Elliptic curve data - 196800.jb1

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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': '196800cd', 'Clabel': '196800cd1', 'Cnumber': 1, 'abc_quality': 0.9429210147333399, 'absD': 870580224000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 328, 'ainvs': [0, 1, 0, -106433, -13324737], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 41], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 196800, 'degree': 1179648, 'elladic_images': ['8.6.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7025757859483187150190734263', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 235, 'isogeny_degrees': [1, 2], 'jinv': [32553430057, 212544], 'lmfdb_iso': '196800.jb', 'lmfdb_label': '196800.jb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -66, 180], 'min_quad_twist_disc': -40, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.d.1', '82.6.0.?', '328.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0250313770450851665697626070', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1025], [3, 4, 65600], [5, 14, 7872], [41, 42, 4800]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.14186394110864943640715442250', 'prec': 107}, 'szpiro_ratio': 3.801447168437571, '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, 0, 0, 2, 0, 1, 0, -4, 0, -4, 0, 0, 0, 2, 0, -8, 0], 'aplist': [0, 1, 0, 2, -4, -4, 2, -8, 4, 8, -4, 2, -1, -4, -2, 4, 12, 6, -16, -6, 2, 14, -4, -6, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 196800, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '196800.jb', 'trace_hash': 1387290750762136425}
• 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': '0.033201787242717730047250162637', 'prec': 107}, 'conductor': 196800, 'gens': [[-182, 225, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0250313770450851665697626070', 'prec': 100}], 'lmfdb_label': '196800.jb1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.26442406594005171076571467350', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.5674724859910930937769925163082074116', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-177, 0, 1]], 'xcoord_integral_points': [-182, -177, 2383]}
• lmfdb_label 196800.jb1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8645570
    {'degree': 2, 'field': [-10, -1, 1], 'lmfdb_label': '196800.jb1', 'torsion': [2, 2]}
  • id: 8645571
    {'degree': 4, 'field': [66, -8, 9, -2, 1], 'lmfdb_label': '196800.jb1', 'torsion': [4]}
  • id: 8645574
    {'degree': 8, 'field': [-120000, 0, 53000, 0, 1200, 0, 0, 0, 1], 'lmfdb_label': '196800.jb1', 'torsion': [6]}
  • id: 8645572
    {'degree': 8, 'field': [1314, 312, 421, 214, 97, -60, 7, -2, 1], 'lmfdb_label': '196800.jb1', 'torsion': [2, 4]}
  • id: 8645573
    {'degree': 8, 'field': [69696, 48576, -2456, 1168, 916, -84, -59, -2, 1], 'lmfdb_label': '196800.jb1', 'torsion': [2, 4]}
  • id: 8645575
    {'degree': 16, 'field': [167184, -800064, 1631664, -1910928, 1822222, -1466768, 930096, -517168, 233507, -87528, 31680, -8016, 2306, -400, 84, -8, 1], 'lmfdb_label': '196800.jb1', 'torsion': [8]}
  • id: 8645576
    {'degree': 16, 'field': [289111580000, 100005820000, -101725427000, 3517944000, -1943862800, 188350400, -6605600, -48795920, 13039641, -616328, 178028, -28456, 3590, 504, -52, -8, 1], 'lmfdb_label': '196800.jb1', '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: 4873619
    {'conductor': 196800, 'conductor_valuation': 6, 'discriminant_valuation': 24, 'j_denominator_valuation': 6, 'kodaira_symbol': -18, 'lmfdb_label': '196800.jb1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4873620
    {'conductor': 196800, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '196800.jb1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4873621
    {'conductor': 196800, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '196800.jb1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4873622
    {'conductor': 196800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '196800.jb1', 'prime': 41, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 2926404
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [325, 4, 324, 5], [1, 2, 2, 5], [1, 4, 0, 1], [165, 4, 2, 9], [209, 124, 40, 287], [258, 1, 199, 0]], 'adelic_image': '328.12.0.?', 'conductor': 196800, 'lmfdb_label': '196800.jb1', 'prime': 0}
  • id: 731377
    {'conductor': 196800, 'elladic_image': '8.6.0.4', 'lmfdb_label': '196800.jb1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 196800.jb does not appear in ec_padic