Elliptic curve data - 32.a1

Formats: - HTML - YAML - JSON - 2023-01-29T21:20:05.274805

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '32a', 'Clabel': '32a3', 'Cnumber': 3, 'absD': 512, 'ainvs': [0, 0, 0, -11, -14], 'analytic_rank': 0, 'bad_primes': [2], 'class_deg': 4, 'class_size': 4, 'cm': -16, 'conductor': 32, 'degree': 4, 'elladic_images': ['16.192.3.554'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.61738574535156420883504296185', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [287496, 1], 'lmfdb_iso': '32.a', 'lmfdb_label': '32.a1', 'lmfdb_number': 1, 'manin_constant': 2, 'min_quad_twist_ainvs': [0, 0, 0, -11, -14], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 1, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1372461307715231908979670529', 'prec': 103}, '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, 0, 0, -2, 0, 0, 0, -3, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, -2, 0, 0, 6, 2, 0, 0, -10, 0, -2, 10, 0, 0, 14, 0, -10, 0, 0, -6, 0, 0, 10, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 32, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '32.a', 'trace_hash': 1485208795141819780}
• 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': '3.4375929090101864137450478899', 'prec': 100}, 'conductor': 32, 'gens': [], 'heights': [], 'lmfdb_label': '32.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.6220575542921198104648395899', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.65551438857302995261620989747275764966', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [[-2, 0, 1]], 'xcoord_integral_points': [-2]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a'}, 'iwp0': 3, 'lmfdb_label': '32.a1'}
• ec_torsion_growth •

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

  
  
  • id: 850
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [2, 2]}
  • id: 851
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [4]}
  • id: 852
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [4]}
  • id: 854
    {'degree': 4, 'field': [-2, 0, 0, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [2, 4]}
  • id: 853
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [2, 4]}
  • id: 855
    {'degree': 4, 'field': [2, 0, -2, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [8]}
  • id: 859
    {'degree': 8, 'field': [-3, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [6]}
  • id: 856
    {'degree': 8, 'field': [1, 0, -4, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [4, 4]}
  • id: 857
    {'degree': 8, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [2, 8]}
  • id: 858
    {'degree': 8, 'field': [1, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [2, 8]}
  • id: 860
    {'degree': 8, 'field': [5, 0, 0, 0, -2, 0, 0, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [20]}
  • id: 864
    {'degree': 16, 'field': [1, -8, 26, -48, 80, -172, 328, -444, 451, -372, 256, -152, 80, -36, 14, -4, 1], 'lmfdb_label': '32.a1', 'torsion': [3, 12]}
  • id: 862
    {'degree': 16, 'field': [1, -8, 36, -104, 220, -368, 516, -624, 664, -624, 516, -368, 220, -104, 36, -8, 1], 'lmfdb_label': '32.a1', 'torsion': [4, 8]}
  • id: 867
    {'degree': 16, 'field': [1, -4, 4, 16, -62, 88, 0, -240, 532, -700, 660, -472, 262, -112, 36, -8, 1], 'lmfdb_label': '32.a1', 'torsion': [2, 20]}
  • id: 861
    {'degree': 16, 'field': [1, 0, -8, 0, 12, 0, 8, 0, -34, 0, 8, 0, 12, 0, -8, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [2, 8]}
  • id: 863
    {'degree': 16, 'field': [1, 0, -8, 0, 24, 0, -40, 0, 54, 0, -40, 0, 24, 0, -8, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [2, 16]}
  • id: 865
    {'degree': 16, 'field': [1, 0, 0, 0, 18, 0, 0, 0, -41, 0, 0, 0, 2, 0, 0, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [10]}
  • id: 869
    {'degree': 16, 'field': [1, 0, 4, 0, 12, 0, 20, 0, 6, 0, -20, 0, 12, 0, -4, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [40]}
  • id: 866
    {'degree': 16, 'field': [4, 0, -16, 0, 16, 0, 8, 0, -20, 0, -16, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [2, 6]}
  • id: 868
    {'degree': 16, 'field': [4, 0, 16, 0, 16, 0, -8, 0, -20, 0, 16, 0, 4, 0, 4, 0, 1], 'lmfdb_label': '32.a1', 'torsion': [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

  
  {'conductor': 32, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '32.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  {'conductor': 32, 'elladic_image': '16.192.3.554', 'lmfdb_label': '32.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 32.a does not appear in ec_padic