Elliptic curve data - 291312.bg1

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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': '291312bg', 'Clabel': '291312bg3', 'Cnumber': 3, 'abc_quality': 1.108049552899778, 'absD': 153186882740639741952, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2856, 'ainvs': [0, 0, 0, -471736670691, 124708934902298434], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 291312, 'degree': 637009920, 'elladic_images': ['8.12.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.8569201218692561652910833421', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4], 'jinv': [322159999717985454060440834, 4250799], 'lmfdb_iso': '291312.bg', 'lmfdb_label': '291312.bg1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -181367424, 940067661600], 'min_quad_twist_disc': 204, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.p.1', '84.12.0.?', '168.24.0.?', '408.24.0.?', '952.24.0.?', '2856.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 18207], [3, 6, 4624], [7, 8, 41616], [17, 162, 1008]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2556223899938100791695639700', 'prec': 100}, 'szpiro_ratio': 7.332026905371612, '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, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, -2, -1, 0, 2, 0, 0, 0, 2, 8, 6, -6, -4, 0, -14, -8, -14, -4, -8, -10, 8, -16, -2, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 291312, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '291312.bg', 'trace_hash': 1416966417399075400}
• 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': '0.000060441159058188205619166928088', 'prec': 117}, 'conductor': 291312, 'gens': [], 'heights': [], 'lmfdb_label': '291312.bg1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.041967986168981830892981033442', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.33574388935185464714384826753514848399', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[396542, 0, 1]], 'xcoord_integral_points': [396542]}
• lmfdb_label 291312.bg1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12363385
    {'degree': 2, 'field': [-238, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [2, 2]}
  • id: 12363386
    {'degree': 2, 'field': [-102, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [4]}
  • id: 12363387
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '291312.bg1', 'torsion': [4]}
  • id: 12363388
    {'degree': 4, 'field': [1156, 0, -170, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [2, 4]}
  • id: 12363392
    {'degree': 8, 'field': [-1453, -1890, 304, 1388, 540, -50, -46, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [6]}
  • id: 12363390
    {'degree': 8, 'field': [2401, 0, -6748, 0, 1380, 0, -76, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [8]}
  • id: 12363391
    {'degree': 8, 'field': [28561, 0, 11323, 0, 1728, 0, 67, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [8]}
  • id: 12363389
    {'degree': 8, 'field': [41209, 0, 97020, 0, 2170, 0, 84, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [2, 4]}
  • id: 12363398
    {'degree': 16, 'field': [751689, 0, -589560, 0, 2052478, 0, -69360, 0, -446505, 0, 14960, 0, -2346, 0, 0, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [12]}
  • id: 12363397
    {'degree': 16, 'field': [2625328, -2825856, -15404096, -18810944, -9622544, 376672, 3308816, 1601152, 48752, -193408, -44560, 7760, 3244, -88, -92, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [12]}
  • id: 12363394
    {'degree': 16, 'field': [4879681, 0, -9374996, 0, 6877088, 0, -2497296, 0, 489743, 0, -53328, 0, 3152, 0, -92, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [2, 8]}
  • id: 12363395
    {'degree': 16, 'field': [151462249, 0, 76651074, 0, 216265045, 0, 52029654, 0, 5401716, 0, 299514, 0, 9397, 0, 150, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [2, 8]}
  • id: 12363393
    {'degree': 16, 'field': [1629817641, 0, 1544050860, 0, 205629886, 0, -9020704, 0, 729183, 0, 19096, 0, -126, 0, 44, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [4, 4]}
  • id: 12363396
    {'degree': 16, 'field': [2857222944, -24991490496, 869822048, -5465864448, -908423984, 346788448, 24658704, -15995968, -3060624, 84528, 77496, 33304, -2376, -184, -64, 0, 1], 'lmfdb_label': '291312.bg1', 'torsion': [2, 6]}
• 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: 7217080
    {'conductor': 291312, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '291312.bg1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7217081
    {'conductor': 291312, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '291312.bg1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7217082
    {'conductor': 291312, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '291312.bg1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7217083
    {'conductor': 291312, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '291312.bg1', '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: 3499059
    {'adelic_gens': [[2320, 3, 141, 1906], [1784, 2253, 2733, 800], [1312, 2745, 1539, 574], [1, 0, 8, 1], [2288, 2853, 2739, 950], [1903, 0, 0, 2855], [7, 6, 2850, 2851], [2849, 8, 2848, 9], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '2856.48.0.?', 'conductor': 291312, 'lmfdb_label': '291312.bg1', 'prime': 0}
  • id: 1031387
    {'conductor': 291312, 'elladic_image': '8.12.0.9', 'lmfdb_label': '291312.bg1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 291312.bg does not appear in ec_padic