Elliptic curve data - 264264.i5

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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': '264264i', 'Clabel': '264264i2', 'Cnumber': 2, 'abc_quality': 0.9686459833518319, 'absD': 22671965595372597504, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 24024, 'ainvs': [0, -1, 0, -1365404, 570226164], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 264264, 'degree': 5898240, 'elladic_images': ['4.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4570891825678452347135567285', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2, 4], 'jinv': [620742479063632, 49991146569], 'lmfdb_iso': '264264.i', 'lmfdb_label': '264264.i5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -11284, -424316], 'min_quad_twist_disc': -11, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '12.24.0.c.1', '44.24.0-4.b.1.3', '56.24.0.h.1', '104.24.0.?', '132.48.0.?', '168.48.0.?', '312.48.0.?', '616.48.0.?', '728.48.0.?', '1144.48.0.?', '1848.96.0.?', '2184.96.1.?', '3432.96.0.?', '8008.96.0.?', '24024.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 121], [3, 4, 88088], [7, 8, 37752], [11, 62, 2184], [13, 14, 20328]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.79604342579536308973776352521', 'prec': 103}, 'szpiro_ratio': 4.3248511950274, '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, -1, 0, 1, 0, 0, 0, -1, 0, 2, 0, 6, 0, -4, 0], 'aplist': [0, -1, -2, -1, 0, -1, 6, -4, 0, -6, 0, 6, 6, -4, 0, -2, 4, 2, 4, 0, 6, -8, -12, 10, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 264264, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '264264.i', 'trace_hash': 1332565441725466988}
• 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': '0.0073417476507793863716557386289', 'prec': 110}, 'conductor': 264264, 'gens': [], 'heights': [], 'lmfdb_label': '264264.i5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20919950978187446860072124277', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.83679803912749787440288497108475593006', 'prec': 133}, 'tamagawa_product': 64, 'torsion_generators': [[521, 0, 1], [818, 0, 1]], 'xcoord_integral_points': [-1338, 521, 818]}
• lmfdb_label 264264.i5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11315542
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '264264.i5', 'torsion': [2, 4]}
  • id: 11315543
    {'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '264264.i5', 'torsion': [2, 4]}
  • id: 11315544
    {'degree': 4, 'field': [121, 0, 11, 0, 1], 'lmfdb_label': '264264.i5', 'torsion': [2, 4]}
  • id: 11315545
    {'degree': 8, 'field': [81, 0, 45, 0, 16, 0, 5, 0, 1], 'lmfdb_label': '264264.i5', 'torsion': [4, 4]}
  • id: 11315548
    {'degree': 8, 'field': [38097, 159408, 58068, 2916, -774, -420, -12, 0, 1], 'lmfdb_label': '264264.i5', 'torsion': [2, 6]}
  • id: 11315547
    {'degree': 8, 'field': [544041, 26088, -24586, -3012, 1527, -28, 14, -4, 1], 'lmfdb_label': '264264.i5', 'torsion': [2, 8]}
  • id: 11315546
    {'degree': 8, 'field': [2313217, 236884, -222620, -28316, 13629, 632, -206, -4, 1], 'lmfdb_label': '264264.i5', 'torsion': [2, 8]}
  • id: 11315549
    {'degree': 16, 'field': [1369, -13468, -3684, 13876, 2958, 25368, -7856, -4220, -12537, 7040, 3160, -2124, -126, 212, -12, -8, 1], 'lmfdb_label': '264264.i5', 'torsion': [2, 8]}
  • id: 11315550
    {'degree': 16, 'field': [24649, 0, 595888, 0, 11224708, 0, -3616880, 0, 504862, 0, 95824, 0, 4948, 0, 112, 0, 1], 'lmfdb_label': '264264.i5', 'torsion': [2, 8]}
  • id: 11315551
    {'degree': 16, 'field': [5863401, -4833432, 4323492, 881856, -55566, -574776, 377712, -158568, 41371, -5912, 6304, -3272, 970, -224, 52, -8, 1], 'lmfdb_label': '264264.i5', 'torsion': [2, 12]}
• 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: 6549355
    {'conductor': 264264, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '264264.i5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6549356
    {'conductor': 264264, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '264264.i5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6549357
    {'conductor': 264264, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '264264.i5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6549358
    {'conductor': 264264, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '264264.i5', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6549359
    {'conductor': 264264, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '264264.i5', 'prime': 13, '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: 3336804
    {'adelic_gens': [[1, 0, 8, 1], [3433, 6556, 0, 1], [1, 8, 0, 1], [15291, 12562, 13112, 22397], [18569, 9284, 9284, 12013], [12937, 13112, 10252, 4401], [5831, 15290, 6534, 2179], [19655, 0, 0, 24023], [24017, 8, 24016, 9], [5, 4, 24020, 24021]], 'adelic_image': '24024.192.1.?', 'conductor': 264264, 'lmfdb_label': '264264.i5', 'prime': 0}
  • id: 947364
    {'conductor': 264264, 'elladic_image': '4.12.0.3', 'lmfdb_label': '264264.i5', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 264264.i does not appear in ec_padic