {'lmfdb_iso': '19600.dl', 'p': 47, 'prec': 20, 'unit': 16134150003922205856295923944123, 'val': 1}
  • id: 909307
    {'lmfdb_iso': '19600.dl', 'p': 53, 'prec': 20, 'unit': 255617888716056964958742607800323, 'val': 1}
  • id: 909308
    {'lmfdb_iso': '19600.dl', 'p': 59, 'prec': 20, 'unit': 2460448957346457860482656343769728, 'val': 1}
  • id: 909312
    {'lmfdb_iso': '19600.dl', 'p': 61, 'prec': 20, 'unit': 4281162033957919703482460511414404, 'val': 1}
  • id: 909298
    {'lmfdb_iso': '19600.dl', 'p': 67, 'prec': 20, 'unit': 28495613121464020258142872693381478, 'val': 1}
  • id: 909309
    {'lmfdb_iso': '19600.dl', 'p': 73, 'prec': 20, 'unit': 188620214006880034980310427629972666, 'val': 1}
  • id: 909304
    {'lmfdb_iso': '19600.dl', 'p': 79, 'prec': 20, 'unit': 131066834085161042912604302141393716, 'val': 1}
  • id: 909297
    {'lmfdb_iso': '19600.dl', 'p': 83, 'prec': 20, 'unit': 183915735455573446700169323963236369, 'val': 1}
  • id: 909310
    {'lmfdb_iso': '19600.dl', 'p': 89, 'prec': 20, 'unit': 6893839881393011347521052083296922549, 'val': 1}
  • id: 909296
    {'lmfdb_iso': '19600.dl', 'p': 97, 'prec': 20, 'unit': 7260737387936666656573853755742469403, 'val': 1}