Elliptic curve data - 32448.db2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '32448bf', 'Clabel': '32448bf3', 'Cnumber': 3, 'abc_quality': 1.0784914154165677, 'absD': 917674080123940522426368, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 1, 0, -25304257, -16625231713], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 32448, 'degree': 5160960, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2902731018882273134260354973', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 79, 'isogeny_degrees': [1, 2, 4], 'jinv': [1416134368422073, 725251155408], 'lmfdb_iso': '32448.db', 'lmfdb_label': '32448.db2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -2339, -15747], 'min_quad_twist_disc': 104, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '24.24.0-24.ba.1.11', '26.6.0.b.1', '52.12.0.g.1', '104.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.96807765231754098127344359433', 'prec': 103}, 'szpiro_ratio': 6.041270038297213, '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, -4, 0, 1, 0, -4, 0, 0, 0, 2, 0, 2, 0, -8, 0], 'aplist': [0, 1, 2, -4, -4, 0, 2, -8, 0, -6, 4, -2, 10, -4, -8, 10, 4, 2, -16, 8, -2, 8, 12, -14, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 32448, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '32448.db', 'trace_hash': 2166090719640041796}
• 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': '0.0013870914532967360954741366738', 'prec': 110}, 'conductor': 32448, 'gens': [], 'heights': [], 'lmfdb_label': '32448.db2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.071113472026831450236001472215', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4222694405366290047200294442938786372', 'prec': 130}, 'tamagawa_product': 80, 'torsion_generators': [[-4663, 0, 1]], 'xcoord_integral_points': [-4663]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [9, 0], '5': [2, 0], '13': 'a'}, 'iwp0': 7, 'lmfdb_label': '32448.db2'}
• ec_torsion_growth •

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

  
  
  • id: 1614952
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '32448.db2', 'torsion': [2, 2]}
  • id: 1614953
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '32448.db2', 'torsion': [4]}
  • id: 1614954
    {'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '32448.db2', 'torsion': [4]}
  • id: 1614955
    {'degree': 4, 'field': [27, 2, -1, -2, 1], 'lmfdb_label': '32448.db2', 'torsion': [2, 4]}
  • id: 1614959
    {'degree': 8, 'field': [-8112, 0, 4160, 0, -312, 0, 0, 0, 1], 'lmfdb_label': '32448.db2', 'torsion': [6]}
  • id: 1614956
    {'degree': 8, 'field': [9, 0, -20, 0, -5, 0, -2, 0, 1], 'lmfdb_label': '32448.db2', 'torsion': [2, 4]}
  • id: 1614957
    {'degree': 8, 'field': [144, 0, 240, 0, 241, 0, -32, 0, 1], 'lmfdb_label': '32448.db2', 'torsion': [8]}
  • id: 1614958
    {'degree': 8, 'field': [888, 432, 136, -64, 80, 8, -4, -4, 1], 'lmfdb_label': '32448.db2', 'torsion': [8]}
  • id: 1614962
    {'degree': 16, 'field': [81, 108, 198, -504, 138, -252, 634, -428, 423, -856, 950, -612, 284, -112, 36, -8, 1], 'lmfdb_label': '32448.db2', 'torsion': [2, 8]}
  • id: 1614960
    {'degree': 16, 'field': [289, -1564, 4232, -4676, 2694, -440, 760, -1372, 1255, -584, 232, -172, 126, -76, 32, -8, 1], 'lmfdb_label': '32448.db2', 'torsion': [4, 4]}
  • id: 1614964
    {'degree': 16, 'field': [4761, 0, -2448, 0, 3924, 0, -1204, 0, -358, 0, 176, 0, -32, 0, 4, 0, 1], 'lmfdb_label': '32448.db2', 'torsion': [12]}
  • id: 1614963
    {'degree': 16, 'field': [11664, 0, -140184, 0, -231084, 0, 1512, 0, 21228, 0, 1796, 0, -204, 0, 0, 0, 1], 'lmfdb_label': '32448.db2', 'torsion': [2, 6]}
  • id: 1614965
    {'degree': 16, 'field': [257049, 0, 8858304, 0, 3692988, 0, 891644, 0, 142298, 0, 16016, 0, 1144, 0, 52, 0, 1], 'lmfdb_label': '32448.db2', 'torsion': [12]}
  • id: 1614961
    {'degree': 16, 'field': [810000, 0, 75600, 0, -26244, 0, -11292, 0, -203, 0, 128, 0, 27, 0, 8, 0, 1], 'lmfdb_label': '32448.db2', '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: 758781
    {'conductor': 32448, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '32448.db2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 758782
    {'conductor': 32448, 'conductor_valuation': 1, 'discriminant_valuation': 20, 'j_denominator_valuation': 20, 'kodaira_symbol': 24, 'lmfdb_label': '32448.db2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 20}
  • id: 758783
    {'conductor': 32448, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '32448.db2', '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: 1880879
    {'adelic_gens': [[7, 6, 306, 307], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [88, 309, 211, 310], [203, 196, 242, 45], [269, 270, 182, 29], [305, 8, 304, 9], [209, 8, 212, 33]], 'adelic_image': '312.48.0.?', 'conductor': 32448, 'lmfdb_label': '32448.db2', 'prime': 0}
  • id: 145038
    {'conductor': 32448, 'elladic_image': '8.12.0.7', 'lmfdb_label': '32448.db2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 32448.db does not appear in ec_padic