Elliptic curve data - 221760.dp6

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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': '221760ks', 'Clabel': '221760ks3', 'Cnumber': 3, 'abc_quality': 1.080406817362685, 'absD': 20865309696000000000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, 0, 0, -11664588, 16835301488], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 221760, 'degree': 15925248, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0183013658154572653311923362', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 93, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [-918468938249433649, 109183593750000], 'lmfdb_iso': '221760.dp', 'lmfdb_label': '221760.dp6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -20251, -1219519], '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', '12.24.0.g.1', '24.48.0-12.g.1.16', '84.48.0.?', '88.12.0.?', '120.96.0.?', '132.48.0.?', '168.96.0.?', '264.96.0.?', '280.12.0.?', '462.24.0.?', '840.192.1.?', '924.96.1.?', '1320.192.1.?', '1848.192.1.?', '3080.24.0.?', '9240.384.5.?'], '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': '15.003363415975875527441378535', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4292744506414844555077215356', 'prec': 100}, 'szpiro_ratio': 4.924437783756357, '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, -1, 0, -2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, -1, 1, -1, -2, -6, 4, 0, 6, 8, 10, 6, -8, 0, 6, 12, -2, 4, -12, -10, -4, -12, -6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 221760, 'isogeny_matrix': [[1, 4, 2, 12, 3, 4, 6, 12], [4, 1, 2, 3, 12, 4, 6, 12], [2, 2, 1, 6, 6, 2, 3, 6], [12, 3, 6, 1, 4, 12, 2, 4], [3, 12, 6, 4, 1, 12, 2, 4], [4, 4, 2, 12, 12, 1, 6, 3], [6, 6, 3, 2, 2, 6, 1, 2], [12, 12, 6, 4, 4, 3, 2, 1]], 'lmfdb_iso': '221760.dp', 'trace_hash': 452319732271173606}
• 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': '0.0023896634672602391391865912234', 'prec': 110}, 'conductor': 221760, 'gens': [[35266094, 135961948672, 145]], 'heights': [{'__RealLiteral__': 0, 'data': '15.003363415975875527441378535', 'prec': 100}], 'lmfdb_label': '221760.dp6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.11778835128982035545030325763', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.0688857622792222093071182609803742212', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-3986, 0, 1]], 'xcoord_integral_points': [-3986]}
• lmfdb_label 221760.dp6 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9651289
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [4]}
  • id: 9651291
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [6]}
  • id: 9651290
    {'degree': 2, 'field': [22, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [4]}
  • id: 9651288
    {'degree': 2, 'field': [58, -1, 1], 'lmfdb_label': '221760.dp6', 'torsion': [2, 2]}
  • id: 9651294
    {'degree': 4, 'field': [7, 14, -13, -2, 1], 'lmfdb_label': '221760.dp6', 'torsion': [12]}
  • id: 9651295
    {'degree': 4, 'field': [23, -2, 3, -2, 1], 'lmfdb_label': '221760.dp6', 'torsion': [12]}
  • id: 9651292
    {'degree': 4, 'field': [256, 0, -10, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [2, 4]}
  • id: 9651293
    {'degree': 4, 'field': [3598, -112, 113, -2, 1], 'lmfdb_label': '221760.dp6', 'torsion': [2, 6]}
  • id: 9651296
    {'degree': 6, 'field': [1980, 1512, 108, -84, 18, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [6]}
  • id: 9651298
    {'degree': 8, 'field': [576, 0, -8880, 0, 1417, 0, -50, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [8]}
  • id: 9651300
    {'degree': 8, 'field': [3364, 0, 804, 0, 197, 0, -18, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [2, 12]}
  • id: 9651299
    {'degree': 8, 'field': [43681, 0, 10648, 0, 1518, 0, 88, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [8]}
  • id: 9651297
    {'degree': 8, 'field': [8179600, 0, 186098, 0, 5841, 0, -22, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [2, 4]}
  • id: 9651303
    {'degree': 12, 'field': [1450, 2580, -198, -4840, 2670, -480, 497, -366, 195, -80, 27, -6, 1], 'lmfdb_label': '221760.dp6', 'torsion': [12]}
  • id: 9651301
    {'degree': 12, 'field': [3083536, 885024, 232944, -288960, -31656, 7056, 10640, 0, 24, -168, 6, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [3, 6]}
  • id: 9651304
    {'degree': 12, 'field': [6770800, 6884640, 1894704, -301056, -212088, -17136, 14672, 0, 636, -168, 42, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [12]}
  • id: 9651302
    {'degree': 12, 'field': [1764000000, 0, 0, 0, 0, 0, 71526, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [2, 6]}
  • id: 9651309
    {'degree': 16, 'field': [163216, 0, -1639280, 0, 1334924, 0, -52380, 0, 6401, 0, -3120, 0, 194, 0, -20, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [24]}
  • id: 9651310
    {'degree': 16, 'field': [12222016, 0, 12361824, 0, 5163892, 0, 1278300, 0, 237801, 0, 31200, 0, 2482, 0, 84, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [24]}
  • id: 9651307
    {'degree': 16, 'field': [100000000, 0, -18200000, 0, -7603900, 0, 601020, 0, 211361, 0, 3192, 0, 554, 0, 28, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [2, 8]}
  • id: 9651306
    {'degree': 16, 'field': [429697024, 29207552, -44167360, 32131584, -21235048, 5148808, 177118, -1904556, 849211, -282096, 91078, -20548, 4820, -672, 116, -8, 1], 'lmfdb_label': '221760.dp6', 'torsion': [2, 8]}
  • id: 9651305
    {'degree': 16, 'field': [3949871104, -1854267392, 435243008, 189532928, 48340880, -183669280, 85444128, -42847344, 10285348, 295488, -103488, 38840, -6412, -64, 32, -8, 1], 'lmfdb_label': '221760.dp6', 'torsion': [4, 4]}
  • id: 9651308
    {'degree': 16, 'field': [12045062500, 0, -868957500, 0, -68482775, 0, 11426328, 0, 807456, 0, -684, 0, -1268, 0, -12, 0, 1], 'lmfdb_label': '221760.dp6', 'torsion': [2, 12]}
  • id: 9651311
    {'degree': 18, 'field': [-62775205742592, 0, 8026532704512, 0, 142275631680, 0, 64410401412, 0, -6609305808, 0, 269181864, 0, -5284574, 0, 68940, 0, -444, 0, 1], 'lmfdb_label': '221760.dp6', '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: 5500040
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '221760.dp6', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 5500041
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '221760.dp6', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5500042
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '221760.dp6', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5500043
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '221760.dp6', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5500044
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '221760.dp6', 'prime': 11, '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: 3079534
    {'adelic_gens': [[1, 12, 12, 145], [15, 106, 7934, 11], [3697, 24, 7404, 289], [1336, 3, 6141, 9154], [3376, 21, 2235, 8866], [7311, 8852, 340, 1891], [9217, 24, 9216, 25], [1, 24, 0, 1], [6144, 7687, 3889, 8646], [6937, 24, 7422, 1687], [1, 0, 24, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 221760, 'lmfdb_label': '221760.dp6', 'prime': 0}
  • id: 812415
    {'conductor': 221760, 'elladic_image': '4.6.0.1', 'lmfdb_label': '221760.dp6', 'modell_image': '2B', 'prime': 2}
  • id: 812416
    {'conductor': 221760, 'elladic_image': '3.4.0.1', 'lmfdb_label': '221760.dp6', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 221760.dp does not appear in ec_padic