Elliptic curve data - 1680.g5

Formats: - HTML - YAML - JSON - 2024-05-04T18:27:18.030185

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1680m', 'Clabel': '1680m3', 'Cnumber': 3, 'abc_quality': 1.0154697965758581, 'absD': 353561707806720, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 840, 'ainvs': [0, -1, 0, -23560, 1065712], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 1680, 'degree': 6912, 'elladic_images': ['8.12.0.6', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5022650063104486806767562050', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [353108405631241, 86318776320], 'lmfdb_iso': '1680.g', 'lmfdb_label': '1680.g5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1473, -16652], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '8.12.0-4.c.1.5', '12.48.0-12.g.1.4', '20.12.0-4.c.1.1', '24.96.0-24.bt.2.3', '40.24.0-40.ba.1.2', '60.96.0-60.c.1.10', '84.96.0.?', '120.192.1.?', '168.192.1.?', '210.24.0.?', '420.192.1.?', '840.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.0891985548147912517953548275', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.80911782575050337125952408354', 'prec': 103}, 'szpiro_ratio': 5.630550876713398, '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, -1, 0, 1, 0, 0, 0, 2, 0, -1, 0, -6, 0, -8, 0], 'aplist': [0, -1, 1, -1, 0, 2, -6, -8, 0, 6, 4, -10, -6, 4, 0, -6, 12, -10, 4, -12, -10, -8, -12, -6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 1680, 'isogeny_matrix': [[1, 2, 4, 3, 4, 6, 12, 12], [2, 1, 2, 6, 2, 3, 6, 6], [4, 2, 1, 12, 4, 6, 12, 3], [3, 6, 12, 1, 12, 2, 4, 4], [4, 2, 4, 12, 1, 6, 3, 12], [6, 3, 6, 2, 6, 1, 2, 2], [12, 6, 12, 4, 3, 2, 1, 4], [12, 6, 3, 4, 12, 2, 4, 1]], 'lmfdb_iso': '1680.g', 'trace_hash': 1653484370542573193}
• 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': '0.049562042389873514655034781884', 'prec': 107}, 'conductor': 1680, 'gens': [[-3, 1066, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.0891985548147912517953548275', 'prec': 100}], 'lmfdb_label': '1680.g5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.50545013393832235342839350451', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5723360911698527936053925969710470064', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-172, 0, 1]], 'xcoord_integral_points': [-172, -3]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [4, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1680.g5'}
• ec_torsion_growth •

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

  
  
  • id: 84829
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 2]}
  • id: 84832
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [6]}
  • id: 84830
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [4]}
  • id: 84831
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [4]}
  • id: 84836
    {'degree': 4, 'field': [4, 0, 1, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [12]}
  • id: 84834
    {'degree': 4, 'field': [16, -8, 14, -2, 1], 'lmfdb_label': '1680.g5', 'torsion': [8]}
  • id: 84833
    {'degree': 4, 'field': [16, 0, 13, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 4]}
  • id: 84837
    {'degree': 4, 'field': [22, 2, -1, -2, 1], 'lmfdb_label': '1680.g5', 'torsion': [12]}
  • id: 84835
    {'degree': 4, 'field': [64, 0, -19, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 6]}
  • id: 84838
    {'degree': 6, 'field': [225, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [6]}
  • id: 84840
    {'degree': 8, 'field': [16, 0, 172, 0, 129, 0, 22, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [8]}
  • id: 84842
    {'degree': 8, 'field': [16, 40, -2, -86, 69, -34, 16, -4, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 12]}
  • id: 84843
    {'degree': 8, 'field': [96, 192, 160, 72, 14, -2, -5, -2, 1], 'lmfdb_label': '1680.g5', 'torsion': [24]}
  • id: 84841
    {'degree': 8, 'field': [196, 0, 329, 0, 51, 0, -1, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 8]}
  • id: 84839
    {'degree': 8, 'field': [7396, 13416, 4153, -1605, 96, -165, 22, -3, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 4]}
  • id: 84845
    {'degree': 12, 'field': [14400, 0, 0, 0, 0, 0, 17985, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 6]}
  • id: 84846
    {'degree': 12, 'field': [54676, 61380, 12834, -13230, -6045, -90, 1395, 0, 30, -60, 9, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [12]}
  • id: 84844
    {'degree': 12, 'field': [65536, 0, 22272, 0, 6801, 0, 773, 0, 96, 0, -3, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [3, 6]}
  • id: 84847
    {'degree': 12, 'field': [180100, 382500, 271050, 45570, -11325, 7110, 4331, 0, 438, -60, 33, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [12]}
  • id: 84849
    {'degree': 16, 'field': [16, 0, 7848, 0, 23977, 0, 26508, 0, 13548, 0, 3594, 0, 508, 0, 36, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 8]}
  • id: 84852
    {'degree': 16, 'field': [256, 0, 832, 0, 1984, 0, 1924, 0, 1333, 0, 481, 0, 124, 0, 13, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [24]}
  • id: 84853
    {'degree': 16, 'field': [256, 0, 2836, 0, 7820, 0, -3291, 0, 749, 0, 54, 0, -10, 0, 1, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 24]}
  • id: 84851
    {'degree': 16, 'field': [37636, 0, -5064, 0, -10295, 0, -576, 0, 1104, 0, 234, 0, -20, 0, -24, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [2, 12]}
  • id: 84850
    {'degree': 16, 'field': [56216, 150256, 169168, 94992, 71026, 40136, 25720, 8186, 4589, 1492, 560, 8, 56, 4, -8, -2, 1], 'lmfdb_label': '1680.g5', 'torsion': [16]}
  • id: 84848
    {'degree': 16, 'field': [3519376, 5357856, 4078368, 3062304, 1703128, 596736, 267120, 94920, 4041, 4110, 5490, 1224, -137, -144, 18, -6, 1], 'lmfdb_label': '1680.g5', 'torsion': [4, 4]}
  • id: 84854
    {'degree': 18, 'field': [-29767500, 0, 357210000, 0, 174069000, 0, 26044425, 0, 222750, 0, -268245, 0, -17088, 0, 459, 0, 54, 0, 1], 'lmfdb_label': '1680.g5', 'torsion': [18]}
• 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: 26617
    {'conductor': 1680, 'conductor_valuation': 4, 'discriminant_valuation': 36, 'j_denominator_valuation': 24, 'kodaira_symbol': -32, 'lmfdb_label': '1680.g5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 26618
    {'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1680.g5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 26619
    {'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1680.g5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 26620
    {'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '1680.g5', 'prime': 7, '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: 1674992
    {'adelic_gens': [[681, 808, 836, 509], [1, 12, 12, 145], [352, 21, 555, 466], [623, 816, 726, 329], [15, 106, 374, 11], [576, 719, 305, 546], [817, 24, 816, 25], [496, 3, 261, 754], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '840.384.5.?', 'conductor': 1680, 'lmfdb_label': '1680.g5', 'prime': 0}
  • id: 8176
    {'conductor': 1680, 'elladic_image': '8.12.0.6', 'lmfdb_label': '1680.g5', 'modell_image': '2B', 'prime': 2}
  • id: 8177
    {'conductor': 1680, 'elladic_image': '3.4.0.1', 'lmfdb_label': '1680.g5', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 46135
    {'lmfdb_iso': '1680.g', 'p': 13, 'prec': 20, 'unit': 106389479071881593151, 'val': 1}
  • id: 46137
    {'lmfdb_iso': '1680.g', 'p': 17, 'prec': 20, 'unit': 191147851075232301969043, 'val': 1}
  • id: 46127
    {'lmfdb_iso': '1680.g', 'p': 19, 'prec': 20, 'unit': 1136981382265158072313586, 'val': 1}
  • id: 46134
    {'lmfdb_iso': '1680.g', 'p': 29, 'prec': 20, 'unit': 3063496892073124991409298143, 'val': 1}
  • id: 46144
    {'lmfdb_iso': '1680.g', 'p': 31, 'prec': 20, 'unit': 154133115294375290852900529, 'val': 2}
  • id: 46130
    {'lmfdb_iso': '1680.g', 'p': 37, 'prec': 20, 'unit': 420152068206172678427583542809, 'val': 1}
  • id: 46132
    {'lmfdb_iso': '1680.g', 'p': 41, 'prec': 20, 'unit': 2508146771914808172812928625241, 'val': 1}
  • id: 46133
    {'lmfdb_iso': '1680.g', 'p': 43, 'prec': 20, 'unit': 196264166919074839404512853575, 'val': 1}
  • id: 46139
    {'lmfdb_iso': '1680.g', 'p': 53, 'prec': 20, 'unit': 224083203157127135938065457822753, 'val': 1}
  • id: 46142
    {'lmfdb_iso': '1680.g', 'p': 59, 'prec': 20, 'unit': 1015605645853847333953509644750645, 'val': 1}
  • id: 46143
    {'lmfdb_iso': '1680.g', 'p': 61, 'prec': 20, 'unit': 3456969552389105562234483532801406, 'val': 1}
  • id: 46129
    {'lmfdb_iso': '1680.g', 'p': 67, 'prec': 20, 'unit': 16980148289088262870778016417071995, 'val': 1}
  • id: 46131
    {'lmfdb_iso': '1680.g', 'p': 71, 'prec': 20, 'unit': 139297405010906114493121375219854529, 'val': 1}
  • id: 46140
    {'lmfdb_iso': '1680.g', 'p': 73, 'prec': 20, 'unit': 218074221371864083673894413483062901, 'val': 1}
  • id: 46136
    {'lmfdb_iso': '1680.g', 'p': 79, 'prec': 20, 'unit': 203953938604606579154711459913216068, 'val': 1}
  • id: 46138
    {'lmfdb_iso': '1680.g', 'p': 83, 'prec': 20, 'unit': 916567672350152952735510529852116246, 'val': 1}
  • id: 46141
    {'lmfdb_iso': '1680.g', 'p': 89, 'prec': 20, 'unit': 3856267370130295445522515374260973921, 'val': 1}
  • id: 46128
    {'lmfdb_iso': '1680.g', 'p': 97, 'prec': 20, 'unit': 27012861260976360851758064976407499563, 'val': 1}