Elliptic curve data - 38.a1

Formats: - HTML - YAML - JSON - 2023-12-06T11:26:32.158127

• 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': '38a', 'Clabel': '38a2', 'Cnumber': 2, 'absD': 2550136832, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 4104, 'ainvs': [1, 0, 1, -86, -2456], 'analytic_rank': 0, 'bad_primes': [2, 19], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 38, 'degree': 18, 'elladic_images': ['27.72.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.48516961095724358095196192008', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9], 'jinv': [-69173457625, 2550136832], 'lmfdb_iso': '38.a', 'lmfdb_label': '38.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -86, -2456], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.2'], 'modm_images': ['3.8.0-3.a.1.1', '9.24.0-9.a.1.1', '27.72.0-27.a.1.1', '152.2.0.?', '171.72.0.?', '456.16.0.?', '513.648.16.?', '1368.144.3.?', '4104.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.48516961095724358095196192008', 'prec': 103}, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 1, 1, 0, -1, -1, -1, -2, 0, -6, 1, 5, 1, 0, 1, 3, 2, 1, 0], 'aplist': [-1, 1, 0, -1, -6, 5, 3, 1, 3, 9, -4, 2, 0, 8, 0, -3, 9, -10, 5, -6, -7, -10, -6, -12, -10], 'class_deg': 9, 'class_size': 3, 'conductor': 38, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '38.a', 'trace_hash': 1328635374754788503}
• 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': '0.37895446663782603310385731998', 'prec': 103}, 'conductor': 38, 'gens': [], 'heights': [], 'lmfdb_label': '38.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.63021074331409951207066938986', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.63021074331409951207066938986320807142', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [0, 2], '19': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '38.a1'}
• ec_torsion_growth •

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

  
  
  • id: 1115
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '38.a1', 'torsion': [3]}
  • id: 1117
    {'degree': 3, 'field': [-12, -6, -1, 1], 'lmfdb_label': '38.a1', 'torsion': [3]}
  • id: 1116
    {'degree': 3, 'field': [-2, -2, -1, 1], 'lmfdb_label': '38.a1', 'torsion': [2]}
  • id: 1122
    {'degree': 6, 'field': [4, 4, 2, 6, 3, -1, 1], 'lmfdb_label': '38.a1', 'torsion': [6]}
  • id: 1119
    {'degree': 6, 'field': [12, 6, -5, -3, 4, -3, 1], 'lmfdb_label': '38.a1', 'torsion': [3, 3]}
  • id: 1118
    {'degree': 6, 'field': [16, 16, 34, 4, 5, -2, 1], 'lmfdb_label': '38.a1', 'torsion': [2, 2]}
  • id: 1121
    {'degree': 6, 'field': [19, 0, 0, -8, 0, 0, 1], 'lmfdb_label': '38.a1', 'torsion': [9]}
  • id: 1120
    {'degree': 6, 'field': [6859, 0, 0, -152, 0, 0, 1], 'lmfdb_label': '38.a1', 'torsion': [9]}
  • id: 1123
    {'degree': 9, 'field': [-8, -16, -102, -126, -121, -27, -17, 7, -1, 1], 'lmfdb_label': '38.a1', 'torsion': [6]}
  • id: 1124
    {'degree': 12, 'field': [-2, 10, -25, -4, -15, 50, -137, 0, -25, -10, 5, 0, 1], 'lmfdb_label': '38.a1', 'torsion': [4]}
  • id: 1125
    {'degree': 12, 'field': [100, 240, -38, -552, 623, -354, 21, 66, 12, -30, 17, -6, 1], 'lmfdb_label': '38.a1', 'torsion': [2, 6]}
  • id: 1127
    {'degree': 18, 'field': [64, 128, -560, -384, 7420, 9196, 3374, 9954, 9273, -1699, -226, 2177, 105, -294, 59, 27, -6, -1, 1], 'lmfdb_label': '38.a1', 'torsion': [3, 6]}
  • id: 1129
    {'degree': 18, 'field': [6859, 0, 0, -1824, 0, 0, 19627, 0, 0, 5872, 0, 0, 649, 0, 0, -16, 0, 0, 1], 'lmfdb_label': '38.a1', 'torsion': [18]}
  • id: 1126
    {'degree': 18, 'field': [19683, 0, 0, -5832, 0, 0, 27, 0, 0, 720, 0, 0, 1, 0, 0, -8, 0, 0, 1], 'lmfdb_label': '38.a1', 'torsion': [3, 9]}
  • id: 1130
    {'degree': 18, 'field': [54872, 0, 0, 0, 0, 0, 49457, 0, 0, 0, 0, 0, 114, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '38.a1', 'torsion': [2, 6]}
  • id: 1128
    {'degree': 18, 'field': [47045881, 0, 0, -13292742, 0, 0, 8319967, 0, 0, -677236, 0, 0, 15751, 0, 0, -38, 0, 0, 1], 'lmfdb_label': '38.a1', 'torsion': [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: 148
    {'conductor': 38, 'conductor_valuation': 1, 'discriminant_valuation': 27, 'j_denominator_valuation': 27, 'kodaira_symbol': 31, 'lmfdb_label': '38.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 149
    {'conductor': 38, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '38.a1', 'prime': 19, 'reduction_type': 1, '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

  
  
  • id: 1665956
    {'adelic_gens': [[28, 27, 1521, 3592], [937, 75, 1653, 2144], [31, 36, 2386, 1447], [1, 54, 0, 1], [688, 9, 791, 664], [28, 27, 729, 703], [3079, 54, 0, 1], [4051, 54, 4050, 55], [1, 0, 54, 1]], 'adelic_image': '4104.1296.43.?', 'conductor': 38, 'lmfdb_label': '38.a1', 'prime': 0}
  • id: 89
    {'conductor': 38, 'elladic_image': '27.72.0.2', 'lmfdb_label': '38.a1', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 38.a does not appear in ec_padic