Elliptic curve data - 251826.f3

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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': '251826f', 'Clabel': '251826f4', 'Cnumber': 4, 'abc_quality': 1.0442736790304261, 'absD': 23889473936775236402208, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 21432, 'ainvs': [1, 1, 1, -11734254, 17160943947], 'analytic_rank': 0, 'bad_primes': [2, 3, 19, 47], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 251826, 'degree': 25259520, 'elladic_images': ['8.12.0.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0265130843646238857652257771', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4], 'jinv': [-16576888679672833, 2216253521952], 'lmfdb_iso': '251826.f', 'lmfdb_label': '251826.f3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5312, -167551], 'min_quad_twist_disc': -47, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.d.1', '188.12.0.?', '376.24.0.?', '456.24.0.?', '21432.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1014392835095945923547504422', 'prec': 100}, 'szpiro_ratio': 4.877220287703645, '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, -1, 1, -2, -1, 0, 1, 1, -2, 4, -1, -2, 0, 2, 1, -6, 1, 1, -2], 'aplist': [1, -1, -2, 0, 4, -2, -6, 1, 4, 2, -4, 10, -10, -4, 0, -10, 12, 14, 12, 8, 6, -4, 12, -6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 251826, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '251826.f', 'trace_hash': 162490666610014226}
• 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': '0.0023507375036291973879899172394', 'prec': 110}, 'conductor': 251826, 'gens': [], 'heights': [], 'lmfdb_label': '251826.f3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.11613150378196713938321183473', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3226300756393427876642366946668725944', 'prec': 130}, 'tamagawa_product': 80, 'torsion_generators': [[-16013, 16009, 2]], 'xcoord_integral_points': []}
• lmfdb_label 251826.f3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10831931
    {'degree': 2, 'field': [-47, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [4]}
  • id: 10831930
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [2, 2]}
  • id: 10831932
    {'degree': 2, 'field': [94, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [4]}
  • id: 10831933
    {'degree': 4, 'field': [529, 0, 48, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [2, 4]}
  • id: 10831937
    {'degree': 8, 'field': [-491076, 187992, 153074, 27105, 2772, -277, -15, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [6]}
  • id: 10831935
    {'degree': 8, 'field': [-323276, 128204, 109546, -54940, 5454, -914, 145, -2, 1], 'lmfdb_label': '251826.f3', 'torsion': [8]}
  • id: 10831934
    {'degree': 8, 'field': [21222, -6632, 7500, -1784, 1013, -148, 54, -4, 1], 'lmfdb_label': '251826.f3', 'torsion': [2, 4]}
  • id: 10831936
    {'degree': 8, 'field': [7805980, 1230288, 173928, 51072, 5456, -456, -36, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [8]}
  • id: 10831938
    {'degree': 16, 'field': [228267378, -185624808, 251797748, -145381992, 106808330, -45324848, 22744464, -7218568, 2678963, -634632, 180184, -30984, 6802, -784, 132, -8, 1], 'lmfdb_label': '251826.f3', 'torsion': [4, 4]}
  • id: 10831940
    {'degree': 16, 'field': [295014976, 0, -72173856, 0, 27421204, 0, -4187004, 0, 1130001, 0, -109416, 0, 4906, 0, -108, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [2, 8]}
  • id: 10831942
    {'degree': 16, 'field': [330803344, 0, -253218976, 0, 77746204, 0, -13128975, 0, 1364514, 0, -91143, 0, 3853, 0, -94, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [12]}
  • id: 10831939
    {'degree': 16, 'field': [30472777828, 12318068448, 1069472672, 3126896416, 312818488, 288471536, 220829552, 9105472, 25161352, -55840, 1140608, -7184, 24388, -88, 248, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [2, 8]}
  • id: 10831943
    {'degree': 16, 'field': [94634986384, 0, 31481748968, 0, 4666636276, 0, 398195640, 0, 21268404, 0, 726324, 0, 15472, 0, 188, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [12]}
  • id: 10831941
    {'degree': 16, 'field': [653000780552, 119317605408, 20711057372, 58219144696, 37738464170, 10783696756, 1571111385, 28153060, -20961648, -2637614, 279609, 60304, 5581, -554, -14, 0, 1], 'lmfdb_label': '251826.f3', 'torsion': [2, 6]}
• 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: 6244389
    {'conductor': 251826, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '251826.f3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 6244390
    {'conductor': 251826, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '251826.f3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6244391
    {'conductor': 251826, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '251826.f3', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6244392
    {'conductor': 251826, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '251826.f3', 'prime': 47, '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: 3262081
    {'adelic_gens': [[1, 0, 8, 1], [3191, 0, 0, 21431], [7, 6, 21426, 21427], [1, 8, 0, 1], [2680, 19787, 5875, 6816], [1, 4, 4, 17], [7145, 6392, 10340, 4137], [20352, 3713, 7003, 6534], [21425, 8, 21424, 9], [12409, 6392, 9964, 4137]], 'adelic_image': '21432.48.0.?', 'conductor': 251826, 'lmfdb_label': '251826.f3', 'prime': 0}
  • id: 907900
    {'conductor': 251826, 'elladic_image': '8.12.0.16', 'lmfdb_label': '251826.f3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 251826.f does not appear in ec_padic