Elliptic curve data - 99372.b1

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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': '99372ba', 'Clabel': '99372ba1', 'Cnumber': 1, 'abc_quality': 1.1844185766908968, 'absD': 3192247514571150672, 'adelic_genus': 3, 'adelic_index': 96, 'adelic_level': 4368, 'ainvs': [0, -1, 0, -24963605, 48015742566], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 99372, 'degree': 6635520, 'elladic_images': ['8.12.0.31'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8066064051620786893987148752', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [416013434950254592, 771895089], 'lmfdb_iso': '99372.b', 'lmfdb_label': '99372.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -509461, -140133148], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.e.1', '8.12.0.v.1', '26.6.0.b.1', '28.12.0.m.1', '48.24.0.m.2', '52.12.0.k.1', '56.24.0.ec.1', '104.24.0.?', '336.48.1.?', '364.24.0.?', '624.48.0.?', '728.48.1.?', '4368.96.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 637], [3, 4, 33124], [7, 32, 2028], [13, 50, 588]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.96136493108238941636025593593', 'prec': 103}, 'szpiro_ratio': 5.4501113946711675, '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, -4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0], 'aplist': [0, -1, -4, 0, 0, 0, -2, 0, -4, 2, -8, 8, 4, 8, 0, 6, 8, 10, 8, 0, 4, 12, 8, 12, -12], 'class_deg': 2, 'class_size': 2, 'conductor': 99372, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '99372.b', 'trace_hash': 508029029802776559}
• 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': '0.0036493259111357297593117977891', 'prec': 110}, 'conductor': 99372, 'gens': [], 'heights': [], 'lmfdb_label': '99372.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.21612244197568617099498176899', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2967346518541170259698906139261834280', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[2882, 0, 1]], 'xcoord_integral_points': [2882]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '7': 'a', '13': 'a'}, 'iwp0': 5, 'lmfdb_label': '99372.b1'}
• ec_torsion_growth •

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

  
  
  • id: 4615928
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '99372.b1', 'torsion': [2, 2]}
  • id: 4615929
    {'degree': 4, 'field': [126, 84, 8, -2, 1], 'lmfdb_label': '99372.b1', 'torsion': [4]}
  • id: 4615932
    {'degree': 8, 'field': [-5862, -351, -5438, -5499, -1437, -39, 9, 0, 1], 'lmfdb_label': '99372.b1', 'torsion': [6]}
  • id: 4615931
    {'degree': 8, 'field': [729, -162, -702, -450, -153, 14, 0, -4, 1], 'lmfdb_label': '99372.b1', 'torsion': [2, 4]}
  • id: 4615930
    {'degree': 8, 'field': [25281, 318, 2, -642, 327, -10, 8, -4, 1], 'lmfdb_label': '99372.b1', 'torsion': [2, 4]}
  • id: 4615933
    {'degree': 16, 'field': [2809, 0, -4904, 0, 2458, 0, -936, 0, 603, 0, 312, 0, 118, 0, 16, 0, 1], 'lmfdb_label': '99372.b1', 'torsion': [4, 4]}
  • id: 4615934
    {'degree': 16, 'field': [515524, 0, -604576, 0, 249776, 0, -38136, 0, 4940, 0, -1344, 0, 284, 0, -28, 0, 1], 'lmfdb_label': '99372.b1', 'torsion': [8]}
  • id: 4615935
    {'degree': 16, 'field': [3583459044, 0, -637579392, 0, 26802688, 0, 3192207, 0, -8250, 0, -2641, 0, -363, 0, -18, 0, 1], 'lmfdb_label': '99372.b1', '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: 2439053
    {'conductor': 99372, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '99372.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2439054
    {'conductor': 99372, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '99372.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2439055
    {'conductor': 99372, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '99372.b1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2439056
    {'conductor': 99372, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '99372.b1', '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: 2317307
    {'adelic_gens': [[11, 16, 4304, 4275], [1, 16, 0, 1], [13, 8, 8, 5], [4353, 16, 4352, 17], [1696, 5, 2403, 16], [1877, 26, 3014, 3817], [3, 28, 4292, 3659], [1, 0, 16, 1], [3831, 10, 1010, 4277], [1469, 16, 264, 325], [1105, 16, 264, 325]], 'adelic_image': '4368.96.3.?', 'conductor': 99372, 'lmfdb_label': '99372.b1', 'prime': 0}
  • id: 399666
    {'conductor': 99372, 'elladic_image': '8.12.0.31', 'lmfdb_label': '99372.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 99372.b does not appear in ec_padic