Elliptic curve data - 258570.s1

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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': '258570s', 'Clabel': '258570s3', 'Cnumber': 3, 'abc_quality': 1.042560452096738, 'absD': 15681098596220928000000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 26520, 'ainvs': [1, -1, 0, -6340320, 1210291200], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 258570, 'degree': 26542080, 'elladic_images': ['4.6.0.3', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9492573001068564090894265561', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [8010684753304969, 4456448000000], 'lmfdb_iso': '258570.s', 'lmfdb_label': '258570.s1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -4169, -20724], 'min_quad_twist_disc': -39, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.b.1', '6.12.0.a.1', '12.24.0.f.1', '24.48.0.bq.2', '34.6.0.a.1', '39.8.0-3.a.1.1', '68.12.0.e.1', '78.24.0.?', '102.24.0.?', '156.48.0.?', '204.48.1.?', '312.96.0.?', '340.24.0.?', '408.96.3.?', '1020.96.3.?', '1326.48.0.?', '2040.192.9.?', '2652.96.1.?', '5304.192.3.?', '13260.192.3.?', '26520.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 25857], [3, 2, 2873], [5, 6, 51714], [13, 86, 1530], [17, 18, 15210]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1174764770420331953650602169', 'prec': 100}, 'szpiro_ratio': 4.702021226580028, '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, -1, 0, -2, -1, 0, 1, 6, 0, 0, 2, 0, 1, -1, 0, -8, -1], 'aplist': [-1, 0, -1, -2, 6, 0, -1, -8, 6, 6, -2, -2, -6, -4, 12, -6, 0, 2, -8, -6, -2, -10, 12, 6, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 258570, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '258570.s', 'trace_hash': 1774918956134664162}
• 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': '0.0027435170131863273368786443015', 'prec': 110}, 'conductor': 258570, 'gens': [], 'heights': [], 'lmfdb_label': '258570.s1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10754317270783134432245961426', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.86034538166265075457967691405612608570', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[192, -96, 1]], 'xcoord_integral_points': [192]}
• lmfdb_label 258570.s1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11087120
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '258570.s1', 'torsion': [2, 2]}
  • id: 11087121
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '258570.s1', 'torsion': [6]}
  • id: 11087123
    {'degree': 4, 'field': [1, 0, -15, 0, 1], 'lmfdb_label': '258570.s1', 'torsion': [2, 6]}
  • id: 11087122
    {'degree': 4, 'field': [1621, -78, -19, 0, 1], 'lmfdb_label': '258570.s1', 'torsion': [4]}
  • id: 11087124
    {'degree': 6, 'field': [768, -96, -104, 42, 7, -3, 1], 'lmfdb_label': '258570.s1', 'torsion': [6]}
  • id: 11087127
    {'degree': 8, 'field': [625, 0, 218, 0, 75, 0, -10, 0, 1], 'lmfdb_label': '258570.s1', 'torsion': [12]}
  • id: 11087125
    {'degree': 8, 'field': [75076, 0, -66628, 0, 413, 0, -23, 0, 1], 'lmfdb_label': '258570.s1', 'torsion': [2, 4]}
  • id: 11087126
    {'degree': 8, 'field': [151321, 0, 12465, 0, -556, 0, -15, 0, 1], 'lmfdb_label': '258570.s1', 'torsion': [2, 4]}
  • id: 11087128
    {'degree': 12, 'field': [4356, -9306, 8673, -4371, 658, -81, 95, 42, 99, -33, 14, -3, 1], 'lmfdb_label': '258570.s1', 'torsion': [3, 6]}
  • id: 11087129
    {'degree': 12, 'field': [649024, -217474, -80143, 45580, 4434, -7724, 1729, -478, 45, 2, 14, -2, 1], 'lmfdb_label': '258570.s1', 'torsion': [2, 6]}
  • id: 11087133
    {'degree': 16, 'field': [36481, 0, 139052, 0, 79466, 0, 24516, 0, 9995, 0, 2796, 0, 386, 0, 32, 0, 1], 'lmfdb_label': '258570.s1', 'torsion': [2, 12]}
  • id: 11087132
    {'degree': 16, 'field': [18826921, 0, -35019136, 0, 4161078, 0, -3417844, 0, 923703, 0, -92908, 0, 4502, 0, -108, 0, 1], 'lmfdb_label': '258570.s1', 'torsion': [2, 12]}
  • id: 11087130
    {'degree': 16, 'field': [122190916, 0, 2483391592, 0, 3791681313, 0, -104833400, 0, 3115236, 0, 87190, 0, -1072, 0, 48, 0, 1], 'lmfdb_label': '258570.s1', 'torsion': [4, 4]}
  • id: 11087131
    {'degree': 16, 'field': [800618737, -66089660, 59565270, 13940788, -9132844, 2403508, -475738, -290660, 84981, -4588, -2686, 1924, -260, -56, 28, -8, 1], 'lmfdb_label': '258570.s1', 'torsion': [8]}
  • id: 11087134
    {'degree': 18, 'field': [158213501, 334030869, 1040558301, 771371982, -157360716, 94560282, 195659076, -28643202, -51764877, 667485, 6677217, 562158, -364278, -41076, 10188, 1044, -153, -9, 1], 'lmfdb_label': '258570.s1', 'torsion': [18]}
• 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: 6407428
    {'conductor': 258570, 'conductor_valuation': 1, 'discriminant_valuation': 24, 'j_denominator_valuation': 24, 'kodaira_symbol': 28, 'lmfdb_label': '258570.s1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6407429
    {'conductor': 258570, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '258570.s1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6407430
    {'conductor': 258570, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '258570.s1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6407431
    {'conductor': 258570, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '258570.s1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6407432
    {'conductor': 258570, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '258570.s1', '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: 3302435
    {'adelic_gens': [[13261, 22464, 11232, 4369], [1, 12, 12, 145], [21, 4, 26420, 26501], [20658, 14287, 15977, 22400], [7, 24, 492, 1687], [2039, 0, 0, 26519], [2055, 18382, 7514, 1691], [26497, 24, 26496, 25], [1, 24, 0, 1], [6631, 22464, 24492, 4369], [1, 0, 24, 1], [8839, 4056, 8840, 26519]], 'adelic_image': '26520.384.9.?', 'conductor': 258570, 'lmfdb_label': '258570.s1', 'prime': 0}
  • id: 928680
    {'conductor': 258570, 'elladic_image': '4.6.0.3', 'lmfdb_label': '258570.s1', 'modell_image': '2B', 'prime': 2}
  • id: 928681
    {'conductor': 258570, 'elladic_image': '3.4.0.1', 'lmfdb_label': '258570.s1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 258570.s does not appear in ec_padic