Elliptic curve data - 198744.n6

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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': '198744dl', 'Clabel': '198744dl4', 'Cnumber': 4, 'abc_quality': 0.9517736927221875, 'absD': 392209846423674300822528, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 4368, 'ainvs': [0, -1, 0, 14041816, 22304984220], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 198744, 'degree': 16515072, 'elladic_images': ['16.24.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2131299262858586721692358563', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [526556774012, 674481717], 'lmfdb_iso': '198744.n', 'lmfdb_label': '198744.n6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 1696, -29040], 'min_quad_twist_disc': -91, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.2', '24.24.0.bz.2', '28.12.0-4.c.1.1', '48.48.0-24.bz.2.6', '52.12.0.h.1', '56.24.0-8.n.1.9', '104.24.0.?', '112.48.0.?', '168.48.0.?', '208.48.0.?', '312.48.0.?', '336.96.0.?', '364.24.0.?', '624.96.0.?', '728.48.0.?', '1456.96.0.?', '2184.96.0.?', '4368.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 8281], [3, 4, 66248], [7, 32, 4056], [13, 98, 1176]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.38007752256081256040878899591', 'prec': 103}, 'szpiro_ratio': 5.014824289479549, '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, 0, -1, 0, -2, 0, 0, 0, 1, 0, 4, 0, 0, 0, 2, 0, -2, 0, -4, 0], 'aplist': [0, -1, -2, 0, 4, 0, -2, -4, 0, -2, 0, 2, -6, 4, -8, -10, -4, 2, 4, 0, 2, 8, -12, -6, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 198744, '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': '198744.n', 'trace_hash': 673884528648890094}
• 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': '0.0016184929304499379327684011740', 'prec': 110}, 'conductor': 198744, 'gens': [], 'heights': [], 'lmfdb_label': '198744.n6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.063794151554895070566982723209', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.51035321243916056453586178567275500255', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-1395, 0, 1]], 'xcoord_integral_points': [-1395]}
• lmfdb_label 198744.n6 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8720981
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [4]}
  • id: 8720980
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [2, 2]}
  • id: 8720982
    {'degree': 2, 'field': [23, -1, 1], 'lmfdb_label': '198744.n6', 'torsion': [4]}
  • id: 8720983
    {'degree': 4, 'field': [25, 0, 3, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [2, 4]}
  • id: 8720984
    {'degree': 4, 'field': [295, -58, 59, -2, 1], 'lmfdb_label': '198744.n6', 'torsion': [8]}
  • id: 8720985
    {'degree': 4, 'field': [900, 0, -18, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [8]}
  • id: 8720989
    {'degree': 8, 'field': [-16070876, -3380272, 72724, 86372, 6784, -652, -20, -4, 1], 'lmfdb_label': '198744.n6', 'torsion': [6]}
  • id: 8720987
    {'degree': 8, 'field': [9, 0, -5740, 0, 190, 0, -28, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [8]}
  • id: 8720988
    {'degree': 8, 'field': [1849, 0, -894, 0, 311, 0, 30, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [2, 8]}
  • id: 8720986
    {'degree': 8, 'field': [3654, -3276, 1332, -234, 163, -78, 20, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [2, 4]}
  • id: 8720995
    {'degree': 16, 'field': [-1757618028, 4524088464, -2168333640, -777912912, 148596732, 252101928, -51086904, -14156952, 2472292, 100864, 2440, -15008, 1516, 652, -80, -8, 1], 'lmfdb_label': '198744.n6', 'torsion': [12]}
  • id: 8720991
    {'degree': 16, 'field': [39204, 0, 122472, 0, 110632, 0, 20052, 0, -3187, 0, -96, 0, 122, 0, -12, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [2, 8]}
  • id: 8720990
    {'degree': 16, 'field': [1432809, 0, -1283688, 0, 450594, 0, -75816, 0, 4243, 0, -104, 0, 222, 0, 16, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [4, 4]}
  • id: 8720994
    {'degree': 16, 'field': [134189056, 0, 1231314944, 0, 274376704, 0, 73554432, 0, 4195968, 0, 135744, 0, 4144, 0, 104, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [2, 6]}
  • id: 8720993
    {'degree': 16, 'field': [187388721, 0, 0, 0, 277612920, 0, 0, 0, 9834786, 0, 0, 0, 20280, 0, 0, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [16]}
  • id: 8720992
    {'degree': 16, 'field': [223602913, -276225936, 98269248, -16006032, 2758960, -1699488, 3607440, 373632, 262089, 19824, 10956, -168, -290, -168, 36, 0, 1], 'lmfdb_label': '198744.n6', 'torsion': [2, 16]}
  • id: 8720996
    {'degree': 16, 'field': [52816652333, -46980925592, 52048928464, -10459816824, 6057543322, -1044549352, 435905500, -79390544, 25203219, -3736232, 915740, -95296, 18734, -1344, 212, -8, 1], 'lmfdb_label': '198744.n6', '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: 4920392
    {'conductor': 198744, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '198744.n6', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4920393
    {'conductor': 198744, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '198744.n6', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4920394
    {'conductor': 198744, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '198744.n6', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4920395
    {'conductor': 198744, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '198744.n6', 'prime': 13, '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: 2937741
    {'adelic_gens': [[15, 2, 4270, 4355], [2672, 4363, 3405, 14], [5, 4, 4364, 4365], [1469, 16, 2656, 4053], [1, 16, 0, 1], [13, 16, 1356, 1417], [4353, 16, 4352, 17], [3119, 4352, 3112, 4239], [1, 0, 16, 1], [2746, 3283, 1871, 2286]], 'adelic_image': '4368.192.1.?', 'conductor': 198744, 'lmfdb_label': '198744.n6', 'prime': 0}
  • id: 737592
    {'conductor': 198744, 'elladic_image': '16.24.0.8', 'lmfdb_label': '198744.n6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 198744.n does not appear in ec_padic