Elliptic curve data - 12936.t2

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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': '12936j', 'Clabel': '12936j2', 'Cnumber': 2, 'abc_quality': 0.899108725536897, 'absD': 131194635264, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [0, 1, 0, -1584, -17424], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 12936, 'degree': 12288, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.83879448410335982888385161913', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2], 'jinv': [3650692, 1089], 'lmfdb_iso': '12936.t', 'lmfdb_label': '12936.t2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -32, 60], 'min_quad_twist_disc': -7, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '24.12.0.a.1', '56.12.0-2.a.1.1', '84.12.0.?', '88.12.0.?', '132.12.0.?', '168.24.0.?', '264.24.0.?', '308.12.0.?', '616.24.0.?', '924.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 4312], [7, 26, 264], [11, 12, 1176]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.71178324089091791484985152047', 'prec': 107}, 'szpiro_ratio': 3.5612781181684725, '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, 1, 0, -2, 0, -2, 0, -6, 0, 0, 0], 'aplist': [0, 1, -2, 0, 1, -2, -6, 0, 4, 2, 0, -10, -6, -8, 4, -6, 12, -2, 4, 12, 14, 16, 12, -10, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 12936, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '12936.t', 'trace_hash': 1008571738088885620}
• 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': '0.18682387175958380268484037433', 'prec': 103}, 'conductor': 12936, 'gens': [], 'heights': [], 'lmfdb_label': '12936.t2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.77414526532081836776797943174', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5482905306416367355359588634696391622', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-12, 0, 1], [44, 0, 1]], 'xcoord_integral_points': [-33, -12, 44]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '7': 'a', '11': [3, 0]}, 'iwp0': 3, 'lmfdb_label': '12936.t2'}
• ec_torsion_growth •

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

  
  
  • id: 666873
    {'degree': 4, 'field': [4, 0, -18, 0, 1], 'lmfdb_label': '12936.t2', 'torsion': [2, 4]}
  • id: 666874
    {'degree': 4, 'field': [4, 0, 10, 0, 1], 'lmfdb_label': '12936.t2', 'torsion': [2, 4]}
  • id: 666872
    {'degree': 4, 'field': [196, 0, 49, 0, 1], 'lmfdb_label': '12936.t2', 'torsion': [2, 4]}
  • id: 666875
    {'degree': 8, 'field': [-1704, 72, 752, 72, -384, -48, 18, 0, 1], 'lmfdb_label': '12936.t2', 'torsion': [2, 6]}
  • id: 666878
    {'degree': 16, 'field': [-1324791, -3634488, -2956248, 166320, 984608, -192280, -319056, 166144, 112650, -36344, -20696, 2992, 1952, -88, -80, 0, 1], 'lmfdb_label': '12936.t2', 'torsion': [2, 8]}
  • id: 666879
    {'degree': 16, 'field': [66537, -82440, 38808, 44640, 141384, 69384, -5472, 27456, 6010, 1752, 2936, -288, 456, -24, 32, 0, 1], 'lmfdb_label': '12936.t2', 'torsion': [2, 8]}
  • id: 666876
    {'degree': 16, 'field': [110889, 0, -211140, 0, 123822, 0, 19128, 0, 5299, 0, -408, 0, -10, 0, -12, 0, 1], 'lmfdb_label': '12936.t2', 'torsion': [4, 4]}
  • id: 666877
    {'degree': 16, 'field': [6316788, -14351028, 20593422, -19570446, 12949825, -6172426, 2296340, -694728, 188131, -56720, 19102, -4742, 967, -210, 32, -4, 1], 'lmfdb_label': '12936.t2', 'torsion': [2, 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: 280897
    {'conductor': 12936, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '12936.t2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 280898
    {'conductor': 12936, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12936.t2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 280899
    {'conductor': 12936, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '12936.t2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 280900
    {'conductor': 12936, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12936.t2', '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: 1749830
    {'adelic_gens': [[1, 0, 4, 1], [673, 532, 1610, 1065], [263, 0, 0, 1847], [1845, 4, 1844, 5], [1, 4, 0, 1], [463, 532, 0, 1], [925, 266, 0, 1], [267, 266, 350, 1583]], 'adelic_image': '1848.48.0.?', 'conductor': 12936, 'lmfdb_label': '12936.t2', 'prime': 0}
  • id: 61445
    {'conductor': 12936, 'elladic_image': '2.6.0.1', 'lmfdb_label': '12936.t2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 12936.t does not appear in ec_padic