Elliptic curve data - 381150.e4

Formats: - HTML - YAML - JSON - 2025-10-21T11:18:13.478495

• 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': '381150e', 'Clabel': '381150e1', 'Cnumber': 1, 'abc_quality': 1.0002264121867963, 'absD': 56501723643750000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9240, 'ainvs': [1, -1, 0, 62958, -9701884], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 381150, 'degree': 3932160, 'elladic_images': ['8.12.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8988132280049812420094479369', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [1367631, 2800], 'lmfdb_iso': '381150.e', 'lmfdb_label': '381150.e4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, 2, -3], 'min_quad_twist_disc': 165, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.p.1', '14.6.0.b.1', '28.12.0.g.1', '56.24.0.bn.1', '660.12.0.?', '1320.24.0.?', '4620.24.0.?', '9240.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.7183417589804696899096814673', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 190575], [3, 6, 42350], [5, 18, 15246], [7, 8, 54450], [11, 62, 3150]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.65415950894530906301952613716', 'prec': 107}, 'szpiro_ratio': 3.555812271450009, '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, 0, 0, -1, -1, 0, 0, 0, 0, -6, 1, 0, 1, -2, 0, 0, 0], 'aplist': [-1, 0, 0, -1, 0, -6, -2, 0, 0, 6, 8, 10, 2, 4, 8, -2, 8, 14, 12, 16, 2, 8, -8, -10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 381150, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '381150.e', 'trace_hash': 1832981050198426619}
• 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': '0.022423932932375926549599952204', 'prec': 107}, 'conductor': 381150, 'gens': [[224, 3838, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.7183417589804696899096814673', 'prec': 100}], 'lmfdb_label': '381150.e4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.18377313751687927699794313045', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.4666506512629810932896375712194678349', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[124, -62, 1]], 'xcoord_integral_points': [124, 224, 1213]}
• lmfdb_label 381150.e4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 15777287
    {'degree': 2, 'field': [-41, -1, 1], 'lmfdb_label': '381150.e4', 'torsion': [4]}
  • id: 15777286
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '381150.e4', 'torsion': [2, 2]}
  • id: 15777288
    {'degree': 2, 'field': [289, -1, 1], 'lmfdb_label': '381150.e4', 'torsion': [4]}
  • id: 15777289
    {'degree': 4, 'field': [1849, 0, -79, 0, 1], 'lmfdb_label': '381150.e4', 'torsion': [2, 4]}
  • id: 15777293
    {'degree': 8, 'field': [-69330, 68685, -22725, 975, 585, 75, -39, -3, 1], 'lmfdb_label': '381150.e4', 'torsion': [6]}
  • id: 15777291
    {'degree': 8, 'field': [-2351, -25326, -13393, 1462, 1494, -74, -87, -2, 1], 'lmfdb_label': '381150.e4', 'torsion': [8]}
  • id: 15777290
    {'degree': 8, 'field': [4111606, -99026, 104993, -12068, 6370, -406, 140, -4, 1], 'lmfdb_label': '381150.e4', 'torsion': [2, 4]}
  • id: 15777292
    {'degree': 8, 'field': [50909380, -2316360, 2356874, -81352, 41487, -976, 330, -4, 1], 'lmfdb_label': '381150.e4', 'torsion': [8]}
  • id: 15777298
    {'degree': 16, 'field': [4223025, 0, 396196155, 0, 75169314, 0, 7788357, 0, 217650, 0, -68595, 0, 3450, 0, -93, 0, 1], 'lmfdb_label': '381150.e4', 'torsion': [12]}
  • id: 15777299
    {'degree': 16, 'field': [445364956, -189546692, 383792304, -131357320, 116368250, -7626234, 3994129, -389342, -851640, 259180, 40525, -24948, 2633, 470, -90, -2, 1], 'lmfdb_label': '381150.e4', 'torsion': [12]}
  • id: 15777295
    {'degree': 16, 'field': [870796444, -66329480, 85542522, -40572032, 25753601, -6855236, 2795516, -479924, 177558, -45784, 17090, -5024, 1444, -308, 64, -8, 1], 'lmfdb_label': '381150.e4', 'torsion': [2, 8]}
  • id: 15777297
    {'degree': 16, 'field': [3233987584, 7076736392, 6171018188, 2616716124, 440531600, -56148176, -28689554, 2606436, 2560153, 215610, -74156, -8890, 2294, 162, -70, -2, 1], 'lmfdb_label': '381150.e4', 'torsion': [2, 6]}
  • id: 15777294
    {'degree': 16, 'field': [159265644561, 86201496, 23328, -167683572, 72736426, 11058684, 94248, -3242908, 815459, -5692, 3752, -1540, 378, -84, 32, -8, 1], 'lmfdb_label': '381150.e4', 'torsion': [4, 4]}
  • id: 15777296
    {'degree': 16, 'field': [6559514934025, 0, -1390611744680, 0, 127309714534, 0, -6542979700, 0, 206310375, 0, -4088444, 0, 49750, 0, -340, 0, 1], 'lmfdb_label': '381150.e4', 'torsion': [2, 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: 9426139
    {'conductor': 381150, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '381150.e4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9426140
    {'conductor': 381150, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '381150.e4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9426141
    {'conductor': 381150, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '381150.e4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9426142
    {'conductor': 381150, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '381150.e4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9426143
    {'conductor': 381150, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '381150.e4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 4032785
    {'adelic_gens': [[9233, 8, 9232, 9], [1, 8, 0, 1], [6719, 0, 0, 9239], [1, 0, 8, 1], [6931, 990, 1650, 331], [5543, 0, 0, 9239], [3079, 0, 0, 9239], [1, 3300, 6270, 4951], [1, 4, 4, 17], [2476, 6105, 3135, 2806], [7, 6, 9234, 9235]], 'adelic_image': '9240.48.0.?', 'conductor': 381150, 'lmfdb_label': '381150.e4', 'prime': 0}
  • id: 1303437
    {'conductor': 381150, 'elladic_image': '8.12.0.9', 'lmfdb_label': '381150.e4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 381150.e does not appear in ec_padic