Elliptic curve data - 291312.ba2

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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': '291312ba', 'Clabel': '291312ba1', 'Cnumber': 1, 'abc_quality': 1.1378021506949256, 'absD': 354538463260122288, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 84, 'ainvs': [0, 0, 0, -15606, -28657529], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 291312, 'degree': 3096576, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0465017799850567023254242219', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2], 'jinv': [-40310784, 34000561], 'lmfdb_iso': '291312.ba', 'lmfdb_label': '291312.ba2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -486, -157491], 'min_quad_twist_disc': 204, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '28.6.0.d.1', '84.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '15.594328405239205937564046793', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 867], [3, 6, 4624], [7, 8, 41616], [17, 162, 1008]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.12419297560327280287943489658', 'prec': 103}, 'szpiro_ratio': 3.804198689035841, '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, -6, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, -2, -1, -6, 2, 0, 0, 6, -4, -4, 6, 6, -4, -12, 4, 4, -2, -4, -14, -10, -16, 8, 10, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 291312, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '291312.ba', 'trace_hash': 768230485807911227}
• 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': '0.016689031696625996755648809398', 'prec': 107}, 'conductor': 291312, 'gens': [[100148751, 1002225625282, 53]], 'heights': [{'__RealLiteral__': 0, 'data': '15.594328405239205937564046793', 'prec': 100}], 'lmfdb_label': '291312.ba2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.13646769502257856232147798456', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2562441057762357473779343662346224962', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[323, 0, 1]], 'xcoord_integral_points': [323]}
• lmfdb_label 291312.ba2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12363176
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '291312.ba2', 'torsion': [2, 2]}
  • id: 12363177
    {'degree': 4, 'field': [-867, 0, 51, 0, 1], 'lmfdb_label': '291312.ba2', 'torsion': [4]}
  • id: 12363180
    {'degree': 8, 'field': [-1453, -1890, 304, 1388, 540, -50, -46, 0, 1], 'lmfdb_label': '291312.ba2', 'torsion': [6]}
  • id: 12363178
    {'degree': 8, 'field': [17689, 0, -5657, 0, 699, 0, -41, 0, 1], 'lmfdb_label': '291312.ba2', 'torsion': [2, 4]}
  • id: 12363179
    {'degree': 8, 'field': [751689, 0, 44217, 0, 3468, 0, -51, 0, 1], 'lmfdb_label': '291312.ba2', 'torsion': [2, 4]}
  • id: 12363182
    {'degree': 16, 'field': [751689, 0, -117912, 0, -69938, 0, -13872, 0, 11271, 0, -272, 0, 102, 0, 0, 0, 1], 'lmfdb_label': '291312.ba2', 'torsion': [2, 6]}
  • id: 12363181
    {'degree': 16, 'field': [101103025, 0, 35109712, 0, -3409726, 0, -123992, 0, 47491, 0, -3448, 0, -346, 0, 8, 0, 1], 'lmfdb_label': '291312.ba2', 'torsion': [8]}
• 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: 7217004
    {'conductor': 291312, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '291312.ba2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7217005
    {'conductor': 291312, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '291312.ba2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7217006
    {'conductor': 291312, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '291312.ba2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7217007
    {'conductor': 291312, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '291312.ba2', 'prime': 17, 'reduction_type': 0, '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: 3499043
    {'adelic_gens': [[1, 2, 2, 5], [3, 4, 8, 11], [81, 4, 80, 5], [32, 1, 55, 0], [1, 4, 0, 1], [65, 22, 20, 63], [73, 4, 62, 9], [1, 0, 4, 1]], 'adelic_image': '84.12.0.?', 'conductor': 291312, 'lmfdb_label': '291312.ba2', 'prime': 0}
  • id: 1031372
    {'conductor': 291312, 'elladic_image': '2.3.0.1', 'lmfdb_label': '291312.ba2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 291312.ba does not appear in ec_padic