Elliptic curve data - 264264.i4

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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': '264264i4', 'Cnumber': 4, 'abc_quality': 0.991751601068022, 'absD': 1957774782674034035712, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 48048, 'ainvs': [0, -1, 0, -4567064, -3093753540], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 264264, 'degree': 11796480, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8036627728478178894221727892', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [5807363790481348, 1079211743883], 'lmfdb_iso': '264264.i', 'lmfdb_label': '264264.i4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -37744, 2338108], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '12.12.0.h.1', '24.24.0.bl.1', '44.12.0-4.c.1.2', '56.24.0.bu.1', '88.24.0.?', '132.24.0.?', '168.48.0.?', '208.24.0.?', '264.48.0.?', '616.48.0.?', '624.48.0.?', '1456.48.0.?', '1848.96.0.?', '2288.48.0.?', '4368.96.1.?', '6864.96.0.?', '16016.96.0.?', '48048.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 363], [3, 4, 88088], [7, 8, 37752], [11, 62, 2184], [13, 14, 20328]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0270924859820115262101742323', 'prec': 100}, 'szpiro_ratio': 4.6149870362208825, '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, -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': '0.0036708738253896931858278693145', 'prec': 110}, 'conductor': 264264, 'gens': [], 'heights': [], 'lmfdb_label': '264264.i4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10459975489093723430036062139', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.83679803912749787440288497108475593006', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-1635, 0, 1]], 'xcoord_integral_points': [-1635]}
• lmfdb_label 264264.i4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11315562
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '264264.i4', 'torsion': [2, 2]}
  • id: 11315564
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '264264.i4', 'torsion': [4]}
  • id: 11315563
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '264264.i4', 'torsion': [4]}
  • id: 11315565
    {'degree': 4, 'field': [33, 0, 1, -2, 1], 'lmfdb_label': '264264.i4', 'torsion': [2, 4]}
  • id: 11315566
    {'degree': 4, 'field': [275, 22, -21, -2, 1], 'lmfdb_label': '264264.i4', 'torsion': [8]}
  • id: 11315567
    {'degree': 4, 'field': [1983, 78, -77, -2, 1], 'lmfdb_label': '264264.i4', 'torsion': [8]}
  • id: 11315568
    {'degree': 8, 'field': [526, 1312, -1348, 82, -65, 26, -4, -4, 1], 'lmfdb_label': '264264.i4', 'torsion': [2, 4]}
  • id: 11315569
    {'degree': 8, 'field': [5625, 0, -2700, 0, 507, 0, -36, 0, 1], 'lmfdb_label': '264264.i4', 'torsion': [8]}
  • id: 11315570
    {'degree': 8, 'field': [18001, -836, 1576, -1436, 609, 128, -38, -4, 1], 'lmfdb_label': '264264.i4', 'torsion': [2, 8]}
  • id: 11315571
    {'degree': 8, 'field': [38097, 159408, 58068, 2916, -774, -420, -12, 0, 1], 'lmfdb_label': '264264.i4', 'torsion': [6]}
  • id: 11315573
    {'degree': 16, 'field': [8244, -6120, 26820, -49464, 49782, -45240, 45102, -36012, 23809, -13112, 6226, -2444, 832, -224, 52, -8, 1], 'lmfdb_label': '264264.i4', 'torsion': [2, 8]}
  • id: 11315572
    {'degree': 16, 'field': [276676, -1281336, 1397328, 2689344, 1061446, -253932, 89028, -34482, -10209, 1386, 3096, -714, 169, 0, -12, 0, 1], 'lmfdb_label': '264264.i4', 'torsion': [4, 4]}
  • id: 11315578
    {'degree': 16, 'field': [5863401, -4833432, 4323492, 881856, -55566, -574776, 377712, -158568, 41371, -5912, 6304, -3272, 970, -224, 52, -8, 1], 'lmfdb_label': '264264.i4', 'torsion': [12]}
  • id: 11315576
    {'degree': 16, 'field': [3345587268, 5062474944, 3737172616, 1788980096, 635210188, 227706616, 83294072, 28248784, 7270356, 1545312, 293808, 43528, 3128, -500, -140, -4, 1], 'lmfdb_label': '264264.i4', 'torsion': [2, 6]}
  • id: 11315577
    {'degree': 16, 'field': [4202539929, 0, -2287096560, 0, 992631024, 0, 31116960, 0, 876366, 0, -59760, 0, -612, 0, 0, 0, 1], 'lmfdb_label': '264264.i4', 'torsion': [12]}
  • id: 11315574
    {'degree': 16, 'field': [109652135553, 2594759976, 5502604488, -16556721720, 9188371612, -1105965896, 391534752, -18882384, 3860389, 495144, -21140, -41944, 6566, 168, -4, -8, 1], 'lmfdb_label': '264264.i4', 'torsion': [16]}
  • id: 11315575
    {'degree': 16, 'field': [22624082184825, 4011015385080, -3668071622688, -669016960920, 292840709616, 48586219416, -13864054176, -1944277296, 419188057, 43580872, -7716380, -536648, 82222, 3304, -452, -8, 1], 'lmfdb_label': '264264.i4', 'torsion': [16]}
• 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: 6549365
    {'conductor': 264264, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '264264.i4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6549366
    {'conductor': 264264, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '264264.i4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6549367
    {'conductor': 264264, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '264264.i4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6549368
    {'conductor': 264264, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '264264.i4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6549369
    {'conductor': 264264, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '264264.i4', '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: 3336803
    {'adelic_gens': [[33496, 43681, 23375, 8746], [1, 16, 0, 1], [24586, 29491, 45551, 15390], [16237, 26224, 47168, 34629], [1, 0, 16, 1], [15, 2, 47950, 48035], [5, 4, 48044, 48045], [43679, 0, 0, 48047], [48033, 16, 48032, 17], [43693, 26224, 36300, 14521], [36961, 26224, 20504, 17601]], 'adelic_image': '48048.192.1.?', 'conductor': 264264, 'lmfdb_label': '264264.i4', 'prime': 0}
  • id: 947363
    {'conductor': 264264, 'elladic_image': '8.12.0.5', 'lmfdb_label': '264264.i4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 264264.i does not appear in ec_padic