Elliptic curve data - 32448.p3

Formats: - HTML - YAML - JSON - 2025-11-04T19:54:25.129057

• 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': '32448r', 'Clabel': '32448r2', 'Cnumber': 2, 'abc_quality': 1.065463153454839, 'absD': 656602650091220631552, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 1560, 'ainvs': [0, -1, 0, -2287809, -503315775], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 32448, 'degree': 1198080, 'elladic_images': ['2.3.0.1', '5.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6874823467264054874807635744', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [476379541, 236196], 'lmfdb_iso': '32448.p', 'lmfdb_label': '32448.p3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -212, -466], 'min_quad_twist_disc': 104, 'modell_images': ['2B', '5B'], 'modm_images': ['2.3.0.a.1', '5.6.0.a.1', '10.36.0.b.2', '12.6.0.f.1', '26.6.0.b.1', '60.72.1.dy.2', '65.12.0.a.2', '130.72.1.?', '156.12.0.?', '520.144.1.?', '780.144.5.?', '1560.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 13], [3, 4, 10816], [5, 2, 10816], [13, 62, 192]], 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27595044220966502868520018896', 'prec': 107}, 'szpiro_ratio': 5.347146594402113, '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, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 6, 0], 'aplist': [0, -1, -2, 2, 0, 0, 2, 6, -4, 10, 10, 8, 10, 4, 12, 6, 4, -2, 2, 0, 4, 0, 4, 6, -12], 'class_deg': 10, 'class_size': 4, 'conductor': 32448, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '32448.p', 'trace_hash': 411386747379556043}
• 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': '0.0046310822381704152334703296447', 'prec': 110}, 'conductor': 32448, 'gens': [], 'heights': [], 'lmfdb_label': '32448.p3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.12918106535538045836082695441', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3252591763968482504948851794307054817', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-225, 0, 1]], 'xcoord_integral_points': [-225]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [0, 0], '13': 'a'}, 'iwp0': 7, 'lmfdb_label': '32448.p3'}
• ec_torsion_growth •

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

  
  
  • id: 1614721
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '32448.p3', 'torsion': [2, 2]}
  • id: 1614723
    {'degree': 4, 'field': [52, 0, 26, 0, 1], 'lmfdb_label': '32448.p3', 'torsion': [2, 10]}
  • id: 1614722
    {'degree': 4, 'field': [208, 0, 26, 0, 1], 'lmfdb_label': '32448.p3', 'torsion': [4]}
  • id: 1614726
    {'degree': 8, 'field': [-129792, 0, 23998, 0, -1248, 0, 0, 0, 1], 'lmfdb_label': '32448.p3', 'torsion': [6]}
  • id: 1614724
    {'degree': 8, 'field': [81, 0, -306, 0, 63, 0, 8, 0, 1], 'lmfdb_label': '32448.p3', 'torsion': [2, 4]}
  • id: 1614725
    {'degree': 8, 'field': [43264, 0, -5408, 0, 468, 0, -26, 0, 1], 'lmfdb_label': '32448.p3', 'torsion': [2, 4]}
  • id: 1614730
    {'degree': 16, 'field': [81, 0, 378, 0, 976, 0, 1092, 0, 786, 0, 312, 0, 81, 0, 12, 0, 1], 'lmfdb_label': '32448.p3', 'torsion': [2, 20]}
  • id: 1614727
    {'degree': 16, 'field': [1600, 0, -10176, 0, 14080, 0, 27144, 0, 16905, 0, 4524, 0, 586, 0, 36, 0, 1], 'lmfdb_label': '32448.p3', 'torsion': [8]}
  • id: 1614729
    {'degree': 16, 'field': [2313441, 0, -1028196, 0, 634933, 0, 79092, 0, 12168, 0, 1352, 0, 117, 0, 0, 0, 1], 'lmfdb_label': '32448.p3', 'torsion': [2, 20]}
  • id: 1614728
    {'degree': 16, 'field': [28065761, 115737056, 8313768, -231485580, 74873046, 47153316, -12527276, -2815436, 806979, -72164, 17812, -1812, 302, -28, 24, -8, 1], 'lmfdb_label': '32448.p3', 'torsion': [2, 6]}
  • id: 1614731
    {'degree': 20, 'field': [7425860, 0, -14851720, 0, 12452596, 0, -6397664, 0, 1827904, 0, -96668, 0, 2704, 0, -5746, 0, 936, 0, -52, 0, 1], 'lmfdb_label': '32448.p3', 'torsion': [10]}
• 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: 758694
    {'conductor': 32448, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '32448.p3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 758695
    {'conductor': 32448, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '32448.p3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 758696
    {'conductor': 32448, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '32448.p3', '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: 1880935
    {'adelic_gens': [[822, 1555, 905, 1478], [1541, 20, 1540, 21], [1549, 1544, 1020, 1129], [391, 20, 10, 201], [799, 1540, 800, 1539], [779, 0, 0, 1559], [11, 16, 1320, 1211], [521, 20, 530, 201], [471, 20, 760, 647], [1, 10, 10, 101], [1, 0, 20, 1], [1, 20, 0, 1]], 'adelic_image': '1560.288.5.?', 'conductor': 32448, 'lmfdb_label': '32448.p3', 'prime': 0}
  • id: 145099
    {'conductor': 32448, 'elladic_image': '2.3.0.1', 'lmfdb_label': '32448.p3', 'modell_image': '2B', 'prime': 2}
  • id: 145100
    {'conductor': 32448, 'elladic_image': '5.6.0.1', 'lmfdb_label': '32448.p3', 'modell_image': '5B', 'prime': 5}
• lmfdb_iso 32448.p does not appear in ec_padic