Elliptic curve data - 25886.d1

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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': '25886a', 'Clabel': '25886a6', 'Cnumber': 6, 'abc_quality': 1.0648884149541868, 'absD': 158590356173312, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 21672, 'ainvs': [1, 1, 1, -5048733, 4364278259], 'analytic_rank': 1, 'bad_primes': [2, 7, 43], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 25886, 'degree': 471744, 'elladic_images': ['8.6.0.6', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2937010382698656693172036115', 'prec': 97}, 'faltings_index': 5, 'faltings_ratio': 18, 'intrinsic_torsion': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [2251439055699625, 25088], 'lmfdb_iso': '25886.d', 'lmfdb_label': '25886.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -2731, -55146], 'min_quad_twist_disc': -43, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.b.1', '9.12.0.a.1', '18.36.0.a.1', '24.24.0.y.1', '28.6.0.c.1', '56.12.0.k.1', '63.36.0.d.1', '72.72.1.?', '84.24.0.?', '126.108.2.?', '129.8.0.?', '168.48.1.?', '252.216.7.?', '258.24.0.?', '387.24.0.?', '504.432.21.?', '774.72.0.?', '1032.48.0.?', '2709.72.0.?', '3096.144.1.?', '3612.48.0.?', '5418.216.2.?', '7224.96.1.?', '10836.432.7.?', '21672.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.0552475265220546043050847513', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 1849], [3, 2, 12943], [7, 8, 3698], [43, 926, 14]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.41310098042308445758078235483', 'prec': 97}, 'szpiro_ratio': 5.699728246017661, '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, 2, 1, 0, 2, -1, 1, 1, 0, 0, 2, -4, -1, 0, 1, 6, 1, -2, 0], 'aplist': [1, 2, 0, -1, 0, -4, 6, -2, 0, 6, -4, -2, 6, 0, -12, 6, -6, -8, -4, 0, -2, 8, -6, 6, -10], 'class_deg': 18, 'class_size': 6, 'conductor': 25886, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '25886.d', 'trace_hash': 1427945667270373716}
• 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': '0.010179269013883783668596337089', 'prec': 97}, 'conductor': 25886, 'gens': [[1281, 346, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.0552475265220546043050847513', 'prec': 97}], 'lmfdb_label': '25886.d1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.40427103807994209896552581636', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '11.116332802244218004140499384899309912', 'prec': 127}, 'tamagawa_product': 36, 'torsion_generators': [[5187, -5191, 2]], 'xcoord_integral_points': [1281]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 0], '5': [1, 3, 0], '7': [1, 0], '11': [1, 3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': 'a', '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '25886.d1'}
• ec_torsion_growth •

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

  
  
  • id: 1303442
    {'degree': 2, 'field': [-32, -1, 1], 'lmfdb_label': '25886.d1', 'torsion': [6]}
  • id: 1303441
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '25886.d1', 'torsion': [2, 2]}
  • id: 1303444
    {'degree': 4, 'field': [898, 68, -67, -2, 1], 'lmfdb_label': '25886.d1', 'torsion': [2, 6]}
  • id: 1303443
    {'degree': 4, 'field': [3698, 0, 43, 0, 1], 'lmfdb_label': '25886.d1', 'torsion': [4]}
  • id: 1303446
    {'degree': 6, 'field': [-288, -7776, 3438, 219, -135, -3, 1], 'lmfdb_label': '25886.d1', 'torsion': [18]}
  • id: 1303445
    {'degree': 6, 'field': [1604, -804, 375, -53, 36, -3, 1], 'lmfdb_label': '25886.d1', 'torsion': [6]}
  • id: 1303449
    {'degree': 8, 'field': [40000, 0, 4600, 0, 758, 0, 23, 0, 1], 'lmfdb_label': '25886.d1', 'torsion': [12]}
  • id: 1303447
    {'degree': 8, 'field': [80656, 0, -5984, 0, -122, 0, -8, 0, 1], 'lmfdb_label': '25886.d1', 'torsion': [2, 4]}
  • id: 1303448
    {'degree': 8, 'field': [896809, 0, 30318, 0, 2122, 0, 46, 0, 1], 'lmfdb_label': '25886.d1', 'torsion': [2, 4]}
  • id: 1303453
    {'degree': 12, 'field': [-71369864, 92113536, 15089820, -51168984, 10667310, 3650088, -921715, -102030, 25377, 1308, -273, -6, 1], 'lmfdb_label': '25886.d1', 'torsion': [2, 18]}
  • id: 1303451
    {'degree': 12, 'field': [1952704, -1378896, 1339260, -555750, 313497, -92760, 37787, -7854, 2454, -342, 81, -6, 1], 'lmfdb_label': '25886.d1', 'torsion': [18]}
  • id: 1303450
    {'degree': 12, 'field': [2572816, -1289616, 44916, -131476, 40269, 33201, -9895, -462, 762, -2, -27, -3, 1], 'lmfdb_label': '25886.d1', 'torsion': [3, 6]}
  • id: 1303452
    {'degree': 12, 'field': [4579868, -2007528, 2679168, -1007040, 416739, -119970, 32977, -6186, 1902, -262, 69, -6, 1], 'lmfdb_label': '25886.d1', 'torsion': [2, 6]}
  • id: 1303455
    {'degree': 16, 'field': [597704704, 0, -274927616, 0, -55887648, 0, -955648, 0, 844004, 0, -2800, 0, -1836, 0, -8, 0, 1], 'lmfdb_label': '25886.d1', 'torsion': [2, 12]}
  • id: 1303456
    {'degree': 16, 'field': [2749114624, 0, 1100070400, 0, 150035472, 0, 10403104, 0, 824088, 0, 44992, 0, 1697, 0, 30, 0, 1], 'lmfdb_label': '25886.d1', 'torsion': [2, 12]}
  • id: 1303454
    {'degree': 16, 'field': [41965980736, 0, -5479258624, 0, 1074338066, 0, -18313988, 0, -349315, 0, -63602, 0, 5436, 0, -126, 0, 1], 'lmfdb_label': '25886.d1', 'torsion': [8]}
• 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: 596537
    {'conductor': 25886, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '25886.d1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 596538
    {'conductor': 25886, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '25886.d1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 596539
    {'conductor': 25886, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '25886.d1', '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: 1836997
    {'adelic_gens': [[21637, 36, 21636, 37], [16255, 1548, 14878, 15481], [1, 0, 36, 1], [18143, 0, 0, 21671], [1, 18, 14, 253], [1, 36, 0, 1], [21415, 1548, 6794, 11095], [19, 36, 3240, 6139], [6580, 6579, 18705, 7354], [17029, 1548, 18232, 15653]], 'adelic_image': '21672.864.21.?', 'conductor': 25886, 'lmfdb_label': '25886.d1', 'prime': 0}
  • id: 117976
    {'conductor': 25886, 'elladic_image': '8.6.0.6', 'lmfdb_label': '25886.d1', 'modell_image': '2B', 'prime': 2}
  • id: 117977
    {'conductor': 25886, 'elladic_image': '9.12.0.1', 'lmfdb_label': '25886.d1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1234894
    {'lmfdb_iso': '25886.d', 'p': 13, 'prec': 20, 'unit': 1321489935879391083109, 'val': 1}
  • id: 1234896
    {'lmfdb_iso': '25886.d', 'p': 17, 'prec': 20, 'unit': 227181513904412682466909, 'val': 1}
  • id: 1234888
    {'lmfdb_iso': '25886.d', 'p': 19, 'prec': 20, 'unit': 932891597919485671840300, 'val': 1}
  • id: 1234893
    {'lmfdb_iso': '25886.d', 'p': 29, 'prec': 20, 'unit': 345581235330418874869032534, 'val': 1}
  • id: 1234904
    {'lmfdb_iso': '25886.d', 'p': 31, 'prec': 20, 'unit': 951583228407670919812734306, 'val': 1}
  • id: 1234891
    {'lmfdb_iso': '25886.d', 'p': 37, 'prec': 20, 'unit': 258424937826325756844623511434, 'val': 1}
  • id: 1234892
    {'lmfdb_iso': '25886.d', 'p': 41, 'prec': 20, 'unit': 3805018600378251827406870804957, 'val': 1}
  • id: 1234902
    {'lmfdb_iso': '25886.d', 'p': 47, 'prec': 20, 'unit': 49494585120423627683950483258443, 'val': 1}
  • id: 1234898
    {'lmfdb_iso': '25886.d', 'p': 53, 'prec': 20, 'unit': 289118675886762199401733868458930, 'val': 1}
  • id: 1234899
    {'lmfdb_iso': '25886.d', 'p': 59, 'prec': 20, 'unit': 4104061986015061801479775446430373, 'val': 1}
  • id: 1234903
    {'lmfdb_iso': '25886.d', 'p': 61, 'prec': 20, 'unit': 3330698512945758784031058319684919, 'val': 1}
  • id: 1234890
    {'lmfdb_iso': '25886.d', 'p': 67, 'prec': 20, 'unit': 34446521140480907517801613639024653, 'val': 1}
  • id: 1234900
    {'lmfdb_iso': '25886.d', 'p': 73, 'prec': 20, 'unit': 225306837900310333863024607319799793, 'val': 1}
  • id: 1234895
    {'lmfdb_iso': '25886.d', 'p': 79, 'prec': 20, 'unit': 1064143513688706981118507868936874576, 'val': 1}
  • id: 1234897
    {'lmfdb_iso': '25886.d', 'p': 83, 'prec': 20, 'unit': 415546316676310098380173447070938459, 'val': 1}
  • id: 1234901
    {'lmfdb_iso': '25886.d', 'p': 89, 'prec': 20, 'unit': 627474919666511914735370949136059543, 'val': 1}
  • id: 1234889
    {'lmfdb_iso': '25886.d', 'p': 97, 'prec': 20, 'unit': 14566089821525593264392418536008519498, 'val': 1}