Elliptic curve data - 52800.hs2

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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': '52800hf', 'Clabel': '52800hf2', 'Cnumber': 2, 'abc_quality': 1.0066941367119941, 'absD': 361304064000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1320, 'ainvs': [0, 1, 0, -18433, -308737], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 52800, 'degree': 196608, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4852340696603068984751656679', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 200, 'isogeny_degrees': [1, 2], 'jinv': [169112377, 88209], 'lmfdb_iso': '52800.hs', 'lmfdb_label': '52800.hs2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -11, 0], 'min_quad_twist_disc': -40, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0.a.1', '40.12.0-2.a.1.1', '44.12.0.b.1', '120.24.0.?', '132.24.0.?', '440.24.0.?', '1320.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 17600], [5, 14, 2112], [11, 12, 4800]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.35920565739666125295106218090', 'prec': 107}, 'szpiro_ratio': 3.7776663689210896, '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, 0, 0, 4, 0, 1, 0, 1, 0, -2, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 1, 0, 4, 1, -2, 2, 0, 8, 6, 8, 6, -2, 0, 8, 6, -4, -6, 4, 0, 14, 4, -12, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 52800, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '52800.hs', 'trace_hash': 1775233359522840667}
• 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': '0.051279298855871657371704796255', 'prec': 107}, 'conductor': 52800, 'gens': [], 'heights': [], 'lmfdb_label': '52800.hs2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.43396463758336653332901095247', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2075756510003983999481314296077568022', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-17, 0, 1], [143, 0, 1]], 'xcoord_integral_points': [-127, -17, 143]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '11': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '52800.hs2'}
• ec_torsion_growth •

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

  
  
  • id: 2558756
    {'degree': 4, 'field': [25, 0, -20, 0, 1], 'lmfdb_label': '52800.hs2', 'torsion': [2, 4]}
  • id: 2558754
    {'degree': 4, 'field': [59, -26, 27, -2, 1], 'lmfdb_label': '52800.hs2', 'torsion': [2, 4]}
  • id: 2558755
    {'degree': 4, 'field': [400, 0, 70, 0, 1], 'lmfdb_label': '52800.hs2', 'torsion': [2, 4]}
  • id: 2558757
    {'degree': 8, 'field': [-30000, 0, -19000, 0, -600, 0, 0, 0, 1], 'lmfdb_label': '52800.hs2', 'torsion': [2, 6]}
  • id: 2558761
    {'degree': 16, 'field': [1521, 0, -9000, 0, 17526, 0, -13908, 0, 5851, 0, -1564, 0, 282, 0, -28, 0, 1], 'lmfdb_label': '52800.hs2', 'torsion': [2, 8]}
  • id: 2558758
    {'degree': 16, 'field': [776161, 609652, 996892, -19256, 373763, -101024, 190704, -69128, 15248, 5324, -2994, 188, 23, 8, -2, -4, 1], 'lmfdb_label': '52800.hs2', 'torsion': [4, 4]}
  • id: 2558760
    {'degree': 16, 'field': [11723776, 0, -24946688, 0, 10177600, 0, 3884800, 0, 468928, 0, 26320, 0, 1600, 0, 64, 0, 1], 'lmfdb_label': '52800.hs2', 'torsion': [2, 8]}
  • id: 2558759
    {'degree': 16, 'field': [247779081, 0, 126811872, 0, 32135290, 0, 5361576, 0, 623483, 0, 48936, 0, 2450, 0, 72, 0, 1], 'lmfdb_label': '52800.hs2', '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: 1266716
    {'conductor': 52800, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '52800.hs2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1266717
    {'conductor': 52800, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '52800.hs2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 1266718
    {'conductor': 52800, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '52800.hs2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1266719
    {'conductor': 52800, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '52800.hs2', 'prime': 11, '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: 2015188
    {'adelic_gens': [[659, 0, 0, 1319], [789, 790, 970, 1189], [1, 4, 0, 1], [331, 530, 0, 1], [263, 0, 0, 1319], [779, 260, 1030, 519], [1317, 4, 1316, 5], [1, 0, 4, 1], [399, 260, 400, 259]], 'adelic_image': '1320.48.0.?', 'conductor': 52800, 'lmfdb_label': '52800.hs2', 'prime': 0}
  • id: 225961
    {'conductor': 52800, 'elladic_image': '2.6.0.1', 'lmfdb_label': '52800.hs2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 52800.hs does not appear in ec_padic