Elliptic curve data - 238.a1

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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': '238b', 'Clabel': '238b2', 'Cnumber': 2, 'abc_quality': 0.8978116586804944, 'absD': 28322, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 952, 'ainvs': [1, -1, 0, -8, 6], 'analytic_rank': 1, 'bad_primes': [2, 7, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 238, 'degree': 16, 'elladic_images': ['8.6.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.45127815670060783901545892267', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [60698457, 28322], 'lmfdb_iso': '238.a', 'lmfdb_label': '238.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -8, 6], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.b.1', '476.6.0.?', '952.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.32098345420787208189836373227', 'prec': 103}, 'semistable': True, 'serre_invariants': [[2, 4, 1], [7, 8, 34], [17, 18, 14]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.45127815670060783901545892267', 'prec': 107}, 'szpiro_ratio': 3.2749529225285703, '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, -2, 0, 0, 1, 0, 1, -1, 3, -2, -2], 'aplist': [-1, 0, -2, -1, -2, 0, -1, -2, -8, 0, 8, -4, -6, 4, 8, -6, 10, 10, 8, 4, -10, -4, -6, -6, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 238, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '238.a', 'trace_hash': 1284335553466925369}
• 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': '2.4658986708351395481463355626', 'prec': 100}, 'conductor': 238, 'gens': [[5, 6, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.32098345420787208189836373227', 'prec': 103}], 'lmfdb_label': '238.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '3.3407446902280344485568697517', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0723237702960020987773751221677197996', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[3, -3, 2]], 'xcoord_integral_points': [-1, 3, 5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [5, 1, 0], '5': [1, 0], '7': [1, 0], '11': [3, 0], '13': [1, 1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '238.a1'}
• ec_torsion_growth •

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

  
  
  • id: 10033
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '238.a1', 'torsion': [2, 2]}
  • id: 10034
    {'degree': 4, 'field': [32, 0, -3, 0, 1], 'lmfdb_label': '238.a1', 'torsion': [4]}
  • id: 10037
    {'degree': 8, 'field': [-74, -67, 100, -67, 37, -7, 7, -4, 1], 'lmfdb_label': '238.a1', 'torsion': [6]}
  • id: 10035
    {'degree': 8, 'field': [196, 0, -256, 0, 98, 0, -16, 0, 1], 'lmfdb_label': '238.a1', 'torsion': [2, 4]}
  • id: 10036
    {'degree': 8, 'field': [900, 0, 532, 0, 109, 0, -14, 0, 1], 'lmfdb_label': '238.a1', 'torsion': [2, 4]}
  • id: 10039
    {'degree': 16, 'field': [1024, 0, -6304, 0, 4324, 0, -10480, 0, 3184, 0, -532, 0, 88, 0, -16, 0, 1], 'lmfdb_label': '238.a1', 'torsion': [2, 6]}
  • id: 10038
    {'degree': 16, 'field': [4096, 0, 82176, 0, 1262656, 0, -22080, 0, 2448, 0, -4188, 0, 689, 0, -18, 0, 1], 'lmfdb_label': '238.a1', 'torsion': [8]}
• 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: 2119
    {'conductor': 238, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '238.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2120
    {'conductor': 238, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '238.a1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2121
    {'conductor': 238, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '238.a1', 'prime': 17, 'reduction_type': -1, '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: 1666768
    {'adelic_gens': [[409, 4, 818, 9], [1, 2, 2, 5], [121, 834, 832, 119], [1, 4, 0, 1], [1, 0, 4, 1], [3, 4, 8, 11], [949, 4, 948, 5], [785, 4, 618, 9], [2, 1, 475, 0]], 'adelic_image': '952.12.0.?', 'conductor': 238, 'lmfdb_label': '238.a1', 'prime': 0}
  • id: 986
    {'conductor': 238, 'elladic_image': '8.6.0.6', 'lmfdb_label': '238.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 2171
    {'lmfdb_iso': '238.a', 'p': 5, 'prec': 20, 'unit': 8393067226109, 'val': 1}
  • id: 2162
    {'lmfdb_iso': '238.a', 'p': 11, 'prec': 20, 'unit': 4848257535720812066, 'val': 2}
  • id: 2164
    {'lmfdb_iso': '238.a', 'p': 19, 'prec': 20, 'unit': 1843592331082815167777273, 'val': 1}
  • id: 2167
    {'lmfdb_iso': '238.a', 'p': 23, 'prec': 20, 'unit': 38124353341086262049132374, 'val': 1}
  • id: 2158
    {'lmfdb_iso': '238.a', 'p': 31, 'prec': 20, 'unit': 13742037703509038536136035323, 'val': 1}
  • id: 2156
    {'lmfdb_iso': '238.a', 'p': 37, 'prec': 20, 'unit': 43535479930187384417787319911, 'val': 1}
  • id: 2159
    {'lmfdb_iso': '238.a', 'p': 41, 'prec': 20, 'unit': 3727756436009725180830066113427, 'val': 1}
  • id: 2160
    {'lmfdb_iso': '238.a', 'p': 43, 'prec': 20, 'unit': 8741971690698320827523275594165, 'val': 1}
  • id: 2169
    {'lmfdb_iso': '238.a', 'p': 47, 'prec': 20, 'unit': 25985368246804520989427964997454, 'val': 1}
  • id: 2165
    {'lmfdb_iso': '238.a', 'p': 53, 'prec': 20, 'unit': 211372662148910039036982165833245, 'val': 1}
  • id: 2163
    {'lmfdb_iso': '238.a', 'p': 59, 'prec': 20, 'unit': 342381990982194116505058869130822, 'val': 1}
  • id: 2170
    {'lmfdb_iso': '238.a', 'p': 61, 'prec': 20, 'unit': 5384414950832122419261004704826755, 'val': 1}
  • id: 2155
    {'lmfdb_iso': '238.a', 'p': 67, 'prec': 20, 'unit': 39526282901890544919817377998529715, 'val': 1}
  • id: 2157
    {'lmfdb_iso': '238.a', 'p': 71, 'prec': 20, 'unit': 102748677760064724325358632348008124, 'val': 1}
  • id: 2166
    {'lmfdb_iso': '238.a', 'p': 73, 'prec': 20, 'unit': 194104983981244738843769118369683592, 'val': 1}
  • id: 2161
    {'lmfdb_iso': '238.a', 'p': 79, 'prec': 20, 'unit': 273083765753472568112040907801330905, 'val': 1}
  • id: 2154
    {'lmfdb_iso': '238.a', 'p': 83, 'prec': 20, 'unit': 2619308426305039606784638365753661767, 'val': 1}
  • id: 2168
    {'lmfdb_iso': '238.a', 'p': 89, 'prec': 20, 'unit': 16503957332906731103043158425993650, 'val': 2}
  • id: 2153
    {'lmfdb_iso': '238.a', 'p': 97, 'prec': 20, 'unit': 55471497454906526545487252247217199918, 'val': 1}