Elliptic curve data - 209814.bl1

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

  
  {'Ciso': '209814bv', 'Clabel': '209814bv3', 'Cnumber': 3, 'abc_quality': 0.96548780150265, 'absD': 2804868770121323045625474, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1496, 'ainvs': [1, 0, 1, -67735682, 198862833530], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 209814, 'degree': 53084160, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4338136649598371772086792570', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 37, 'isogeny_degrees': [1, 2, 4], 'jinv': [803760366578833, 65593817586], 'lmfdb_iso': '209814.bl', 'lmfdb_label': '209814.bl1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1937, -31219], 'min_quad_twist_disc': -187, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '44.12.0-4.c.1.1', '88.24.0.?', '136.24.0.?', '1496.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '23.042272898962816922121689431', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 34969], [3, 4, 69938], [11, 72, 1734], [17, 162, 726]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.81825935653254386505294015908', 'prec': 103}, 'szpiro_ratio': 5.362093921277024, '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, 4, -1, 1, 2, 0, 1, 2, -4, -2, 1, 0, -1, -4, -2], 'aplist': [-1, 1, -2, 4, 0, 2, 0, -4, 4, -6, 4, -2, 10, -4, -8, 6, -4, -6, 12, 12, 2, 4, 4, 10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 209814, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '209814.bl', 'trace_hash': 2199669218815840275}
• 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': '0.0010409439534750477057699758794', 'prec': 110}, 'conductor': 209814, 'gens': [[291373588047, 78172198041866231, 6278]], 'heights': [{'__RealLiteral__': 0, 'data': '23.042272898962816922121689431', 'prec': 100}], 'lmfdb_label': '209814.bl1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.078712982676104519846008177320', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.2549041100565315262968086901554608124', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[23063, -23067, 2]], 'xcoord_integral_points': []}
• lmfdb_label 209814.bl1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9171818
    {'degree': 2, 'field': [-374, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [4]}
  • id: 9171816
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 2]}
  • id: 9171817
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [4]}
  • id: 9171819
    {'degree': 4, 'field': [529, 0, -90, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 4]}
  • id: 9171821
    {'degree': 8, 'field': [-14522, 30078, -14465, -4870, 3581, 250, -123, -2, 1], 'lmfdb_label': '209814.bl1', 'torsion': [8]}
  • id: 9171822
    {'degree': 8, 'field': [68644, 0, 7824, 0, 902, 0, 48, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [8]}
  • id: 9171820
    {'degree': 8, 'field': [1489689, -39276, 36882, 4776, -2357, -40, 18, -4, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 4]}
  • id: 9171823
    {'degree': 8, 'field': [2567151, 2608425, 776349, 70470, 1332, 936, 73, -1, 1], 'lmfdb_label': '209814.bl1', 'torsion': [6]}
  • id: 9171826
    {'degree': 16, 'field': [668286, 1020780, -3377670, -5536524, 3275395, 5810228, -1613790, -2126428, 497565, 305572, -70794, -18644, 4377, 476, -114, -4, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 8]}
  • id: 9171825
    {'degree': 16, 'field': [5564900, 399520, 1681216, -3129248, 718296, -874320, 215024, -100288, 122248, -17856, 25360, -1520, 2068, -56, 72, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 8]}
  • id: 9171828
    {'degree': 16, 'field': [7750656, 0, -25850619, 0, -2521494, 0, -781613, 0, -42373, 0, 223, 0, 607, 0, -22, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [12]}
  • id: 9171827
    {'degree': 16, 'field': [780420096, 0, -571162752, 0, 63137664, 0, -6297952, 0, 388976, 0, -44632, 0, 1660, 0, -68, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 6]}
  • id: 9171824
    {'degree': 16, 'field': [9188947881, 0, 1822692780, 0, 242132670, 0, 10260000, 0, 331231, 0, 5080, 0, 1410, 0, -20, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [4, 4]}
  • id: 9171829
    {'degree': 16, 'field': [641485661184, 0, 357820563744, 0, 78325769124, 0, 7041726288, 0, 198258804, 0, -3467988, 0, -47612, 0, -22, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [12]}
• 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: 5199746
    {'conductor': 209814, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '209814.bl1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5199747
    {'conductor': 209814, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '209814.bl1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5199748
    {'conductor': 209814, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '209814.bl1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5199749
    {'conductor': 209814, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '209814.bl1', 'prime': 17, '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: 3006535
    {'adelic_gens': [[331, 1276, 506, 397], [7, 6, 1490, 1491], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [496, 297, 451, 166], [384, 1221, 1243, 406], [1087, 0, 0, 1495], [1489, 8, 1488, 9]], 'adelic_image': '1496.48.0.?', 'conductor': 209814, 'lmfdb_label': '209814.bl1', 'prime': 0}
  • id: 774312
    {'conductor': 209814, 'elladic_image': '8.12.0.11', 'lmfdb_label': '209814.bl1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 209814.bl does not appear in ec_padic