Elliptic curve data - 265598.a2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '265598a', 'Clabel': '265598a2', 'Cnumber': 2, 'abc_quality': 0.967983438848399, 'absD': 149887145272217536, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 116604, 'ainvs': [1, 1, 0, -137036, -5912432], 'analytic_rank': 1, 'bad_primes': [2, 41, 79], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 265598, 'degree': 2592000, 'elladic_images': ['3.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9873379583998843707089793804', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [59914169497, 31554496], 'lmfdb_iso': '265598.a', 'lmfdb_label': '265598.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -82, -92], 'min_quad_twist_disc': 41, 'modell_images': ['3Cs'], 'modm_images': ['3.12.0.a.1', '123.24.0.?', '316.2.0.?', '711.36.0.?', '948.24.1.?', '2844.72.3.?', '29151.72.0.?', '38868.48.1.?', '116604.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.4103698172380138062967324774', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.13055192504773046877559769388', 'prec': 103}, 'szpiro_ratio': 3.7709043110704257, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 3, 1, 1, -1, -2, -3, 0, -1, -5, -1, -3, 1, 0, 2, -2, 3], 'aplist': [-1, -1, 3, 1, 0, -5, 0, -2, -6, 0, -4, 2, 0, 8, 9, -6, -9, 8, 4, 9, 2, -1, 18, -9, -17], 'class_deg': 9, 'class_size': 3, 'conductor': 265598, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '265598.a', 'trace_hash': 1254112484170647729}
• 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': '0.018785388537111725059914618690', 'prec': 107}, 'conductor': 265598, 'gens': [[-2344, 315164, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '4.4103698172380138062967324774', 'prec': 100}], 'lmfdb_label': '265598.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.26319866303424969477517619125', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6432137575346136267155701771228871575', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 265598.a2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11368196
    {'degree': 2, 'field': [-10, -1, 1], 'lmfdb_label': '265598.a2', 'torsion': [3]}
  • id: 11368197
    {'degree': 2, 'field': [31, -1, 1], 'lmfdb_label': '265598.a2', 'torsion': [3]}
  • id: 11368198
    {'degree': 3, 'field': [2, -4, -1, 1], 'lmfdb_label': '265598.a2', 'torsion': [2]}
  • id: 11368199
    {'degree': 4, 'field': [100, 10, 11, -1, 1], 'lmfdb_label': '265598.a2', 'torsion': [3, 3]}
  • id: 11368201
    {'degree': 6, 'field': [-344, -142, 328, 25, -39, -1, 1], 'lmfdb_label': '265598.a2', 'torsion': [6]}
  • id: 11368200
    {'degree': 6, 'field': [8, -8, -34, 54, -17, -2, 1], 'lmfdb_label': '265598.a2', 'torsion': [2, 2]}
  • id: 11368202
    {'degree': 6, 'field': [37909, -839, 2870, -57, 84, -1, 1], 'lmfdb_label': '265598.a2', 'torsion': [6]}
  • id: 11368205
    {'degree': 12, 'field': [-366304, 899184, -425532, -351192, 241564, 47404, -41335, -2978, 3055, 104, -97, -2, 1], 'lmfdb_label': '265598.a2', 'torsion': [2, 6]}
  • id: 11368204
    {'degree': 12, 'field': [118336, 48848, 132996, -29376, 97718, -2532, 12587, -461, 1218, -11, 40, -1, 1], 'lmfdb_label': '265598.a2', 'torsion': [3, 6]}
  • id: 11368203
    {'degree': 12, 'field': [1471401644, 299781608, -89483330, -14019708, 1348691, -330069, -29221, 16018, -1342, 8, 59, -3, 1], 'lmfdb_label': '265598.a2', 'torsion': [4]}
  • id: 11368206
    {'degree': 12, 'field': [2208632557, 97039018, 301116225, 5328866, 17345206, -122582, 559725, -13802, 11378, -306, 149, -2, 1], 'lmfdb_label': '265598.a2', 'torsion': [2, 6]}
  • id: 11368207
    {'degree': 18, 'field': [-671542681, -1225869459, 524645013, 785054816, -108841473, -217661016, 8523916, 38384883, -331776, -4722002, 85446, 388839, -15617, -20259, 1251, 630, -54, -9, 1], 'lmfdb_label': '265598.a2', 'torsion': [9]}
  • id: 11368208
    {'degree': 18, 'field': [43129760362839, -5397185507121, 3835374291657, -2006382528432, 963895812462, -301995220698, 107438575122, -19690017840, 5474077281, -700420095, 161700543, -16190280, 3200958, -252234, 42174, -2268, 315, -9, 1], 'lmfdb_label': '265598.a2', 'torsion': [9]}
• 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: 6583146
    {'conductor': 265598, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '265598.a2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6583147
    {'conductor': 265598, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '265598.a2', 'prime': 41, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6583148
    {'conductor': 265598, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '265598.a2', 'prime': 79, '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: 3344842
    {'adelic_gens': [[1, 18, 0, 1], [1, 9, 9, 82], [61501, 19926, 59409, 20419], [116587, 18, 116586, 19], [1, 6, 6, 37], [58303, 19926, 9963, 62731], [1, 0, 18, 1], [1, 12, 0, 1], [76787, 0, 0, 116603], [95285, 19926, 53874, 113653]], 'adelic_image': '116604.144.3.?', 'conductor': 265598, 'lmfdb_label': '265598.a2', 'prime': 0}
  • id: 951548
    {'conductor': 265598, 'elladic_image': '3.12.0.1', 'lmfdb_label': '265598.a2', 'modell_image': '3Cs', 'prime': 3}
• lmfdb_iso 265598.a does not appear in ec_padic