Elliptic curve data - 281775.k3

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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': '281775k', 'Clabel': '281775k2', 'Cnumber': 2, 'abc_quality': 0.9140273049268122, 'absD': 573644413265625, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 13260, 'ainvs': [1, 1, 1, -32663, -1971844], 'analytic_rank': 1, 'bad_primes': [3, 5, 13, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 281775, 'degree': 1310720, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5563855758367981197677538977', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [10218313, 1521], 'lmfdb_iso': '281775.k', 'lmfdb_label': '281775.k3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -4, -5], 'min_quad_twist_disc': 85, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0.a.1', '52.12.0.b.1', '156.24.0.?', '340.12.0.?', '1020.24.0.?', '4420.24.0.?', '13260.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 12, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5277203619867715226813943219', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 7225], [3, 4, 93925], [5, 14, 11271], [13, 14, 21675], [17, 146, 975]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.66494005240836010765739307785', 'prec': 107}, 'szpiro_ratio': 3.4103165877761406, '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, -1, -1, -1, 0, 1, -4, 3, 1, 0, -4, 1, -1, 4, 0, -1, 0, -1, 0, 0], 'aplist': [-1, -1, 0, -4, -4, -1, 0, 0, 0, 10, -4, -2, -6, 12, 0, -6, 12, 2, 8, 0, 2, -8, -4, -2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 281775, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '281775.k', 'trace_hash': 1511454774139716004}
• 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': '0.044477530421808570408378339747', 'prec': 107}, 'conductor': 281775, 'gens': [[-84, 475, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5277203619867715226813943219', 'prec': 100}], 'lmfdb_label': '281775.k3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.35866754783939681637218607248', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1917748640724439865930010224125460821', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-135, 67, 1], [205, -103, 1]], 'xcoord_integral_points': [-135, -120, -84, 205, 290, 349, 1310]}
• lmfdb_label 281775.k3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11993762
    {'degree': 4, 'field': [324, 0, -49, 0, 1], 'lmfdb_label': '281775.k3', 'torsion': [2, 4]}
  • id: 11993764
    {'degree': 4, 'field': [484, 0, 41, 0, 1], 'lmfdb_label': '281775.k3', 'torsion': [2, 4]}
  • id: 11993763
    {'degree': 4, 'field': [69970, 490, -489, -2, 1], 'lmfdb_label': '281775.k3', 'torsion': [2, 4]}
  • id: 11993765
    {'degree': 8, 'field': [-609231, -43641, -82481, 6534, -1545, -177, -9, 0, 1], 'lmfdb_label': '281775.k3', 'torsion': [2, 6]}
  • id: 11993767
    {'degree': 16, 'field': [23338499024, 11424420976, -9233998184, -4154133384, 1524450760, 624030776, -144473846, -51212732, 8836647, 2502208, -360790, -73012, 9560, 1176, -148, -8, 1], 'lmfdb_label': '281775.k3', 'torsion': [2, 8]}
  • id: 11993769
    {'degree': 16, 'field': [75926716261, 4116660936, 23357409414, 839130792, 3216469036, 66903612, 261293526, 2491752, 13783005, 33108, 485826, -408, 11224, -12, 156, 0, 1], 'lmfdb_label': '281775.k3', 'torsion': [2, 8]}
  • id: 11993766
    {'degree': 16, 'field': [80453918736, 0, 22824103500, 0, 3100215433, 0, 252793464, 0, 13548504, 0, 484106, 0, 11256, 0, 156, 0, 1], 'lmfdb_label': '281775.k3', 'torsion': [4, 4]}
  • id: 11993768
    {'degree': 16, 'field': [3723236370497536, -145455569485824, 249095256655872, -1470708974592, 7467376433536, 70378149504, 139205773152, 1696878144, 1710820722, 16504020, 14337738, 42432, 85867, -156, 354, 0, 1], 'lmfdb_label': '281775.k3', '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: 6979797
    {'conductor': 281775, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '281775.k3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6979798
    {'conductor': 281775, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '281775.k3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6979799
    {'conductor': 281775, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '281775.k3', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6979800
    {'conductor': 281775, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '281775.k3', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 3441614
    {'adelic_gens': [[11221, 11390, 0, 1], [13257, 4, 13256, 5], [6631, 9520, 11390, 5781], [1, 4, 0, 1], [5303, 0, 0, 13259], [4421, 9520, 6970, 5781], [1, 0, 4, 1], [779, 0, 0, 13259]], 'adelic_image': '13260.48.0.?', 'conductor': 281775, 'lmfdb_label': '281775.k3', 'prime': 0}
  • id: 1001920
    {'conductor': 281775, 'elladic_image': '2.6.0.1', 'lmfdb_label': '281775.k3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 281775.k does not appear in ec_padic