Elliptic curve data - 177870.bg4

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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': '177870he', 'Clabel': '177870he2', 'Cnumber': 2, 'abc_quality': 0.9486074789755161, 'absD': 16021815314432303237400, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 9240, 'ainvs': [1, 1, 0, 4499988, -4854836664], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 177870, 'degree': 19906560, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9458803577729851003794112713', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [48351870250991, 76871856600], 'lmfdb_iso': '177870.bg', 'lmfdb_label': '177870.bg4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 759, -10575], 'min_quad_twist_disc': 77, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '24.24.0.cb.1', '60.24.0-6.a.1.5', '120.48.0.?', '231.8.0.?', '462.24.0.?', '1540.6.0.?', '1848.48.0.?', '4620.48.0.?', '9240.96.1.?'], '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, 'serre_invariants': [[2, 4, 17787], [3, 4, 29645], [5, 6, 35574], [7, 32, 3630], [11, 72, 1470]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.77397764684614317579576311060', 'prec': 103}, 'szpiro_ratio': 4.808613001281028, '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, -1, 1, 1, 1, 0, -1, 1, -1, 0, -1, -4, 0, -1, 1, 0, -1, 8, 1], 'aplist': [-1, -1, 1, 0, 0, -4, 0, 8, 6, -6, 4, 8, 6, 4, -12, 6, 12, -10, -10, 0, 14, -8, 0, 12, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 177870, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '177870.bg', 'trace_hash': 365307118682859215}
• 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': '0.0027621091244919771276052846574', 'prec': 110}, 'conductor': 177870, 'gens': [], 'heights': [], 'lmfdb_label': '177870.bg4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.065391030901443168664169270883', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0925129888461813972534166682562015351', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[3643, -3643, 2]], 'xcoord_integral_points': []}
• lmfdb_label 177870.bg4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7881705
    {'degree': 2, 'field': [-19, -1, 1], 'lmfdb_label': '177870.bg4', 'torsion': [6]}
  • id: 7881704
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '177870.bg4', 'torsion': [2, 2]}
  • id: 7881706
    {'degree': 4, 'field': [-384, 0, 2, 0, 1], 'lmfdb_label': '177870.bg4', 'torsion': [4]}
  • id: 7881707
    {'degree': 4, 'field': [631, 26, -25, -2, 1], 'lmfdb_label': '177870.bg4', 'torsion': [2, 6]}
  • id: 7881708
    {'degree': 6, 'field': [11328, -2964, 691, -17, 38, -1, 1], 'lmfdb_label': '177870.bg4', 'torsion': [6]}
  • id: 7881711
    {'degree': 8, 'field': [71, 1126, -790, -706, 439, -106, 40, -4, 1], 'lmfdb_label': '177870.bg4', 'torsion': [12]}
  • id: 7881710
    {'degree': 8, 'field': [129600, 0, 26880, 0, -524, 0, 28, 0, 1], 'lmfdb_label': '177870.bg4', 'torsion': [2, 4]}
  • id: 7881709
    {'degree': 8, 'field': [2064892, -750192, 213160, -10656, 10920, -552, 52, 0, 1], 'lmfdb_label': '177870.bg4', 'torsion': [2, 4]}
  • id: 7881712
    {'degree': 12, 'field': [48804196, 0, -15868825, 0, 2268303, 0, -144905, 0, 5493, 0, -115, 0, 1], 'lmfdb_label': '177870.bg4', 'torsion': [3, 6]}
  • id: 7881713
    {'degree': 12, 'field': [119845980, -71160120, 8281320, 455592, -654245, 20342, 93437, -11146, 4798, -170, 113, -2, 1], 'lmfdb_label': '177870.bg4', 'torsion': [2, 6]}
  • id: 7881715
    {'degree': 16, 'field': [89818492, 14410544, 19966152, -69103232, 35408592, -973320, 217588, 115504, -44763, -10888, 23104, -10728, 1242, 224, -12, -8, 1], 'lmfdb_label': '177870.bg4', 'torsion': [2, 12]}
  • id: 7881716
    {'degree': 16, 'field': [881975329, -292571652, -200117856, 74632152, 28426715, -9038868, -1829682, -170448, 425556, -27420, -2484, -4776, 731, -12, 30, 0, 1], 'lmfdb_label': '177870.bg4', 'torsion': [2, 12]}
  • id: 7881714
    {'degree': 16, 'field': [755063675136, 0, 185729477760, 0, -31226132784, 0, 1480148880, 0, -44467724, 0, 978880, 0, -2464, 0, -20, 0, 1], 'lmfdb_label': '177870.bg4', 'torsion': [8]}
  • id: 7881717
    {'degree': 18, 'field': [-2029612897507, -1831272491091, -1428658404255, 312176968112, 193334938638, -20591044842, -2595841946, 367957896, -429179025, 10586103, 17391891, 208608, -369034, -24258, 10506, 140, -135, -3, 1], 'lmfdb_label': '177870.bg4', '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: 4403280
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '177870.bg4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4403281
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '177870.bg4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4403282
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '177870.bg4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4403283
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '177870.bg4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4403284
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '177870.bg4', 'prime': 11, '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: 2809425
    {'adelic_gens': [[1, 6, 6, 37], [1, 12, 0, 1], [11, 2, 9190, 9231], [6719, 9228, 3354, 9167], [3959, 9228, 5274, 9167], [3697, 12, 3702, 73], [7706, 11, 3069, 9220], [6555, 5008, 6518, 4997], [10, 3, 4593, 9232], [1, 0, 12, 1], [9229, 12, 9228, 13]], 'adelic_image': '9240.96.1.?', 'conductor': 177870, 'lmfdb_label': '177870.bg4', 'prime': 0}
  • id: 668427
    {'conductor': 177870, 'elladic_image': '2.3.0.1', 'lmfdb_label': '177870.bg4', 'modell_image': '2B', 'prime': 2}
  • id: 668428
    {'conductor': 177870, 'elladic_image': '3.4.0.1', 'lmfdb_label': '177870.bg4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 177870.bg does not appear in ec_padic