Elliptic curve data - 277350.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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '277350x', 'Clabel': '277350x1', 'Cnumber': 1, 'abc_quality': 1.1033940611435318, 'absD': 9482044573500, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 5160, 'ainvs': [1, 1, 0, -5585, 216225], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 43], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 277350, 'degree': 645120, 'elladic_images': ['2.3.0.1', '5.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1953288752326503613187622608', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [-24389, 12], 'lmfdb_iso': '277350.x', 'lmfdb_label': '277350.x4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3, -3], 'min_quad_twist_disc': -43, 'modell_images': ['2B', '5B.4.2'], 'modm_images': ['2.3.0.a.1', '5.12.0.a.2', '10.36.0.a.1', '24.6.0.j.1', '30.72.1.i.2', '40.72.1.bl.1', '120.144.5.?', '215.24.0.?', '430.72.0.?', '1290.144.1.?', '1720.144.1.?', '5160.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.3451929826965156907535409832', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 27735], [3, 4, 92450], [43, 926, 150]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0876306607226559440678488292', 'prec': 103}, 'szpiro_ratio': 3.040979661280335, '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, -1, 1, 0, 1, 2, -1, 1, 0, 2, -1, -6, -2, 0, 1, -2, -1, 0, 0], 'aplist': [-1, -1, 0, 2, 2, -6, -2, 0, 4, 0, -8, 2, 2, 0, 8, -6, 10, -2, 8, -12, -4, 0, 4, 10, 8], 'class_deg': 10, 'class_size': 4, 'conductor': 277350, 'isogeny_matrix': [[1, 5, 2, 10], [5, 1, 10, 2], [2, 10, 1, 5], [10, 2, 5, 1]], 'lmfdb_iso': '277350.x', 'trace_hash': 499265223948747224}
• 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': '0.091569434227089041938304051255', 'prec': 107}, 'conductor': 277350, 'gens': [[0, 465, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.3451929826965156907535409832', 'prec': 100}], 'lmfdb_label': '277350.x4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.67877100118861301260074518284', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.5412399800680731216444994675999577794', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-90, 45, 1]], 'xcoord_integral_points': [-90, 0]}
• lmfdb_label 277350.x4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11821067
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '277350.x4', 'torsion': [2, 2]}
  • id: 11821068
    {'degree': 4, 'field': [-1809, -318, -111, -2, 1], 'lmfdb_label': '277350.x4', 'torsion': [4]}
  • id: 11821069
    {'degree': 4, 'field': [551, 54, -54, -1, 1], 'lmfdb_label': '277350.x4', 'torsion': [10]}
  • id: 11821072
    {'degree': 8, 'field': [-518344, 497927, 144680, 17797, 3469, 13, -5, -2, 1], 'lmfdb_label': '277350.x4', 'torsion': [6]}
  • id: 11821073
    {'degree': 8, 'field': [303601, 29754, 32670, -1814, 2419, -54, 55, -1, 1], 'lmfdb_label': '277350.x4', 'torsion': [2, 10]}
  • id: 11821071
    {'degree': 8, 'field': [1454436, 270144, -103262, -13460, 4601, 310, -103, -2, 1], 'lmfdb_label': '277350.x4', 'torsion': [2, 4]}
  • id: 11821070
    {'degree': 8, 'field': [22233811, 198208, -522829, 17674, -2426, 302, 119, -4, 1], 'lmfdb_label': '277350.x4', 'torsion': [2, 4]}
  • id: 11821074
    {'degree': 10, 'field': [300737, 10883, 73291, 2396, 11463, -517, 1059, -46, 47, -1, 1], 'lmfdb_label': '277350.x4', 'torsion': [10]}
  • id: 11821077
    {'degree': 16, 'field': [90419873351, 9003568672, -38393294272, -1243121536, 6453336903, 48703316, -582596502, 120752, 31235790, -45744, -1023888, 864, 20131, -4, -218, 0, 1], 'lmfdb_label': '277350.x4', 'torsion': [20]}
  • id: 11821075
    {'degree': 16, 'field': [906420532356, 81062602128, -88363358952, 14490997872, -6957747482, -377369112, 179149984, -45546224, 11101443, 262008, -124544, 39600, -6782, 56, 12, -8, 1], 'lmfdb_label': '277350.x4', 'torsion': [8]}
  • id: 11821076
    {'degree': 16, 'field': [976136096016, 0, -134114143569, 0, 3354555634, 0, 1147970337, 0, -1848741, 0, 271049, 0, 7071, 0, 18, 0, 1], 'lmfdb_label': '277350.x4', 'torsion': [2, 6]}
  • id: 11821078
    {'degree': 20, 'field': [20478700789, 7570902186, 17559575275, 3948719496, 7378746333, 933592722, 1858372656, 129556764, 309498093, 10223418, 35621949, 369192, 2834469, -1296, 152646, -516, 5325, -12, 109, 0, 1], 'lmfdb_label': '277350.x4', 'torsion': [2, 10]}
• 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: 6870457
    {'conductor': 277350, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '277350.x4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6870458
    {'conductor': 277350, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '277350.x4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6870459
    {'conductor': 277350, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '277350.x4', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6870460
    {'conductor': 277350, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '277350.x4', 'prime': 43, '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: 3414984
    {'adelic_gens': [[599, 0, 0, 5159], [3871, 860, 430, 3441], [3656, 4085, 4515, 3226], [1, 10, 10, 101], [5141, 20, 5140, 21], [11, 16, 4920, 4811], [1, 0, 20, 1], [2022, 4085, 3655, 646], [2581, 860, 3010, 3441], [1, 20, 0, 1]], 'adelic_image': '5160.288.5.?', 'conductor': 277350, 'lmfdb_label': '277350.x4', 'prime': 0}
  • id: 988319
    {'conductor': 277350, 'elladic_image': '2.3.0.1', 'lmfdb_label': '277350.x4', 'modell_image': '2B', 'prime': 2}
  • id: 988320
    {'conductor': 277350, 'elladic_image': '5.12.0.2', 'lmfdb_label': '277350.x4', 'modell_image': '5B.4.2', 'prime': 5}
• lmfdb_iso 277350.x does not appear in ec_padic