Elliptic curve data - 12936.a2

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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': '12936f', 'Clabel': '12936f2', 'Cnumber': 2, 'abc_quality': 1.0295665318522507, 'absD': 139444416318670848, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 264, 'ainvs': [0, -1, 0, -390840, 95878476], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 12936, 'degree': 241920, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0802411182557555293954596064', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [-27403349188178, 578739249], 'lmfdb_iso': '12936.a', 'lmfdb_label': '12936.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -7976, -281808], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '132.6.0.?', '264.12.0.?'], '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, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.47190112821481567654365379001', 'prec': 103}, 'szpiro_ratio': 5.310396577637275, '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, -1, 0, -4, 0, 0, 0, 1, 0, -1, 0, 0, 0, 4, 0, 6, 0, -4, 0], 'aplist': [0, -1, -4, 0, -1, 0, 6, -4, -6, 6, 0, 6, 10, -8, -6, -12, 8, -4, -12, 10, -2, 2, -12, 6, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 12936, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '12936.a', 'trace_hash': 37358615594471174}
• 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': '0.015600033200191428805971036036', 'prec': 107}, 'conductor': 12936, 'gens': [], 'heights': [], 'lmfdb_label': '12936.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.32721176458701486908462064093', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.65442352917402973816924128185818395519', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-723, 0, 1]], 'xcoord_integral_points': [-723]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '7': 'a', '11': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '12936.a2'}
• ec_torsion_growth •

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

  
  
  • id: 666839
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '12936.a2', 'torsion': [2, 2]}
  • id: 666840
    {'degree': 4, 'field': [-98, 0, 35, 0, 1], 'lmfdb_label': '12936.a2', 'torsion': [4]}
  • id: 666843
    {'degree': 8, 'field': [-30481, -17522, 2078, 1418, -182, 8, -2, -4, 1], 'lmfdb_label': '12936.a2', 'torsion': [6]}
  • id: 666842
    {'degree': 8, 'field': [1369, 0, 4878, 0, 386, 0, -18, 0, 1], 'lmfdb_label': '12936.a2', 'torsion': [2, 4]}
  • id: 666841
    {'degree': 8, 'field': [4356, 0, -64, 0, 14, 0, 16, 0, 1], 'lmfdb_label': '12936.a2', 'torsion': [2, 4]}
  • id: 666845
    {'degree': 16, 'field': [12082576, 0, 68843968, 0, 62847232, 0, 1238832, 0, 107688, 0, -15624, 0, -140, 0, 4, 0, 1], 'lmfdb_label': '12936.a2', 'torsion': [2, 6]}
  • id: 666844
    {'degree': 16, 'field': [12698368, -6515968, 23232768, -41885696, 40026912, -25493088, 12907696, -4932416, 697128, 229832, -77060, -1824, 1410, 194, -33, -2, 1], 'lmfdb_label': '12936.a2', '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: 280877
    {'conductor': 12936, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '12936.a2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 280878
    {'conductor': 12936, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '12936.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 280879
    {'conductor': 12936, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '12936.a2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 280880
    {'conductor': 12936, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12936.a2', 'prime': 11, 'reduction_type': -1, '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: 1749793
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [145, 4, 26, 9], [1, 4, 0, 1], [261, 4, 260, 5], [2, 1, 131, 0], [100, 169, 33, 232], [89, 4, 178, 9]], 'adelic_image': '264.12.0.?', 'conductor': 12936, 'lmfdb_label': '12936.a2', 'prime': 0}
  • id: 61421
    {'conductor': 12936, 'elladic_image': '8.6.0.5', 'lmfdb_label': '12936.a2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 12936.a does not appear in ec_padic