Elliptic curve data - 36.a3

Formats: - HTML - YAML - JSON - 2025-10-04T01:50:23.892339

• 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': '36a', 'Clabel': '36a3', 'Cnumber': 3, 'absD': 314928, 'ainvs': [0, 0, 0, 0, -27], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 6, 'class_size': 4, 'cm': -3, 'conductor': 36, 'degree': 3, 'elladic_images': ['16.192.9.83', '27.648.18.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.26610915174030720997102456101', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [0, 1], 'lmfdb_iso': '36.a', 'lmfdb_label': '36.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 0, 1], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '3B.1.2'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 2, 4]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 5.613147192765458, '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, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0], 'aplist': [0, 0, 0, -4, 0, 2, 0, 8, 0, 0, -4, -10, 0, 8, 0, 0, 0, 14, -16, 0, -10, -4, 0, 0, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 36, 'isogeny_matrix': [[1, 3, 2, 6], [3, 1, 6, 2], [2, 6, 1, 3], [6, 2, 3, 1]], 'lmfdb_iso': '36.a', 'trace_hash': 1143229866697692889}
• 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': '1.7027052392775188450407315019', 'prec': 100}, 'conductor': 36, 'gens': [], 'heights': [], 'lmfdb_label': '36.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.4021821053254542611750190790', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.70109105266272713058750953952426833642', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[3, 0, 1]], 'xcoord_integral_points': [3]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a'}, 'iwp0': 5, 'lmfdb_label': '36.a3'}
• ec_torsion_growth •

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

  
  
  • id: 1040
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '36.a3', 'torsion': [2, 6]}
  • id: 1041
    {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '36.a3', 'torsion': [6]}
  • id: 1042
    {'degree': 4, 'field': [1, -2, 0, -2, 1], 'lmfdb_label': '36.a3', 'torsion': [4]}
  • id: 1043
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '36.a3', 'torsion': [6, 6]}
  • id: 1044
    {'degree': 8, 'field': [1, -4, 8, -10, 7, -2, 2, -2, 1], 'lmfdb_label': '36.a3', 'torsion': [4, 12]}
  • id: 1046
    {'degree': 12, 'field': [-2, 0, 12, 4, -18, -12, 0, 12, 12, -2, -6, 0, 1], 'lmfdb_label': '36.a3', 'torsion': [12]}
  • id: 1045
    {'degree': 12, 'field': [1, 1, -5, 3, 7, -14, 15, -14, 13, -11, 8, -4, 1], 'lmfdb_label': '36.a3', 'torsion': [2, 42]}
  • id: 1047
    {'degree': 16, 'field': [1, -8, 28, -52, 38, 52, -196, 320, -368, 320, -196, 52, 38, -52, 28, -8, 1], 'lmfdb_label': '36.a3', 'torsion': [8]}
  • id: 1048
    {'degree': 18, 'field': [3, 0, -9, 0, 18, -9, -6, 0, 0, 27, -63, 72, -21, -63, 105, -81, 36, -9, 1], 'lmfdb_label': '36.a3', 'torsion': [6, 18]}
• 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: 138
    {'conductor': 36, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '36.a3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 139
    {'conductor': 36, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '36.a3', 'prime': 3, '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: 1665630
    {'conductor': 36, 'elladic_image': '16.192.9.83', 'lmfdb_label': '36.a3', 'modell_image': '2B', 'prime': 2}
  • id: 1665631
    {'conductor': 36, 'elladic_image': '27.648.18.4', 'lmfdb_label': '36.a3', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 36.a does not appear in ec_padic