Elliptic curve data - 265650.r5

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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': '265650r', 'Clabel': '265650r2', 'Cnumber': 2, 'abc_quality': 1.0243855179901846, 'absD': 73235352996357032250000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 920, 'ainvs': [1, 1, 0, -10516600, 1665478000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 265650, 'degree': 26214400, 'elladic_images': ['8.48.0.97'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0771666569799842813738200956', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [8232463578739844255617, 4687062591766850064], 'lmfdb_iso': '265650.r', 'lmfdb_label': '265650.r5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -420664, 13323824], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.i.1', '20.24.0-4.b.1.3', '40.96.0-8.i.1.2', '92.24.0.?', '184.96.1.?', '460.48.0.?', '920.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2724477007629340940734404290', 'prec': 100}, 'szpiro_ratio': 4.81339575158305, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, -1, 1, 0, -1, -1, 2, 1, 0, 1, -2, -1, -4, 0], 'aplist': [-1, -1, 0, -1, -1, 2, -2, -4, 1, -2, 0, 2, 10, -4, 0, 2, 12, 6, -12, 8, -10, 16, -12, -6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 265650, 'isogeny_matrix': [[1, 8, 2, 4, 4, 8], [8, 1, 4, 8, 2, 4], [2, 4, 1, 2, 2, 4], [4, 8, 2, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '265650.r', 'trace_hash': 101399590412298313}
• 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': '0.0021242567256424481085246111641', 'prec': 110}, 'conductor': 265650, 'gens': [], 'heights': [], 'lmfdb_label': '265650.r5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.093746667988319496588999959031', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.74997334390655597271199967225227789759', 'prec': 133}, 'tamagawa_product': 128, 'torsion_generators': [[-3320, 1660, 1], [3160, -1580, 1]], 'xcoord_integral_points': [-3320, 3160]}
• lmfdb_label 265650.r5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11370422
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 4]}
  • id: 11370425
    {'degree': 4, 'field': [4, 0, -6, 0, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 8]}
  • id: 11370424
    {'degree': 4, 'field': [6, -22, 23, -2, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 4]}
  • id: 11370423
    {'degree': 4, 'field': [49, 0, -9, 0, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 4]}
  • id: 11370429
    {'degree': 8, 'field': [-43749004, 6110989, -6133498, 45017, -22505, -7, 7, -4, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 6]}
  • id: 11370427
    {'degree': 8, 'field': [164, -712, 1050, -712, 447, -112, 42, -4, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 8]}
  • id: 11370426
    {'degree': 8, 'field': [449, -730, 996, -562, 357, -94, 36, -4, 1], 'lmfdb_label': '265650.r5', 'torsion': [4, 4]}
  • id: 11370428
    {'degree': 8, 'field': [484421, -9754, 8376, 2750, -1359, -22, 12, -4, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 8]}
  • id: 11370432
    {'degree': 16, 'field': [2187801, -1952412, 2954734, -2358468, 2146508, -1404284, 910910, -456596, 217941, -81236, 28994, -7868, 2100, -392, 76, -8, 1], 'lmfdb_label': '265650.r5', 'torsion': [4, 8]}
  • id: 11370431
    {'degree': 16, 'field': [991750169, -1539436258, 912947190, -359033206, 153417244, -59481312, 17355288, -3211194, 711597, -236664, 42072, -6402, 1892, -310, 18, -4, 1], 'lmfdb_label': '265650.r5', 'torsion': [4, 8]}
  • id: 11370430
    {'degree': 16, 'field': [14190321784, -4011649904, 1920724316, -794347276, 551801073, -135796636, 15030592, -5748212, 962740, -135208, 43102, -4364, 1620, 4, -52, -4, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 8]}
  • id: 11370434
    {'degree': 16, 'field': [16889081764, 0, 1398379931, 0, 2388609202, 0, 81126717, 0, -862365, 0, -102207, 0, -1757, 0, -10, 0, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 12]}
  • id: 11370433
    {'degree': 16, 'field': [25063744167991, 12409781529344, -11086519401004, -2590112324664, 1155283707272, 164222613256, -48949142288, -4867081032, 1096082269, 79087128, -14453540, -734224, 114302, 3696, -508, -8, 1], 'lmfdb_label': '265650.r5', 'torsion': [2, 16]}
• 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: 6584414
    {'conductor': 265650, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '265650.r5', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6584415
    {'conductor': 265650, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '265650.r5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6584416
    {'conductor': 265650, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '265650.r5', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6584417
    {'conductor': 265650, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '265650.r5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6584418
    {'conductor': 265650, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '265650.r5', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6584419
    {'conductor': 265650, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '265650.r5', 'prime': 23, 'reduction_type': 1, '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: 3345475
    {'adelic_gens': [[1, 0, 8, 1], [913, 8, 912, 9], [1, 8, 0, 1], [183, 0, 0, 919], [281, 880, 480, 61], [311, 370, 830, 731], [5, 4, 916, 917], [741, 420, 710, 291]], 'adelic_image': '920.192.1.?', 'conductor': 265650, 'lmfdb_label': '265650.r5', 'prime': 0}
  • id: 952020
    {'conductor': 265650, 'elladic_image': '8.48.0.97', 'lmfdb_label': '265650.r5', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 265650.r does not appear in ec_padic