Elliptic curve data - 172480.gt2

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

  
  {'Ciso': '172480dk', 'Clabel': '172480dk3', 'Cnumber': 3, 'abc_quality': 1.026119420484522, 'absD': 1067122586055680, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 9240, 'ainvs': [0, -1, 0, -87285, -9771355], 'analytic_rank': 0, 'bad_primes': [2, 5, 7, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 172480, 'degree': 995328, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6874053605330398678828787364', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 175, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [610462990336, 8857805], 'lmfdb_iso': '172480.gt', 'lmfdb_label': '172480.gt2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -445, -3720], 'min_quad_twist_disc': 56, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '10.6.0.a.1', '30.24.0.a.1', '44.6.0.b.1', '132.24.0.?', '168.24.0.?', '220.12.0.?', '660.48.1.?', '840.48.0.?', '1848.48.0.?', '9240.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 245], [3, 2, 15680], [5, 6, 34496], [7, 26, 3520], [11, 12, 15680]], 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.13682763553876212414917559680', 'prec': 103}, 'szpiro_ratio': 3.79368696998481, '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, 1, 0, 0, 0, 1, 0, -1, 0, -4, 0, 2, 0, 0, 0, 4, 0], 'aplist': [0, 2, 1, 0, -1, -4, 0, 4, 6, 6, 8, -2, -6, 8, 6, 6, 12, 2, -10, 12, 16, -8, 0, -6, -14], 'class_deg': 6, 'class_size': 4, 'conductor': 172480, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '172480.gt', 'trace_hash': 208841005082444085}
• 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': '0.034224595693617460995967468737', 'prec': 107}, 'conductor': 172480, 'gens': [], 'heights': [], 'lmfdb_label': '172480.gt2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.27800067710479120507857899158', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.0040121878862416914144218484625301514', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[341, 0, 1]], 'xcoord_integral_points': [341]}
• lmfdb_label 172480.gt2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7657507
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '172480.gt2', 'torsion': [2, 2]}
  • id: 7657508
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '172480.gt2', 'torsion': [6]}
  • id: 7657509
    {'degree': 4, 'field': [245, 0, -56, 0, 1], 'lmfdb_label': '172480.gt2', 'torsion': [4]}
  • id: 7657510
    {'degree': 4, 'field': [1891, -82, 83, -2, 1], 'lmfdb_label': '172480.gt2', 'torsion': [2, 6]}
  • id: 7657511
    {'degree': 6, 'field': [-1405, -710, 575, 56, -47, -2, 1], 'lmfdb_label': '172480.gt2', 'torsion': [6]}
  • id: 7657512
    {'degree': 8, 'field': [2401, 0, 24696, 0, 1666, 0, 56, 0, 1], 'lmfdb_label': '172480.gt2', 'torsion': [2, 4]}
  • id: 7657513
    {'degree': 8, 'field': [23549, 29572, -25884, -7260, 3341, 344, -110, -4, 1], 'lmfdb_label': '172480.gt2', 'torsion': [2, 4]}
  • id: 7657514
    {'degree': 8, 'field': [470596, 0, 52136, 0, 2156, 0, -56, 0, 1], 'lmfdb_label': '172480.gt2', 'torsion': [12]}
  • id: 7657516
    {'degree': 12, 'field': [470596, 0, -134456, 0, 0, 0, 6860, 0, 0, 0, -56, 0, 1], 'lmfdb_label': '172480.gt2', 'torsion': [2, 6]}
  • id: 7657515
    {'degree': 12, 'field': [6767203, 3048798, -2495335, -1054734, 399696, 145422, -35747, -10422, 2004, 390, -67, -6, 1], 'lmfdb_label': '172480.gt2', 'torsion': [3, 6]}
  • id: 7657518
    {'degree': 16, 'field': [3421681, 43477244, 209170204, 302602004, 247817754, -169128784, 82058888, -23260828, 3538391, -929360, 144968, -17348, 5274, -500, 100, -8, 1], 'lmfdb_label': '172480.gt2', 'torsion': [2, 12]}
  • id: 7657519
    {'degree': 16, 'field': [1020866401, 6374735716, 11536891872, 3705316636, 294049010, 683915608, 241451108, 3600820, 1596543, 1430480, 240572, -7364, 70, 748, 28, -8, 1], 'lmfdb_label': '172480.gt2', 'torsion': [2, 12]}
  • id: 7657517
    {'degree': 16, 'field': [1041869284, 0, -537361600, 0, 92003336, 0, -9051824, 0, 654032, 0, -23072, 0, 252, 0, -24, 0, 1], 'lmfdb_label': '172480.gt2', 'torsion': [8]}
  • id: 7657520
    {'degree': 18, 'field': [971562607849, 410388335874, 265173498903, -3411599730, -17474224935, 2680367118, 1617137114, -313886034, 4275372, 26253920, 978765, 47520, -28673, -14322, -1569, -22, 36, 0, 1], 'lmfdb_label': '172480.gt2', '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: 4266450
    {'conductor': 172480, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '172480.gt2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4266451
    {'conductor': 172480, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '172480.gt2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4266452
    {'conductor': 172480, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '172480.gt2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4266453
    {'conductor': 172480, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '172480.gt2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 2775998
    {'adelic_gens': [[1, 6, 6, 37], [1, 12, 0, 1], [11, 2, 9190, 9231], [5559, 4018, 1946, 7001], [4619, 0, 0, 9239], [3970, 1323, 8421, 652], [7699, 3948, 7700, 9239], [2099, 3948, 714, 5207], [7909, 5278, 2030, 5949], [3959, 0, 0, 9239], [1, 0, 12, 1], [9229, 12, 9228, 13], [671, 3948, 672, 3947]], 'adelic_image': '9240.96.1.?', 'conductor': 172480, 'lmfdb_label': '172480.gt2', 'prime': 0}
  • id: 650297
    {'conductor': 172480, 'elladic_image': '2.3.0.1', 'lmfdb_label': '172480.gt2', 'modell_image': '2B', 'prime': 2}
  • id: 650298
    {'conductor': 172480, 'elladic_image': '3.4.0.1', 'lmfdb_label': '172480.gt2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 172480.gt does not appear in ec_padic