Elliptic curve data - 262080.bt8

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

  
  {'Ciso': '262080bt', 'Clabel': '262080bt3', 'Cnumber': 3, 'abc_quality': 1.074254776643201, 'absD': 499241265083656962048000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 10920, 'ainvs': [0, 0, 0, 15990612, -23450027312], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 262080, 'degree': 31850496, 'elladic_images': ['8.12.0.12', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2338066157575279309594664591', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 45, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [2366200373628880151, 2612420149248000], 'lmfdb_iso': '262080.bt', 'lmfdb_label': '262080.bt8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 27761, -1694014], 'min_quad_twist_disc': 24, '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.1.2', '12.24.0.g.1', '24.96.0-24.bt.1.11', '156.48.0.?', '312.192.1.?', '420.48.0.?', '840.192.1.?', '910.6.0.?', '1820.12.0.?', '2730.24.0.?', '3640.24.0.?', '5460.96.1.?', '10920.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '31.888060835253716592189251280', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6447797005835551211359956585', 'prec': 100}, 'szpiro_ratio': 4.9193769932049785, '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, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 6, 0, -4, 0], 'aplist': [0, 0, -1, -1, 0, -1, 6, -4, 0, 6, -8, -2, -6, 8, 12, -6, 12, -14, -4, -12, 2, -8, 0, -6, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 262080, 'isogeny_matrix': [[1, 4, 12, 2, 3, 6, 12, 4], [4, 1, 3, 2, 12, 6, 12, 4], [12, 3, 1, 6, 4, 2, 4, 12], [2, 2, 6, 1, 6, 3, 6, 2], [3, 12, 4, 6, 1, 2, 4, 12], [6, 6, 2, 3, 2, 1, 2, 6], [12, 12, 4, 6, 4, 2, 1, 3], [4, 4, 12, 2, 12, 6, 3, 1]], 'lmfdb_iso': '262080.bt', 'trace_hash': 164980532000910249}
• 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': '0.0015529277923044476800255317784', 'prec': 110}, 'conductor': 262080, 'gens': [[598096630223441, 14729924828510261968761, 134830]], 'heights': [{'__RealLiteral__': 0, 'data': '31.888060835253716592189251280', 'prec': 100}], 'lmfdb_label': '262080.bt8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.050237655974429762090994394145', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.4079257197326543394624573808813778446', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[1322, 0, 1]], 'xcoord_integral_points': [1322]}
• lmfdb_label 262080.bt8 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11230144
    {'degree': 2, 'field': [-78, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [4]}
  • id: 11230146
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [6]}
  • id: 11230143
    {'degree': 2, 'field': [114, -1, 1], 'lmfdb_label': '262080.bt8', 'torsion': [2, 2]}
  • id: 11230145
    {'degree': 2, 'field': [210, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [4]}
  • id: 11230149
    {'degree': 4, 'field': [66, -24, 25, -2, 1], 'lmfdb_label': '262080.bt8', 'torsion': [12]}
  • id: 11230150
    {'degree': 4, 'field': [786, 48, -47, -2, 1], 'lmfdb_label': '262080.bt8', 'torsion': [12]}
  • id: 11230147
    {'degree': 4, 'field': [5184, 0, 66, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [2, 4]}
  • id: 11230148
    {'degree': 4, 'field': [12546, -232, 233, -2, 1], 'lmfdb_label': '262080.bt8', 'torsion': [2, 6]}
  • id: 11230151
    {'degree': 6, 'field': [225, -756, 108, -42, -18, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [6]}
  • id: 11230154
    {'degree': 8, 'field': [3756, -984, 1360, -796, 509, -136, 50, -4, 1], 'lmfdb_label': '262080.bt8', 'torsion': [24]}
  • id: 11230153
    {'degree': 8, 'field': [28224, 0, -12720, 0, 241, 0, 32, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [8]}
  • id: 11230155
    {'degree': 8, 'field': [1865956, 0, -111988, 0, 3573, 0, -58, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [2, 12]}
  • id: 11230152
    {'degree': 8, 'field': [8462281, 0, 2018412, 0, 119374, 0, -132, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [2, 4]}
  • id: 11230158
    {'degree': 12, 'field': [-1930356, -1198152, 474768, -83688, 157887, -29502, 2989, -4146, 834, 166, -39, -6, 1], 'lmfdb_label': '262080.bt8', 'torsion': [12]}
  • id: 11230156
    {'degree': 12, 'field': [201601, -113148, 58116, -40740, 8034, 3528, 2590, 0, 24, -84, -6, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [3, 6]}
  • id: 11230159
    {'degree': 12, 'field': [20575296, 0, 0, 0, 0, 0, 4368, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [12]}
  • id: 11230157
    {'degree': 12, 'field': [959961010176, 0, 0, 0, 0, 0, -638232, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [2, 6]}
  • id: 11230164
    {'degree': 16, 'field': [1404750400, 0, -792616640, 0, 199444436, 0, -29971092, 0, 2972033, 0, -192096, 0, 7406, 0, -140, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [24]}
  • id: 11230161
    {'degree': 16, 'field': [1810162116, 0, -246819468, 0, 33682285, 0, -3551478, 0, 263019, 0, -7472, 0, 195, 0, 18, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [2, 24]}
  • id: 11230162
    {'degree': 16, 'field': [3656137156, 0, -5508178004, 0, 2887758797, 0, -315972930, 0, 12175451, 0, -255840, 0, 8147, 0, -74, 0, 1], 'lmfdb_label': '262080.bt8', 'torsion': [2, 8]}
  • id: 11230160
    {'degree': 16, 'field': [438900950016, -373774943232, 159156306432, -114064391808, 77772646672, -24231796320, 7255791648, -3646908784, 899212100, 6801344, -882112, 334520, -56028, 48, 32, -8, 1], 'lmfdb_label': '262080.bt8', 'torsion': [4, 4]}
  • id: 11230163
    {'degree': 16, 'field': [5513946398496, 8372676944448, 5240796042000, 1744961999760, 333925208284, 35672097088, 5956680968, 1168216100, 161303801, 13869688, 2353748, 200624, 24914, 616, 284, -4, 1], 'lmfdb_label': '262080.bt8', 'torsion': [2, 12]}
  • id: 11230165
    {'degree': 18, 'field': [1482968348831724, -205439754585672, -171536067799260, -15190759177052, 34218567676674, -8503126859400, 611128020457, 62903645160, -11335998000, 378011176, 130114599, 8302236, -1193090, 26328, 5643, -1592, -60, 0, 1], 'lmfdb_label': '262080.bt8', '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: 6496198
    {'conductor': 262080, 'conductor_valuation': 6, 'discriminant_valuation': 42, 'j_denominator_valuation': 24, 'kodaira_symbol': -36, 'lmfdb_label': '262080.bt8', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6496199
    {'conductor': 262080, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '262080.bt8', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6496200
    {'conductor': 262080, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '262080.bt8', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6496201
    {'conductor': 262080, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '262080.bt8', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6496202
    {'conductor': 262080, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '262080.bt8', 'prime': 13, '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: 3323642
    {'adelic_gens': [[9099, 7276, 10912, 5427], [8752, 3, 8277, 10834], [1, 12, 12, 145], [8183, 10896, 8286, 329], [15, 106, 9614, 1691], [7719, 5912, 4, 8731], [10897, 24, 10896, 25], [1, 24, 0, 1], [1696, 21, 3915, 10546], [4696, 3, 1101, 10834], [1, 0, 24, 1]], 'adelic_image': '10920.384.5.?', 'conductor': 262080, 'lmfdb_label': '262080.bt8', 'prime': 0}
  • id: 940392
    {'conductor': 262080, 'elladic_image': '8.12.0.12', 'lmfdb_label': '262080.bt8', 'modell_image': '2B', 'prime': 2}
  • id: 940393
    {'conductor': 262080, 'elladic_image': '3.4.0.1', 'lmfdb_label': '262080.bt8', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 262080.bt does not appear in ec_padic