Elliptic curve data - 209814.t2

Formats: - HTML - YAML - JSON - 2025-10-20T13:01:00.097072

• 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': '209814db', 'Clabel': '209814db3', 'Cnumber': 3, 'abc_quality': 1.0315574162602832, 'absD': 1157151799168559208036, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1496, 'ainvs': [1, 1, 0, -60636974, 181708987200], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 209814, 'degree': 23592960, 'elladic_images': ['8.48.0.137'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1160590037887929116849500939', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 4], 'jinv': [576615941610337, 27060804], 'lmfdb_iso': '209814.t', 'lmfdb_label': '209814.t2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1734, -27936], 'min_quad_twist_disc': -187, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.e.1', '88.96.0.?', '136.96.1.?', '748.24.0.?', '1496.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 34969], [3, 4, 69938], [11, 62, 1734], [17, 162, 726]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.50050469536149959952921099598', 'prec': 103}, 'szpiro_ratio': 5.334990496090574, '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, 2, 1, 0, -1, 1, -2, 0, -1, 2, 0, -2, 1, 0, -1, -4, 2], 'aplist': [-1, -1, 2, 0, 0, 2, 0, -4, 0, -10, -8, 2, 10, -12, 0, 6, 12, -10, -12, 0, 10, -8, -4, -6, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 209814, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '209814.t', 'trace_hash': 866701622051950969}
• 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': '0.0019652849969192308678094309800', 'prec': 110}, 'conductor': 209814, 'gens': [], 'heights': [], 'lmfdb_label': '209814.t2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14530117739920386412445346560', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.58120470959681545649781386241642861655', 'prec': 133}, 'tamagawa_product': 64, 'torsion_generators': [[-8992, 4496, 1], [4472, -2236, 1]], 'xcoord_integral_points': [-8992, 4472]}
• lmfdb_label 209814.t2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9172307
    {'degree': 2, 'field': [-187, 0, 1], 'lmfdb_label': '209814.t2', 'torsion': [2, 4]}
  • id: 9172309
    {'degree': 4, 'field': [2027, -98, 99, -2, 1], 'lmfdb_label': '209814.t2', 'torsion': [2, 4]}
  • id: 9172308
    {'degree': 4, 'field': [2399, -90, 91, -2, 1], 'lmfdb_label': '209814.t2', 'torsion': [2, 4]}
  • id: 9172314
    {'degree': 8, 'field': [-1929831, -542280, -784, 23976, 2274, -256, -12, 0, 1], 'lmfdb_label': '209814.t2', 'torsion': [2, 6]}
  • id: 9172312
    {'degree': 8, 'field': [-18, 228, 146, -708, 255, 116, -34, -4, 1], 'lmfdb_label': '209814.t2', 'torsion': [2, 8]}
  • id: 9172311
    {'degree': 8, 'field': [53, -262, 492, -490, 321, -94, 36, -4, 1], 'lmfdb_label': '209814.t2', 'torsion': [2, 8]}
  • id: 9172310
    {'degree': 8, 'field': [4879681, 0, 0, 0, 4231, 0, 0, 0, 1], 'lmfdb_label': '209814.t2', 'torsion': [4, 4]}
  • id: 9172313
    {'degree': 8, 'field': [4956163, -405212, 418502, -26768, 13855, -568, 194, -4, 1], 'lmfdb_label': '209814.t2', 'torsion': [2, 8]}
  • id: 9172317
    {'degree': 16, 'field': [2809, 0, -12460, 0, 56718, 0, -71864, 0, 35059, 0, 376, 0, 390, 0, -4, 0, 1], 'lmfdb_label': '209814.t2', 'torsion': [4, 8]}
  • id: 9172315
    {'degree': 16, 'field': [18722929, 0, 5476884, 0, -2342714, 0, -301248, 0, 128823, 0, -2088, 0, 178, 0, -12, 0, 1], 'lmfdb_label': '209814.t2', 'torsion': [2, 8]}
  • id: 9172318
    {'degree': 16, 'field': [112956169824, 134931562416, 127009486188, 66200652636, 5939417361, 257600484, 393564268, -125569828, 21502383, -2506180, 149968, -45132, 6775, -520, -12, -4, 1], 'lmfdb_label': '209814.t2', 'torsion': [2, 12]}
  • id: 9172316
    {'degree': 16, 'field': [14419779627289, 633936842160, -2840686567968, -66501228048, 245307309808, 2662272960, -11829656904, -46059456, 344518449, 217632, -6177036, 2568, 66598, -24, -396, 0, 1], 'lmfdb_label': '209814.t2', 'torsion': [4, 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: 5199970
    {'conductor': 209814, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '209814.t2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5199971
    {'conductor': 209814, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '209814.t2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5199972
    {'conductor': 209814, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '209814.t2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5199973
    {'conductor': 209814, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '209814.t2', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 3006659
    {'adelic_gens': [[5, 4, 1492, 1493], [683, 110, 638, 1475], [1, 0, 8, 1], [1, 8, 0, 1], [1, 858, 0, 375], [439, 264, 396, 1055], [1087, 0, 0, 1495], [1489, 8, 1488, 9]], 'adelic_image': '1496.192.1.?', 'conductor': 209814, 'lmfdb_label': '209814.t2', 'prime': 0}
  • id: 774429
    {'conductor': 209814, 'elladic_image': '8.48.0.137', 'lmfdb_label': '209814.t2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 209814.t does not appear in ec_padic