Elliptic curve data - 3192.b1

Formats: - HTML - YAML - JSON - 2025-04-22T03:25:37.626135

• 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': '3192c', 'Clabel': '3192c3', 'Cnumber': 3, 'abc_quality': 1.0120375317308423, 'absD': 3707605343232, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1064, 'ainvs': [0, -1, 0, -592824, 175883580], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3192, 'degree': 24576, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8141540726524812049530872321', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [22501000029889239268, 3620708343], 'lmfdb_iso': '3192.b', 'lmfdb_label': '3192.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -592824, 175883580], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '28.24.0-28.h.1.2', '152.24.0.?', '1064.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 7], [3, 4, 152], [7, 8, 456], [19, 20, 168]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2365314221858601137720604642', 'prec': 100}, 'szpiro_ratio': 6.381877987241211, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, -1, 0, 1, 0, -4, 0, 2, 0, 2, 0, -6, 0, 1, 0], 'aplist': [0, -1, -2, -1, -4, 2, -6, 1, 0, -10, 8, -2, 6, 4, -8, 6, -4, -10, 8, 12, -14, -4, -4, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 3192, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '3192.b', 'trace_hash': 2278949429915027169}
• 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': '0.026561083910987635975845600873', 'prec': 107}, 'conductor': 3192, 'gens': [], 'heights': [], 'lmfdb_label': '3192.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.61750109449594611849769173845', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.61750109449594611849769173845055423355', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[426, 684, 1]], 'xcoord_integral_points': [426, 445]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '7': [0, 0], '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '3192.b1'}
• ec_torsion_growth •

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

  
  
  • id: 166433
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '3192.b1', 'torsion': [2, 4]}
  • id: 166434
    {'degree': 4, 'field': [28, 0, 6, 0, 1], 'lmfdb_label': '3192.b1', 'torsion': [8]}
  • id: 166436
    {'degree': 8, 'field': [-6779, -14196, -7192, 1848, 1601, -84, -82, 0, 1], 'lmfdb_label': '3192.b1', 'torsion': [2, 8]}
  • id: 166438
    {'degree': 8, 'field': [-12, 0, -20, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '3192.b1', 'torsion': [12]}
  • id: 166435
    {'degree': 8, 'field': [1, -2, 2, 4, -1, 4, 2, -2, 1], 'lmfdb_label': '3192.b1', 'torsion': [4, 4]}
  • id: 166437
    {'degree': 8, 'field': [2209, 0, -1244, 0, 251, 0, -20, 0, 1], 'lmfdb_label': '3192.b1', 'torsion': [2, 8]}
  • id: 166440
    {'degree': 16, 'field': [8048569, 0, -7451888, 0, 2470132, 0, -692472, 0, 144558, 0, -18912, 0, 1396, 0, -56, 0, 1], 'lmfdb_label': '3192.b1', 'torsion': [2, 12]}
  • id: 166439
    {'degree': 16, 'field': [248155780267521, 0, 23473109115036, 0, 962322025392, 0, 23293806984, 0, 378384615, 0, 4096008, 0, 33156, 0, 180, 0, 1], 'lmfdb_label': '3192.b1', 'torsion': [16]}
• 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: 57635
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '3192.b1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57636
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '3192.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57637
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '3192.b1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 57638
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '3192.b1', 'prime': 19, 'reduction_type': 1, '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: 1684717
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [920, 3, 309, 2], [1, 4, 4, 17], [1057, 8, 1056, 9], [1009, 8, 844, 33], [7, 6, 1058, 1059], [403, 402, 146, 675], [400, 939, 403, 432]], 'adelic_image': '1064.48.0.?', 'conductor': 3192, 'lmfdb_label': '3192.b1', 'prime': 0}
  • id: 15988
    {'conductor': 3192, 'elladic_image': '4.12.0.7', 'lmfdb_label': '3192.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3192.b does not appear in ec_padic