Elliptic curve data - 238.d4

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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': '238c', 'Clabel': '238c4', 'Cnumber': 4, 'abc_quality': 0.9883270273272311, 'absD': 196003234, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 136, 'ainvs': [1, -1, 1, 131, -377], 'analytic_rank': 0, 'bad_primes': [2, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 238, 'degree': 64, 'elladic_images': ['8.24.0.103'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.27912911165657707602308291471', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4], 'jinv': [250404380127, 196003234], 'lmfdb_iso': '238.d', 'lmfdb_label': '238.d4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, 131, -377], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.p.1.7', '68.12.0-4.c.1.1', '136.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 17], [7, 8, 34], [17, 18, 14]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.27912911165657707602308291471', 'prec': 103}, 'szpiro_ratio': 4.796243558422165, '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, 1, 0, 1, 2, 0, 1, 1, -3, 2, 0, 0, -2, 1, 0, 1, 1, -3, 4, 2], 'aplist': [1, 0, 2, 1, 0, -2, 1, 4, 0, -6, 0, -6, -6, -12, 8, -2, 4, 2, 12, 0, 2, -8, 12, 10, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 238, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '238.d', 'trace_hash': 257641944930011138}
• 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': '0.57220484944586078542968476296', 'prec': 103}, 'conductor': 238, 'gens': [], 'heights': [], 'lmfdb_label': '238.d4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.99566410155831132199025013981', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9913282031166226439805002796259681488', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[11, -15, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 2], '7': [1, 0], '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '238.d4'}
• ec_torsion_growth •

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

  
  
  • id: 10073
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [4]}
  • id: 10074
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [4]}
  • id: 10072
    {'degree': 2, 'field': [34, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [2, 2]}
  • id: 10076
    {'degree': 4, 'field': [-34, 0, 8, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [8]}
  • id: 10075
    {'degree': 4, 'field': [81, 0, 16, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [2, 4]}
  • id: 10080
    {'degree': 8, 'field': [-48, 0, -132, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [6]}
  • id: 10079
    {'degree': 8, 'field': [81, 0, -36, 0, 56, 0, -4, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [2, 8]}
  • id: 10078
    {'degree': 8, 'field': [256, 0, 132, 0, 40, 0, 13, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [8]}
  • id: 10077
    {'degree': 8, 'field': [1444, 0, -784, 0, 92, 0, 8, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [2, 4]}
  • id: 10082
    {'degree': 16, 'field': [65536, 0, 0, 0, -3056, 0, 0, 0, -1320, 0, 0, 0, 89, 0, 0, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [2, 8]}
  • id: 10081
    {'degree': 16, 'field': [83521, 0, 0, 0, 0, 0, 0, 0, 9826, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [4, 4]}
  • id: 10085
    {'degree': 16, 'field': [153664, 0, -153664, 0, 38416, 0, -1408, 0, -2000, 0, -904, 0, 64, 0, -16, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [12]}
  • id: 10083
    {'degree': 16, 'field': [1336336, 0, 2515456, 0, -194208, 0, -64736, 0, 52598, 0, 1904, 0, -168, 0, -64, 0, 1], 'lmfdb_label': '238.d4', 'torsion': [16]}
  • id: 10086
    {'degree': 16, 'field': [14864458, -5199824, 6287904, -2525122, 2187872, -1260966, 678823, -237056, 79656, -15230, 4729, -996, 257, -70, 30, -8, 1], 'lmfdb_label': '238.d4', 'torsion': [12]}
  • id: 10084
    {'degree': 16, 'field': [64064016, 0, -42031728, 0, 14047380, 0, -2673000, 0, 313212, 0, -21684, 0, 972, 0, 0, 0, 1], 'lmfdb_label': '238.d4', '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: 2131
    {'conductor': 238, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '238.d4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2132
    {'conductor': 238, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '238.d4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 2133
    {'conductor': 238, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '238.d4', 'prime': 17, '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: 1666777
    {'adelic_gens': [[88, 25, 43, 30], [120, 59, 123, 16], [24, 3, 117, 2], [1, 0, 8, 1], [1, 4, 4, 17], [7, 6, 130, 131], [129, 8, 128, 9], [1, 8, 0, 1]], 'adelic_image': '136.48.0.?', 'conductor': 238, 'lmfdb_label': '238.d4', 'prime': 0}
  • id: 995
    {'conductor': 238, 'elladic_image': '8.24.0.103', 'lmfdb_label': '238.d4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 238.d does not appear in ec_padic