Elliptic curve data - 32448.bt2

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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': '32448u', 'Clabel': '32448u1', 'Cnumber': 1, 'abc_quality': 1.0396667971967286, 'absD': 14760465408, 'adelic_genus': 5, 'adelic_index': 192, 'adelic_level': 624, 'ainvs': [0, -1, 0, -1421, 20253], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 32448, 'degree': 36864, 'elladic_images': ['8.24.0.119'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.71250167343537276156108412422', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 45, 'isogeny_degrees': [1, 2], 'jinv': [141150208, 6561], 'lmfdb_iso': '32448.bt', 'lmfdb_label': '32448.bt2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -355, 2354], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.d.1', '8.24.0.bl.1', '26.6.0.b.1', '48.48.1.hj.1', '52.12.0.i.1', '104.96.1.?', '624.192.5.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 13], [3, 4, 10816], [13, 50, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.50635831639663251363331450405', 'prec': 107}, 'szpiro_ratio': 3.2146325425550755, '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, 4, 0, -2, 0, 1, 0, -2, 0, 0, 0, -4, 0, 6, 0, 2, 0], 'aplist': [0, -1, 4, -2, -2, 0, 6, 2, -8, -6, 10, 4, 0, -4, -2, 10, 14, 2, 2, -6, -8, 0, -6, 0, 0], 'class_deg': 2, 'class_size': 2, 'conductor': 32448, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '32448.bt', 'trace_hash': 1367071642356757835}
• 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': '0.24050765825894960504031438151', 'prec': 103}, 'conductor': 32448, 'gens': [], 'heights': [], 'lmfdb_label': '32448.bt2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2337148904670627738031496648', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4674297809341255476062993295927861061', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-43, 0, 1]], 'xcoord_integral_points': [-43]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '32448.bt2'}
• ec_torsion_growth •

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

  
  
  • id: 1614782
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '32448.bt2', 'torsion': [2, 2]}
  • id: 1614783
    {'degree': 4, 'field': [52, 0, 26, 0, 1], 'lmfdb_label': '32448.bt2', 'torsion': [2, 4]}
  • id: 1614786
    {'degree': 8, 'field': [-507, 0, -338, 0, -78, 0, 0, 0, 1], 'lmfdb_label': '32448.bt2', 'torsion': [6]}
  • id: 1614784
    {'degree': 8, 'field': [169, 0, -1352, 0, 299, 0, -26, 0, 1], 'lmfdb_label': '32448.bt2', 'torsion': [2, 4]}
  • id: 1614785
    {'degree': 8, 'field': [169, 0, 1352, 0, 299, 0, 26, 0, 1], 'lmfdb_label': '32448.bt2', 'torsion': [2, 8]}
  • id: 1614787
    {'degree': 16, 'field': [2401, 1372, 4116, 560, 6528, 13732, 13680, 10136, 3154, 668, -132, -224, 72, -28, 24, -8, 1], 'lmfdb_label': '32448.bt2', 'torsion': [4, 8]}
  • id: 1614788
    {'degree': 16, 'field': [34596, 0, -350664, 0, -198260, 0, -89784, 0, -30912, 0, -5172, 0, -420, 0, -24, 0, 1], 'lmfdb_label': '32448.bt2', 'torsion': [2, 6]}
• 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: 758715
    {'conductor': 32448, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '32448.bt2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 758716
    {'conductor': 32448, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '32448.bt2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 758717
    {'conductor': 32448, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '32448.bt2', '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: 1880804
    {'adelic_gens': [[1, 16, 0, 1], [1, 8, 8, 65], [609, 16, 608, 17], [3, 2, 610, 615], [209, 16, 424, 129], [399, 326, 304, 577], [1, 0, 16, 1], [536, 9, 391, 8], [623, 608, 156, 155]], 'adelic_image': '624.192.5.?', 'conductor': 32448, 'lmfdb_label': '32448.bt2', 'prime': 0}
  • id: 144955
    {'conductor': 32448, 'elladic_image': '8.24.0.119', 'lmfdb_label': '32448.bt2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 32448.bt does not appear in ec_padic