Elliptic curve data - 172480.be4

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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': '172480ed', 'Clabel': '172480ed1', 'Cnumber': 1, 'abc_quality': 0.9670463504502834, 'absD': 1822147712000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 9240, 'ainvs': [0, 1, 0, -8885, -318725], 'analytic_rank': 2, 'bad_primes': [2, 5, 7, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 172480, 'degree': 331776, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1380992161989850221852561179', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 30, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [643956736, 15125], 'lmfdb_iso': '172480.be', 'lmfdb_label': '172480.be4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -45, 100], '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': 13, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '3.2416255059871374497182792910', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.41247850879529272154844702170', 'prec': 107}, 'szpiro_ratio': 3.225241073576659, '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.be', 'trace_hash': 701795337957306010}
• 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': '0.10267378708085238298790240621', 'prec': 103}, 'conductor': 172480, 'gens': [[-50, 55, 1], [115, 440, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5324544756936562770218293446', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.1678532663083297344873957981', 'prec': 100}], 'lmfdb_label': '172480.be4', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.49243902640879743245650372028', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.5778174489013879086026996770944257244', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-61, 0, 1]], 'xcoord_integral_points': [-61, -57, -50, 115, 135, 478, 4790]}
• lmfdb_label 172480.be4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7657813
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '172480.be4', 'torsion': [2, 2]}
  • id: 7657814
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '172480.be4', 'torsion': [6]}
  • id: 7657816
    {'degree': 4, 'field': [239, -26, 27, -2, 1], 'lmfdb_label': '172480.be4', 'torsion': [2, 6]}
  • id: 7657815
    {'degree': 4, 'field': [245, 0, 56, 0, 1], 'lmfdb_label': '172480.be4', 'torsion': [4]}
  • id: 7657817
    {'degree': 6, 'field': [-2058, 0, 784, 0, -14, 0, 1], 'lmfdb_label': '172480.be4', 'torsion': [6]}
  • id: 7657818
    {'degree': 8, 'field': [2401, 0, -24696, 0, 1666, 0, -56, 0, 1], 'lmfdb_label': '172480.be4', 'torsion': [2, 4]}
  • id: 7657819
    {'degree': 8, 'field': [106205, -24860, 28436, -7260, 3901, -328, 114, -4, 1], 'lmfdb_label': '172480.be4', 'torsion': [2, 4]}
  • id: 7657820
    {'degree': 8, 'field': [121060, -34784, 20496, -2856, 1084, -96, 44, -4, 1], 'lmfdb_label': '172480.be4', 'torsion': [12]}
  • id: 7657822
    {'degree': 12, 'field': [146959, 4086270, -3500257, -1154562, 535470, 45030, -6539, -7062, 1524, 150, -19, -6, 1], 'lmfdb_label': '172480.be4', 'torsion': [2, 6]}
  • id: 7657821
    {'degree': 12, 'field': [4272489, 0, 4102998, 0, 648799, 0, 59060, 0, 2967, 0, 86, 0, 1], 'lmfdb_label': '172480.be4', 'torsion': [3, 6]}
  • id: 7657824
    {'degree': 16, 'field': [31416025, 0, 84914200, 0, 5102640, 0, -2512440, 0, -129194, 0, 16296, 0, 1136, 0, 56, 0, 1], 'lmfdb_label': '172480.be4', 'torsion': [2, 12]}
  • id: 7657823
    {'degree': 16, 'field': [242393761, 0, 125883136, 0, 57456208, 0, 9097384, 0, 611682, 0, 11424, 0, -672, 0, -24, 0, 1], 'lmfdb_label': '172480.be4', 'torsion': [8]}
  • id: 7657825
    {'degree': 16, 'field': [2205886505, -562200140, 675191794, -250264176, 188921878, -85394524, 43820798, -14407068, 5208067, -1150096, 311098, -46596, 9768, -952, 156, -8, 1], 'lmfdb_label': '172480.be4', 'torsion': [2, 12]}
  • id: 7657826
    {'degree': 18, 'field': [32317881775, -22496242550, 24641633975, -11497327150, 7288197765, -2540542990, 1178954736, -323774342, 119002082, -26269904, 7892503, -1392908, 345753, -47122, 9623, -926, 152, -8, 1], 'lmfdb_label': '172480.be4', '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: 4266590
    {'conductor': 172480, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '172480.be4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4266591
    {'conductor': 172480, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '172480.be4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 4266592
    {'conductor': 172480, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '172480.be4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4266593
    {'conductor': 172480, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '172480.be4', '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: 2775717
    {'adelic_gens': [[1, 6, 6, 37], [1, 12, 0, 1], [11, 2, 9190, 9231], [4619, 0, 0, 9239], [3970, 1323, 8421, 652], [2099, 3948, 714, 5207], [7909, 5278, 2030, 5949], [3959, 0, 0, 9239], [449, 3962, 7098, 5293], [9229, 12, 9228, 13], [1, 0, 12, 1], [3681, 5222, 7294, 2239], [671, 3948, 672, 3947]], 'adelic_image': '9240.96.1.?', 'conductor': 172480, 'lmfdb_label': '172480.be4', 'prime': 0}
  • id: 650067
    {'conductor': 172480, 'elladic_image': '2.3.0.1', 'lmfdb_label': '172480.be4', 'modell_image': '2B', 'prime': 2}
  • id: 650068
    {'conductor': 172480, 'elladic_image': '3.4.0.1', 'lmfdb_label': '172480.be4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 172480.be does not appear in ec_padic