Elliptic curve data - 1288.g1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1288i', 'Clabel': '1288i2', 'Cnumber': 2, 'abc_quality': 0.9206797628790026, 'absD': 127459985408, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1288, 'ainvs': [0, -1, 0, -2672, 51212], 'analytic_rank': 0, 'bad_primes': [2, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1288, 'degree': 960, 'elladic_images': ['8.6.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.88336288381931211827580137069', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2], 'jinv': [1030541881826, 62236321], 'lmfdb_iso': '1288.g', 'lmfdb_label': '1288.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -2672, 51212], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.b.1', '644.6.0.?', '1288.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1], [3, 2, 184], [7, 8, 184], [23, 24, 56]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.24797796830602891797667192602', 'prec': 103}, 'szpiro_ratio': 4.927591701423047, '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, 2, 0, 2, 0, 1, 0, 1, 0, 2, 0, 4, 0, 4, 0, -2, 0, 0, 0], 'aplist': [0, 2, 2, 1, 2, 4, -2, 0, 1, -2, 0, -4, 6, 2, 4, 0, 2, -10, 2, -8, -6, 0, 0, 10, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 1288, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1288.g', 'trace_hash': 1704051493285927497}
• 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': '0.17089161264265657275108133094', 'prec': 103}, 'conductor': 1288, 'gens': [], 'heights': [], 'lmfdb_label': '1288.g1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0255723445318292620103423224', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0767170335954877860310269671714420836', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[-59, 0, 1]], 'xcoord_integral_points': [-59]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '7': [1, 0], '23': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '1288.g1'}
• ec_torsion_growth •

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

  
  
  • id: 63686
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '1288.g1', 'torsion': [2, 2]}
  • id: 63687
    {'degree': 4, 'field': [32, 0, 17, 0, 1], 'lmfdb_label': '1288.g1', 'torsion': [4]}
  • id: 63690
    {'degree': 8, 'field': [1, -2, 8, -12, 8, -12, 8, -2, 1], 'lmfdb_label': '1288.g1', 'torsion': [6]}
  • id: 63688
    {'degree': 8, 'field': [50, -20, -158, 32, 147, -36, 34, 0, 1], 'lmfdb_label': '1288.g1', 'torsion': [2, 4]}
  • id: 63689
    {'degree': 8, 'field': [226, 120, -92, -40, -19, 44, -10, -4, 1], 'lmfdb_label': '1288.g1', 'torsion': [2, 4]}
  • id: 63692
    {'degree': 16, 'field': [324, 0, 72, 0, -116, 0, -400, 0, 384, 0, -188, 0, 60, 0, -10, 0, 1], 'lmfdb_label': '1288.g1', 'torsion': [2, 6]}
  • id: 63691
    {'degree': 16, 'field': [20647936, 0, -20475904, 0, 47378576, 0, 7924224, 0, 1777258, 0, 118356, 0, 4011, 0, 34, 0, 1], 'lmfdb_label': '1288.g1', '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: 19162
    {'conductor': 1288, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '1288.g1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 19163
    {'conductor': 1288, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '1288.g1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 19164
    {'conductor': 1288, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1288.g1', 'prime': 23, '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: 1672629
    {'adelic_gens': [[1, 2, 2, 5], [2, 1, 643, 0], [1, 4, 0, 1], [1285, 4, 1284, 5], [1129, 162, 160, 1127], [281, 4, 562, 9], [1, 0, 4, 1], [185, 4, 370, 9], [3, 4, 8, 11]], 'adelic_image': '1288.12.0.?', 'conductor': 1288, 'lmfdb_label': '1288.g1', 'prime': 0}
  • id: 6134
    {'conductor': 1288, 'elladic_image': '8.6.0.6', 'lmfdb_label': '1288.g1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1288.g does not appear in ec_padic