Elliptic curve data - 32448.ch4

Formats: - HTML - YAML - JSON - 2025-09-07T10:17:11.684510

• 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': '32448bh', 'Clabel': '32448bh2', 'Cnumber': 2, 'abc_quality': 0.972547111469975, 'absD': 711741947904, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 312, 'ainvs': [0, 1, 0, -2929, 44591], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 32448, 'degree': 36864, 'elladic_images': ['8.48.0.138'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.98369598293088375007634910468', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 59, 'isogeny_degrees': [1, 2, 4], 'jinv': [35152, 9], 'lmfdb_iso': '32448.ch', 'lmfdb_label': '32448.ch4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -4, 4], 'min_quad_twist_disc': 104, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.h.1', '12.24.0.c.1', '24.96.1.bu.1', '104.96.0.?', '312.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 169], [3, 4, 10816], [13, 86, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1074504064531541456038320911', 'prec': 103}, 'szpiro_ratio': 3.4234951682353643, '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, -2, 0, 0, 0, 1, 0, 4, 0, 0, 0, -2, 0, 2, 0, -4, 0], 'aplist': [0, 1, -2, 0, 4, 0, 2, -4, -8, -6, -8, 6, 6, -4, 0, 2, 4, 2, -4, -8, -10, -8, -4, 6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 32448, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '32448.ch', 'trace_hash': 1335695926380707286}
• 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': '0.13982103915120918771394205132', 'prec': 103}, 'conductor': 32448, 'gens': [], 'heights': [], 'lmfdb_label': '32448.ch4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.84585502830529694458434912361', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6917100566105938891686982472110276996', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[17, 0, 1], [43, 0, 1]], 'xcoord_integral_points': [-61, 17, 43]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '32448.ch4'}
• ec_torsion_growth •

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

  
  
  • id: 1615047
    {'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '32448.ch4', 'torsion': [2, 4]}
  • id: 1615049
    {'degree': 4, 'field': [169, 0, 52, 0, 1], 'lmfdb_label': '32448.ch4', 'torsion': [2, 4]}
  • id: 1615048
    {'degree': 4, 'field': [676, 0, -26, 0, 1], 'lmfdb_label': '32448.ch4', 'torsion': [2, 4]}
  • id: 1615054
    {'degree': 8, 'field': [-85683, 0, -21970, 0, -1014, 0, 0, 0, 1], 'lmfdb_label': '32448.ch4', 'torsion': [2, 6]}
  • id: 1615053
    {'degree': 8, 'field': [-23, 76, 16, -164, 33, 56, -14, -4, 1], 'lmfdb_label': '32448.ch4', 'torsion': [2, 8]}
  • id: 1615052
    {'degree': 8, 'field': [81, 0, 0, 0, 31, 0, 0, 0, 1], 'lmfdb_label': '32448.ch4', 'torsion': [2, 8]}
  • id: 1615051
    {'degree': 8, 'field': [12321, 2664, 3810, -960, 580, -76, 30, -4, 1], 'lmfdb_label': '32448.ch4', 'torsion': [2, 8]}
  • id: 1615050
    {'degree': 8, 'field': [28561, 0, 0, 0, -169, 0, 0, 0, 1], 'lmfdb_label': '32448.ch4', 'torsion': [4, 4]}
  • id: 1615055
    {'degree': 16, 'field': [6561, 0, -20412, 0, 19197, 0, -4032, 0, -704, 0, -238, 0, 129, 0, 14, 0, 1], 'lmfdb_label': '32448.ch4', 'torsion': [2, 8]}
  • id: 1615056
    {'degree': 16, 'field': [6561, 0, 0, 0, -2511, 0, 0, 0, 880, 0, 0, 0, -31, 0, 0, 0, 1], 'lmfdb_label': '32448.ch4', 'torsion': [4, 8]}
  • id: 1615057
    {'degree': 16, 'field': [14164081, -49898336, 123132414, -42601336, 43322058, -7921596, 6185722, -682840, 570243, -51056, 38002, -2640, 1704, -116, 60, -4, 1], 'lmfdb_label': '32448.ch4', 'torsion': [4, 8]}
  • id: 1615058
    {'degree': 16, 'field': [42512831, -333916988, 804536596, -606899692, 231308648, -37576644, -5932472, 4479212, -978370, 151100, -31746, 8708, -1408, 216, -22, -8, 1], 'lmfdb_label': '32448.ch4', 'torsion': [2, 12]}
• 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: 758802
    {'conductor': 32448, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '32448.ch4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 758803
    {'conductor': 32448, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '32448.ch4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 758804
    {'conductor': 32448, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '32448.ch4', 'prime': 13, '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: 1880836
    {'adelic_gens': [[287, 26, 78, 235], [1, 0, 8, 1], [5, 4, 308, 309], [1, 8, 0, 1], [103, 0, 104, 259], [305, 8, 304, 9], [53, 104, 286, 27], [167, 0, 0, 311]], 'adelic_image': '312.192.1.?', 'conductor': 32448, 'lmfdb_label': '32448.ch4', 'prime': 0}
  • id: 144990
    {'conductor': 32448, 'elladic_image': '8.48.0.138', 'lmfdb_label': '32448.ch4', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 32448.ch does not appear in ec_padic