Elliptic curve data - 355488.x4

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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': '355488x', 'Clabel': '355488x3', 'Cnumber': 3, 'abc_quality': 0.9710857330134317, 'absD': 545946884335104, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3864, 'ainvs': [0, -1, 0, 8288, -1088780], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 355488, 'degree': 1576960, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5091138799778631253487274797', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2, 4], 'jinv': [830584, 7203], 'lmfdb_iso': '355488.x', 'lmfdb_label': '355488.x4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 16, 84], 'min_quad_twist_disc': -23, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.v.1', '56.12.0.ba.1', '92.12.0.?', '168.24.0.?', '552.24.0.?', '1288.24.0.?', '3864.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.018050079443104540897425036', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1587], [3, 4, 118496], [7, 8, 50784], [23, 266, 672]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.57849361340667070211757302730', 'prec': 107}, 'szpiro_ratio': 3.2327989506805372, '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, -1, 0, 2, 0, -1, 0, 1, 0, -4, 0, -6, 0, -2, 0, 2, 0, 4, 0], 'aplist': [0, -1, 2, -1, -4, -6, 2, 4, 0, -2, -8, 10, -2, 8, 0, 10, 12, -10, -8, -12, 2, 0, 12, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 355488, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '355488.x', 'trace_hash': 359460280280304553}
• 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': '0.048887782518979178861899803141', 'prec': 107}, 'conductor': 355488, 'gens': [[49113, 11154710, 13]], 'heights': [{'__RealLiteral__': 0, 'data': '11.018050079443104540897425036', 'prec': 100}], 'lmfdb_label': '355488.x4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25722454560034539248059282201', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6682258501732040364677431294587847810', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[77, 0, 1]], 'xcoord_integral_points': [77]}
• lmfdb_label 355488.x4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 14818060
    {'degree': 2, 'field': [-138, 0, 1], 'lmfdb_label': '355488.x4', 'torsion': [4]}
  • id: 14818061
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '355488.x4', 'torsion': [4]}
  • id: 14818059
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '355488.x4', 'torsion': [2, 2]}
  • id: 14818062
    {'degree': 4, 'field': [6, -24, 25, -2, 1], 'lmfdb_label': '355488.x4', 'torsion': [2, 4]}
  • id: 14818066
    {'degree': 8, 'field': [-4238163, -79380, -238878, 21384, -10800, -384, 18, 0, 1], 'lmfdb_label': '355488.x4', 'torsion': [6]}
  • id: 14818065
    {'degree': 8, 'field': [1842, -1464, 1646, -384, 243, -64, 26, -4, 1], 'lmfdb_label': '355488.x4', 'torsion': [8]}
  • id: 14818063
    {'degree': 8, 'field': [91809, 0, 7956, 0, -48, 0, -12, 0, 1], 'lmfdb_label': '355488.x4', 'torsion': [2, 4]}
  • id: 14818064
    {'degree': 8, 'field': [4319638, 309928, -301144, -17432, 8377, 404, -130, -4, 1], 'lmfdb_label': '355488.x4', 'torsion': [8]}
  • id: 14818069
    {'degree': 16, 'field': [131044, 0, 3821856, 0, 3290380, 0, 2256312, 0, 601725, 0, 70620, 0, 4054, 0, 108, 0, 1], 'lmfdb_label': '355488.x4', 'torsion': [2, 8]}
  • id: 14818072
    {'degree': 16, 'field': [2020944, 551328, 566480, -2856544, 3093536, -2326568, 1359628, -577880, 248301, -80976, 28656, -7712, 2074, -392, 76, -8, 1], 'lmfdb_label': '355488.x4', 'torsion': [12]}
  • id: 14818067
    {'degree': 16, 'field': [2643876, 0, -2016432, 0, 1008948, 0, -209616, 0, 58285, 0, -9812, 0, 894, 0, -44, 0, 1], 'lmfdb_label': '355488.x4', 'torsion': [4, 4]}
  • id: 14818068
    {'degree': 16, 'field': [22049658, 31062528, 36783828, 22779792, 9904482, 996912, -56652, -200340, 58771, -7644, 17336, -1092, 1242, -84, 56, 0, 1], 'lmfdb_label': '355488.x4', 'torsion': [2, 8]}
  • id: 14818070
    {'degree': 16, 'field': [424570775494, -641312921960, 390321180564, -109732483792, 7636655768, 3239160144, -683303156, -10183688, 9719496, 1300540, -375704, -19344, 9314, -400, -12, -8, 1], 'lmfdb_label': '355488.x4', 'torsion': [2, 6]}
  • id: 14818071
    {'degree': 16, 'field': [1995780623841, 0, -455169628692, 0, 47460107412, 0, -2779860708, 0, 100029978, 0, -2300724, 0, 33300, 0, -276, 0, 1], 'lmfdb_label': '355488.x4', 'torsion': [12]}
• 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: 8800081
    {'conductor': 355488, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '355488.x4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8800082
    {'conductor': 355488, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '355488.x4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 8800083
    {'conductor': 355488, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '355488.x4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8800084
    {'conductor': 355488, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '355488.x4', 'prime': 23, '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: 3881971
    {'adelic_gens': [[2761, 2024, 460, 369], [1, 0, 8, 1], [7, 6, 3858, 3859], [1, 8, 0, 1], [3857, 8, 3856, 9], [1, 4, 4, 17], [2416, 2691, 1909, 2186], [1007, 0, 0, 3863], [2416, 2507, 529, 3750], [1289, 276, 782, 1703]], 'adelic_image': '3864.48.0.?', 'conductor': 355488, 'lmfdb_label': '355488.x4', 'prime': 0}
  • id: 1227772
    {'conductor': 355488, 'elladic_image': '4.6.0.1', 'lmfdb_label': '355488.x4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 355488.x does not appear in ec_padic