Elliptic curve data - 180336.bg2

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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': '180336bp', 'Clabel': '180336bp3', 'Cnumber': 3, 'abc_quality': 0.9639015803583432, 'absD': 9156002532405064667136, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1768, 'ainvs': [0, -1, 0, -6422832, 4251709440], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 180336, 'degree': 9437184, 'elladic_images': ['8.48.0.101'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9183362075709585686952777851', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4], 'jinv': [296380748763217, 92608836489], 'lmfdb_iso': '180336.bg', 'lmfdb_label': '180336.bg2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1389, -14094], 'min_quad_twist_disc': -68, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.d.2.4', '52.24.0.c.1', '68.24.0-4.b.1.3', '104.96.0.?', '136.96.0.?', '884.48.0.?', '1768.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.2875194037766280881023060186', 'prec': 100}, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.80858235498290521915327835471', 'prec': 103}, 'szpiro_ratio': 4.845225278421187, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, 0, 2, 0, 0, 0, 1, 0, 4, 0, 1, 0, -2, 0, 0, 0, 4, 0], 'aplist': [0, -1, 2, 0, 4, 1, 0, 4, 0, 2, -8, 2, -2, 4, -8, -10, -4, -14, 4, 0, 14, -8, 4, -6, 6], 'class_deg': 8, 'class_size': 6, 'conductor': 180336, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '180336.bg', 'trace_hash': 1458475706167085658}
• 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': '0.0029185381689135744624897014622', 'prec': 110}, 'conductor': 180336, 'gens': [[72, 61560, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.2875194037766280881023060186', 'prec': 100}], 'lmfdb_label': '180336.bg2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12015552612990284418621189357', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.2427063960471695917833977236494969367', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[720, 0, 1], [2097, 0, 1]], 'xcoord_integral_points': [-2816, 72, 720, 2097, 8234]}
• lmfdb_label 180336.bg2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7981998
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '180336.bg2', 'torsion': [2, 4]}
  • id: 7981999
    {'degree': 4, 'field': [1, 0, 15, 0, 1], 'lmfdb_label': '180336.bg2', 'torsion': [2, 4]}
  • id: 7982000
    {'degree': 4, 'field': [417, -28, 29, -2, 1], 'lmfdb_label': '180336.bg2', 'torsion': [2, 4]}
  • id: 7982001
    {'degree': 4, 'field': [458, 60, -59, -2, 1], 'lmfdb_label': '180336.bg2', 'torsion': [2, 8]}
  • id: 7982004
    {'degree': 8, 'field': [-70227, 0, 20961, 0, 918, 0, 0, 0, 1], 'lmfdb_label': '180336.bg2', 'torsion': [2, 6]}
  • id: 7982003
    {'degree': 8, 'field': [256, 0, 0, 0, 49, 0, 0, 0, 1], 'lmfdb_label': '180336.bg2', 'torsion': [2, 8]}
  • id: 7982002
    {'degree': 8, 'field': [3137, 334, -220, -226, 109, 2, 4, -4, 1], 'lmfdb_label': '180336.bg2', 'torsion': [4, 4]}
  • id: 7982006
    {'degree': 16, 'field': [247009, 0, -287216, 0, 180106, 0, -46128, 0, 16923, 0, -3888, 0, 478, 0, -32, 0, 1], 'lmfdb_label': '180336.bg2', 'torsion': [4, 8]}
  • id: 7982007
    {'degree': 16, 'field': [983025, -909840, 1376974, -1015980, 704144, -211904, 29666, 37708, -10323, -2864, 3710, -1316, -84, 112, 4, -8, 1], 'lmfdb_label': '180336.bg2', 'torsion': [4, 8]}
  • id: 7982009
    {'degree': 16, 'field': [1031069, -848042, 638950, 564366, -607949, 283172, 75478, -127520, 12186, 8854, 2066, -1552, -166, 168, -4, -8, 1], 'lmfdb_label': '180336.bg2', 'torsion': [2, 12]}
  • id: 7982005
    {'degree': 16, 'field': [1127844, 0, -974808, 0, 261544, 0, -45036, 0, 13613, 0, 4176, 0, 602, 0, 36, 0, 1], 'lmfdb_label': '180336.bg2', 'torsion': [4, 8]}
  • id: 7982008
    {'degree': 16, 'field': [171157618944, 0, -171157618944, 0, 19157347872, 0, 279669312, 0, 6484192, 0, -1414192, 0, 67938, 0, -676, 0, 1], 'lmfdb_label': '180336.bg2', 'torsion': [2, 16]}
• 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: 4464906
    {'conductor': 180336, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '180336.bg2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4464907
    {'conductor': 180336, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '180336.bg2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4464908
    {'conductor': 180336, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '180336.bg2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4464909
    {'conductor': 180336, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '180336.bg2', '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: 2825026
    {'adelic_gens': [[5, 4, 1764, 1765], [1639, 2, 1342, 1763], [1761, 8, 1760, 9], [1, 0, 8, 1], [1663, 1764, 0, 1767], [1761, 1320, 6, 447], [889, 444, 464, 893], [1, 8, 0, 1]], 'adelic_image': '1768.192.1.?', 'conductor': 180336, 'lmfdb_label': '180336.bg2', 'prime': 0}
  • id: 676781
    {'conductor': 180336, 'elladic_image': '8.48.0.101', 'lmfdb_label': '180336.bg2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 180336.bg does not appear in ec_padic