Elliptic curve data - 21294.q4

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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': '21294o', 'Clabel': '21294o2', 'Cnumber': 2, 'abc_quality': 0.9676277689392396, 'absD': 344836888578, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 6552, 'ainvs': [1, -1, 0, -16002, -774630], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 21294, 'degree': 34560, 'elladic_images': ['8.6.0.6', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1462695148197979799099034572', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [128787625, 98], 'lmfdb_iso': '21294.q', 'lmfdb_label': '21294.q4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -11, 12], 'min_quad_twist_disc': -39, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.b.1', '9.12.0.a.1', '18.36.0.a.1', '24.24.0.y.1', '28.6.0.c.1', '39.8.0-3.a.1.2', '56.12.0.k.1', '63.36.0.d.2', '72.72.1.?', '78.24.0.?', '84.24.0.?', '117.24.0.?', '126.108.2.?', '168.48.1.?', '234.72.0.?', '252.216.7.?', '312.48.0.?', '504.432.21.?', '819.72.0.?', '936.144.1.?', '1092.48.0.?', '1638.216.2.?', '2184.96.1.?', '3276.432.7.?', '6552.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1521], [3, 2, 2366], [7, 8, 3042], [13, 86, 126]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.68551130824502523381446288204', 'prec': 97}, 'szpiro_ratio': 4.0793004569244, '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, -1, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, 1, -6, 0, -2, 0], 'aplist': [-1, 0, 0, -1, 0, 0, -6, -2, 0, 6, 4, -2, 6, 8, -12, -6, -6, 8, 4, 0, -2, 8, -6, -6, 10], 'class_deg': 18, 'class_size': 6, 'conductor': 21294, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '21294.q', 'trace_hash': 2270009455668092353}
• 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': '0.10100966944546216101914826803', 'prec': 97}, 'conductor': 21294, 'gens': [], 'heights': [], 'lmfdb_label': '21294.q4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.42449693019034569325326868127', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '0.84899386038069138650653736254365013784', 'prec': 127}, 'tamagawa_product': 8, 'torsion_generators': [[-285, 285, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '7': [0, 0], '13': 'a'}, 'iwp0': 5, 'lmfdb_label': '21294.q4'}
• ec_torsion_growth •

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

  
  
  • id: 1082820
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '21294.q4', 'torsion': [2, 2]}
  • id: 1082821
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '21294.q4', 'torsion': [6]}
  • id: 1082823
    {'degree': 4, 'field': [142, -16, 17, -2, 1], 'lmfdb_label': '21294.q4', 'torsion': [2, 6]}
  • id: 1082822
    {'degree': 4, 'field': [3042, 0, 39, 0, 1], 'lmfdb_label': '21294.q4', 'torsion': [4]}
  • id: 1082824
    {'degree': 6, 'field': [-183, -93, 56, -5, 0, -1, 1], 'lmfdb_label': '21294.q4', 'torsion': [6]}
  • id: 1082825
    {'degree': 6, 'field': [1429, -81, 295, -17, 25, -1, 1], 'lmfdb_label': '21294.q4', 'torsion': [18]}
  • id: 1082828
    {'degree': 8, 'field': [12364, -3964, 4548, -1206, 699, -118, 44, -4, 1], 'lmfdb_label': '21294.q4', 'torsion': [12]}
  • id: 1082826
    {'degree': 8, 'field': [56644, 0, -4960, 0, -70, 0, -8, 0, 1], 'lmfdb_label': '21294.q4', 'torsion': [2, 4]}
  • id: 1082827
    {'degree': 8, 'field': [609961, 0, 21882, 0, 1730, 0, 42, 0, 1], 'lmfdb_label': '21294.q4', 'torsion': [2, 4]}
  • id: 1082831
    {'degree': 12, 'field': [-4759, 37326, -45813, 17710, -10560, 1686, -15, -366, -30, 70, -3, -6, 1], 'lmfdb_label': '21294.q4', 'torsion': [2, 6]}
  • id: 1082830
    {'degree': 12, 'field': [1252, 1168, -1968, -1194, 1840, 294, -679, 0, 153, -4, -19, 0, 1], 'lmfdb_label': '21294.q4', 'torsion': [18]}
  • id: 1082829
    {'degree': 12, 'field': [1296, 5184, 8568, 6624, -152, -1686, 1085, -573, 114, -33, 14, -3, 1], 'lmfdb_label': '21294.q4', 'torsion': [3, 6]}
  • id: 1082832
    {'degree': 12, 'field': [4495807, -476098, 1468591, -125512, 209715, -16158, 17923, -1282, 999, -64, 39, -2, 1], 'lmfdb_label': '21294.q4', 'torsion': [2, 18]}
  • id: 1082835
    {'degree': 16, 'field': [79100176, -58136704, 80007352, -48715864, 37491390, -17771500, 9458042, -3402832, 1339457, -360512, 108002, -21152, 4860, -644, 112, -8, 1], 'lmfdb_label': '21294.q4', 'torsion': [2, 12]}
  • id: 1082834
    {'degree': 16, 'field': [380141596, -188421120, 233074656, -95817872, 64826734, -22139584, 10577640, -3015728, 1112547, -263152, 77640, -14848, 3506, -504, 92, -8, 1], 'lmfdb_label': '21294.q4', 'torsion': [2, 12]}
  • id: 1082833
    {'degree': 16, 'field': [19169510116, 0, -3149126808, 0, 633705046, 0, -11927772, 0, -316023, 0, -41814, 0, 4384, 0, -114, 0, 1], 'lmfdb_label': '21294.q4', '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: 484430
    {'conductor': 21294, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21294.q4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 484431
    {'conductor': 21294, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21294.q4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 484432
    {'conductor': 21294, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21294.q4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 484433
    {'conductor': 21294, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21294.q4', 'prime': 13, 'reduction_type': 0, '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: 1806433
    {'adelic_gens': [[1, 36, 0, 1], [1639, 6084, 2782, 1873], [1, 0, 36, 1], [4564, 4563, 3081, 4330], [4535, 0, 0, 6551], [727, 468, 0, 6551], [313, 6084, 6474, 5305], [19, 36, 3240, 6139], [6517, 36, 6516, 37], [1, 18, 14, 253]], 'adelic_image': '6552.864.21.?', 'conductor': 21294, 'lmfdb_label': '21294.q4', 'prime': 0}
  • id: 98768
    {'conductor': 21294, 'elladic_image': '8.6.0.6', 'lmfdb_label': '21294.q4', 'modell_image': '2B', 'prime': 2}
  • id: 98769
    {'conductor': 21294, 'elladic_image': '9.12.0.1', 'lmfdb_label': '21294.q4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 21294.q does not appear in ec_padic