Elliptic curve data - 26569.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
  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': '26569a', 'Clabel': '26569a1', 'Cnumber': 1, 'abc_quality': 1.2036213229011967, 'absD': 4330747, 'ainvs': [0, 0, 1, -2174420, 1234136692], 'analytic_rank': 1, 'bad_primes': [163], 'class_deg': 163, 'class_size': 2, 'cm': -163, 'conductor': 26569, 'degree': 59368, 'elladic_images': ['163.26568.1027.57'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8511273564650038098091683491', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 163], 'jinv': [-262537412640768000, 1], 'lmfdb_iso': '26569.a', 'lmfdb_label': '26569.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -2174420, 1234136692], 'min_quad_twist_disc': 1, 'modell_images': ['163B.1.145'], 'nonmax_primes': [163], 'nonmax_rad': 163, 'num_bad_primes': 1, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2912801323260268704544630700', 'prec': 100}, 'semistable': False, 'serre_invariants': [[163, 6806, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.57768980626331322629293525757', 'prec': 103}, 'szpiro_ratio': 5.43709628563842, '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, 0, 0, -2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0], 'aplist': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, 5, 7, 0, -9, 0, 11, 0, 0, 13, 0, -15], 'class_deg': 163, 'class_size': 2, 'conductor': 26569, 'isogeny_matrix': [[1, 163], [163, 1]], 'lmfdb_iso': '26569.a', 'trace_hash': 1415011775310762729}
• 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': '0.024667844812197828858677827653', 'prec': 107}, 'conductor': 26569, 'gens': [[850, 68, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2912801323260268704544630700', 'prec': 100}], 'lmfdb_label': '26569.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.79364722618265765456256125300', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6369362428559680165082260567074875580', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [850]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': [1, 1, 0], '5': [1, 1, 0], '7': [1, 1, 0], '11': [1, 1, 0], '13': [1, 1, 0], '17': [1, 1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 1, 0], '31': [1, 1, 0], '37': [1, 1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '163': 'a'}, 'iwp0': 0, 'lmfdb_label': '26569.a2'}
• ec_torsion_growth •

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

  
  
  • id: 1334248
    {'degree': 3, 'field': [5, 7, -1, 1], 'lmfdb_label': '26569.a2', 'torsion': [2]}
  • id: 1334249
    {'degree': 6, 'field': [227, -85, 94, -19, 12, -3, 1], 'lmfdb_label': '26569.a2', 'torsion': [2, 2]}
  • id: 1334250
    {'degree': 8, 'field': [26428, -34496, -2963, 2152, 478, 118, 4, -2, 1], 'lmfdb_label': '26569.a2', 'torsion': [3]}
  • id: 1334251
    {'degree': 12, 'field': [-67176, -325440, -214416, -143464, -73924, -20456, 1616, 1424, 686, -108, 0, -6, 1], 'lmfdb_label': '26569.a2', 'torsion': [4]}
  • id: 1334252
    {'degree': 16, 'field': [698439184, -911660288, 1268280180, -11534464, 70382177, 29720304, 10329370, 1537084, 97956, 10618, 10390, 4536, -226, -244, 0, -2, 1], 'lmfdb_label': '26569.a2', 'torsion': [3, 3]}
• 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

  
  {'conductor': 26569, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '26569.a2', 'prime': 163, '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

  
  {'conductor': 26569, 'elladic_image': '163.26568.1027.57', 'lmfdb_label': '26569.a2', 'modell_image': '163B.1.145', 'prime': 163}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 1269282
    {'lmfdb_iso': '26569.a', 'p': 41, 'prec': 20, 'unit': 1129764015537706194196512452281, 'val': 1}
  • id: 1269283
    {'lmfdb_iso': '26569.a', 'p': 43, 'prec': 20, 'unit': 9853644056858577604527317379807, 'val': 1}
  • id: 1269284
    {'lmfdb_iso': '26569.a', 'p': 47, 'prec': 20, 'unit': 30903219111947943304997604283798, 'val': 1}
  • id: 1269286
    {'lmfdb_iso': '26569.a', 'p': 53, 'prec': 20, 'unit': 388049201831888915246579690973740, 'val': 1}
  • id: 1269287
    {'lmfdb_iso': '26569.a', 'p': 61, 'prec': 20, 'unit': 1195267767848760617553269909749420, 'val': 1}
  • id: 1269281
    {'lmfdb_iso': '26569.a', 'p': 71, 'prec': 20, 'unit': 119056413426362748410683547419393399, 'val': 1}
  • id: 1269285
    {'lmfdb_iso': '26569.a', 'p': 83, 'prec': 20, 'unit': 1065552614326952358571565579449388869, 'val': 1}
  • id: 1269280
    {'lmfdb_iso': '26569.a', 'p': 97, 'prec': 20, 'unit': 8669502470034679292703352207251748059, 'val': 1}