Elliptic curve data - 162288.bg5

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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': '162288o', 'Clabel': '162288o1', 'Cnumber': 1, 'abc_quality': 0.9458836476842432, 'absD': 233518919495259783168, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 7728, 'ainvs': [0, 0, 0, 888909, -660679054], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 162288, 'degree': 4718592, 'elladic_images': ['16.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5916621816215765549666745115', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [221115865823, 664731648], 'lmfdb_iso': '162288.bg', 'lmfdb_label': '162288.bg5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 126, 1167], 'min_quad_twist_disc': -84, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0.e.1', '24.24.0-8.n.1.4', '46.6.0.a.1', '48.48.0-16.e.1.2', '56.24.0.bv.1', '84.12.0.?', '92.12.0.?', '112.48.0.?', '168.48.0.?', '184.24.0.?', '336.96.0.?', '368.48.0.?', '552.48.0.?', '1104.96.0.?', '1288.48.0.?', '1932.24.0.?', '2576.96.1.?', '3864.96.0.?', '7728.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 10143], [3, 8, 18032], [7, 32, 3312], [23, 24, 7056]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.37625378219991974729914339986', 'prec': 103}, 'szpiro_ratio': 4.512805385275538, '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, -2, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, -2, 0, -4, 2, -6, 4, -1, 2, -8, 6, -6, 4, 8, -6, -4, 10, -4, -8, 6, 0, 12, 2, -10], 'class_deg': 8, 'class_size': 6, 'conductor': 162288, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '162288.bg', 'trace_hash': 1350419464783810234}
• 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': '0.0056093279409649816329384752743', 'prec': 110}, 'conductor': 162288, 'gens': [], 'heights': [], 'lmfdb_label': '162288.bg5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.090304923466503522783217365968', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.72243938773202818226573892774614379622', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[553, 0, 1]], 'xcoord_integral_points': [553]}
• lmfdb_label 162288.bg5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7252003
    {'degree': 2, 'field': [-483, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [4]}
  • id: 7252002
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '162288.bg5', 'torsion': [2, 2]}
  • id: 7252004
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [4]}
  • id: 7252006
    {'degree': 4, 'field': [22, 2, -1, -2, 1], 'lmfdb_label': '162288.bg5', 'torsion': [8]}
  • id: 7252007
    {'degree': 4, 'field': [144, 0, 45, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [8]}
  • id: 7252005
    {'degree': 4, 'field': [246, -54, 55, -2, 1], 'lmfdb_label': '162288.bg5', 'torsion': [2, 4]}
  • id: 7252012
    {'degree': 8, 'field': [-190512, 0, -30828, 0, 1512, 0, 0, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [6]}
  • id: 7252009
    {'degree': 8, 'field': [-22343, 5658, 2680, 138, 381, -138, -44, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [8]}
  • id: 7252011
    {'degree': 8, 'field': [64, 0, 4, 0, 41, 0, -10, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [16]}
  • id: 7252008
    {'degree': 8, 'field': [2787, -972, 1168, -372, 137, 56, -14, -4, 1], 'lmfdb_label': '162288.bg5', 'torsion': [2, 4]}
  • id: 7252010
    {'degree': 8, 'field': [4900, 0, -672, 0, 221, 0, 18, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [2, 8]}
  • id: 7252013
    {'degree': 16, 'field': [519841, 0, -674380, 0, 1022690, 0, -331260, 0, 65507, 0, -7860, 0, 698, 0, -40, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [4, 4]}
  • id: 7252019
    {'degree': 16, 'field': [777924, 0, 6964272, 0, 19375776, 0, 18991665, 0, 1223334, 0, 7581, 0, -63, 0, 42, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [12]}
  • id: 7252016
    {'degree': 16, 'field': [1048576, 0, 553984, 0, 618368, 0, 69844, 0, -359, 0, -172, 0, 302, 0, 32, 0, 1], 'lmfdb_label': '162288.bg5', 'torsion': [2, 16]}
  • id: 7252014
    {'degree': 16, 'field': [4309776, -11783376, 16108488, -14076552, 8622376, -3872196, 1347810, -372278, 70793, 46, -5776, 1966, -261, 0, 8, -4, 1], 'lmfdb_label': '162288.bg5', 'torsion': [2, 8]}
  • id: 7252015
    {'degree': 16, 'field': [5914624, -84205568, 1112456192, -1177931264, 888640576, -238329920, 32055328, -3628704, -609024, 535056, -68360, -9944, 4672, -452, 50, -2, 1], 'lmfdb_label': '162288.bg5', 'torsion': [16]}
  • id: 7252017
    {'degree': 16, 'field': [13503144096, -48089414736, 47306976324, 1526542080, -662646936, -134073408, 66663240, -18375216, 4050061, 317344, -17612, -25928, 5110, -392, 76, -8, 1], 'lmfdb_label': '162288.bg5', 'torsion': [2, 6]}
  • id: 7252018
    {'degree': 16, 'field': [27128735188, 15846790264, -23510008956, 15727351488, -8880255756, 1259976924, -486958007, 57719272, -14811342, 225390, -16071, -15900, 2741, -70, 30, -8, 1], 'lmfdb_label': '162288.bg5', 'torsion': [12]}
• 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: 4015803
    {'conductor': 162288, 'conductor_valuation': 4, 'discriminant_valuation': 28, 'j_denominator_valuation': 16, 'kodaira_symbol': -24, 'lmfdb_label': '162288.bg5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4015804
    {'conductor': 162288, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '162288.bg5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4015805
    {'conductor': 162288, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '162288.bg5', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4015806
    {'conductor': 162288, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '162288.bg5', 'prime': 23, '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: 2713357
    {'adelic_gens': [[4175, 5136, 7470, 737], [2575, 0, 0, 7727], [1, 16, 0, 1], [7713, 16, 7712, 17], [2248, 2577, 303, 10], [6611, 5136, 6144, 2891], [15, 2, 7630, 7715], [5, 4, 7724, 7725], [1, 2592, 3228, 3349], [1, 0, 16, 1]], 'adelic_image': '7728.192.1.?', 'conductor': 162288, 'lmfdb_label': '162288.bg5', 'prime': 0}
  • id: 617261
    {'conductor': 162288, 'elladic_image': '16.24.0.1', 'lmfdb_label': '162288.bg5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 162288.bg does not appear in ec_padic