Elliptic curve data - 182070.df4

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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': '182070v', 'Clabel': '182070v4', 'Cnumber': 4, 'abc_quality': 1.0221395366994406, 'absD': 3247752338270507812500, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 14280, 'ainvs': [1, -1, 1, -11333912, 14431100199], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 182070, 'degree': 14155776, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9188716783385567208015235139', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 83, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [9150443179640281, 184570312500], 'lmfdb_iso': '182070.df', 'lmfdb_label': '182070.df4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -4358, -109132], 'min_quad_twist_disc': -51, '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', '12.48.0.c.3', '40.12.0.ba.1', '42.24.0.c.1', '51.8.0-3.a.1.1', '84.96.1.?', '102.24.0.?', '120.96.1.?', '204.96.0.?', '476.12.0.?', '714.48.0.?', '840.192.5.?', '1428.192.1.?', '2040.192.1.?', '4760.24.0.?', '14280.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.95295886197639383497913358650', 'prec': 103}, 'szpiro_ratio': 4.982067585373815, '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, 1, 0, 1, 1, 0, -1, 1, 0, 1, 0, 0, 2, -1, 0, 1, 0, 0, 8, 1], 'aplist': [1, 0, 1, -1, 0, 2, 0, 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': 182070, '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': '182070.df', 'trace_hash': 1473044435367949879}
• 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': '0.0029154142582278538032373401108', 'prec': 110}, 'conductor': 182070, 'gens': [], 'heights': [], 'lmfdb_label': '182070.df4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14155435120462456696465126634', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.7946088578219792143032607844046321074', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[8603, -8607, 2]], 'xcoord_integral_points': []}
• lmfdb_label 182070.df4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8044847
    {'degree': 2, 'field': [-119, 0, 1], 'lmfdb_label': '182070.df4', 'torsion': [4]}
  • id: 8044848
    {'degree': 2, 'field': [-51, 0, 1], 'lmfdb_label': '182070.df4', 'torsion': [4]}
  • id: 8044846
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '182070.df4', 'torsion': [2, 2]}
  • id: 8044849
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '182070.df4', 'torsion': [6]}
  • id: 8044851
    {'degree': 4, 'field': [60, -54, 19, -1, 1], 'lmfdb_label': '182070.df4', 'torsion': [2, 6]}
  • id: 8044852
    {'degree': 4, 'field': [85, -68, 69, -2, 1], 'lmfdb_label': '182070.df4', 'torsion': [12]}
  • id: 8044853
    {'degree': 4, 'field': [169, 0, -25, 0, 1], 'lmfdb_label': '182070.df4', 'torsion': [12]}
  • id: 8044850
    {'degree': 4, 'field': [289, 0, -85, 0, 1], 'lmfdb_label': '182070.df4', 'torsion': [2, 4]}
  • id: 8044854
    {'degree': 6, 'field': [-314, -116, 78, -3, -3, -1, 1], 'lmfdb_label': '182070.df4', 'torsion': [6]}
  • id: 8044858
    {'degree': 8, 'field': [3600, 0, 636, 0, 373, 0, -37, 0, 1], 'lmfdb_label': '182070.df4', 'torsion': [2, 12]}
  • id: 8044855
    {'degree': 8, 'field': [5028, -1608, 6162, -2088, 631, -482, 123, -2, 1], 'lmfdb_label': '182070.df4', 'torsion': [2, 12]}
  • id: 8044857
    {'degree': 8, 'field': [32536, 18760, -4200, -1040, 1013, -40, -50, 0, 1], 'lmfdb_label': '182070.df4', 'torsion': [8]}
  • id: 8044856
    {'degree': 8, 'field': [422500, 0, -773300, 0, 36861, 0, -458, 0, 1], 'lmfdb_label': '182070.df4', 'torsion': [8]}
  • id: 8044862
    {'degree': 12, 'field': [-43898, 39952, 24066, -29830, -1328, 6996, -455, -870, 99, 82, -11, -6, 1], 'lmfdb_label': '182070.df4', 'torsion': [12]}
  • id: 8044861
    {'degree': 12, 'field': [-3436, 23112, -22884, 880, -3540, 3072, -15, -726, 15, 100, -9, -6, 1], 'lmfdb_label': '182070.df4', 'torsion': [12]}
  • id: 8044860
    {'degree': 12, 'field': [4761, 0, -2409, 0, 2710, 0, -1541, 0, 330, 0, -29, 0, 1], 'lmfdb_label': '182070.df4', 'torsion': [2, 6]}
  • id: 8044859
    {'degree': 12, 'field': [5041, 12567, 15413, 12390, 1251, -2937, 1690, -807, 171, -42, 17, -3, 1], 'lmfdb_label': '182070.df4', 'torsion': [3, 6]}
  • id: 8044864
    {'degree': 16, 'field': [30958900, -53557000, 20742240, 21743040, -8881194, -18144528, 16306660, -3931594, -679317, 445602, -17832, -21474, 2741, 448, -84, -4, 1], 'lmfdb_label': '182070.df4', 'torsion': [2, 8]}
  • id: 8044863
    {'degree': 16, 'field': [40522500, -190283400, 384589980, -438641784, 316537746, -146734728, 38314542, -1333716, -2553521, 705176, -9254, -25396, 4249, -448, 82, -4, 1], 'lmfdb_label': '182070.df4', 'torsion': [4, 12]}
  • id: 8044867
    {'degree': 16, 'field': [516143605, 387437880, -272171804, -212407068, 62651838, 47441084, -8104084, -5971212, 726775, 464412, -48020, -22692, 2326, 644, -72, -8, 1], 'lmfdb_label': '182070.df4', 'torsion': [24]}
  • id: 8044866
    {'degree': 16, 'field': [1632393225, -6377218200, 9510060600, -6833513160, 4882355646, -1889418072, 853134180, -202527360, 64761391, -9811880, 2359036, -222080, 41806, -2240, 340, -8, 1], 'lmfdb_label': '182070.df4', 'torsion': [24]}
  • id: 8044865
    {'degree': 16, 'field': [501766806025, 0, -385360796440, 0, 78023155126, 0, -6979066108, 0, 317283799, 0, -7588084, 0, 92134, 0, -508, 0, 1], 'lmfdb_label': '182070.df4', 'torsion': [2, 8]}
  • id: 8044868
    {'degree': 18, 'field': [88924678875, -45426209400, 52347962610, -36553800933, 21913246107, -10094734476, 3897542578, -1121546199, 301385262, -52525291, 10364823, -837819, 176307, 2565, 3969, 38, 111, -3, 1], 'lmfdb_label': '182070.df4', '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: 4504015
    {'conductor': 182070, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '182070.df4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4504016
    {'conductor': 182070, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '182070.df4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4504017
    {'conductor': 182070, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '182070.df4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 4504018
    {'conductor': 182070, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '182070.df4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4504019
    {'conductor': 182070, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '182070.df4', 'prime': 17, '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: 2834913
    {'adelic_gens': [[681, 5848, 2516, 8909], [6376, 11781, 9435, 3826], [5864, 9639, 5185, 934], [1, 12, 12, 145], [5879, 0, 0, 14279], [10711, 13464, 3162, 4489], [2857, 13464, 12444, 4489], [1, 24, 0, 1], [14257, 24, 14256, 25], [1, 0, 24, 1], [15, 106, 12974, 5051]], 'adelic_image': '14280.384.5.?', 'conductor': 182070, 'lmfdb_label': '182070.df4', 'prime': 0}
  • id: 682015
    {'conductor': 182070, 'elladic_image': '4.6.0.1', 'lmfdb_label': '182070.df4', 'modell_image': '2B', 'prime': 2}
  • id: 682016
    {'conductor': 182070, 'elladic_image': '3.4.0.1', 'lmfdb_label': '182070.df4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 182070.df does not appear in ec_padic