Elliptic curve data - 89232.z3

Formats: - HTML - YAML - JSON - 2024-04-30T17:29:54.867898

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '89232bd', 'Clabel': '89232bd3', 'Cnumber': 3, 'abc_quality': 0.9574733148525506, 'absD': 74405788108598808576, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 3432, 'ainvs': [0, -1, 0, -1281752, -373379280], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 89232, 'degree': 2752512, 'elladic_images': ['8.24.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5167174981976284988137334574', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 4], 'jinv': [11779205551777, 3763454409], 'lmfdb_iso': '89232.z', 'lmfdb_label': '89232.z3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -474, 2619], 'min_quad_twist_disc': -52, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0-4.b.1.8', '12.24.0.c.1', '24.48.0-12.c.1.15', '52.24.0-4.b.1.3', '88.48.0.?', '104.48.0.?', '156.48.0.?', '264.96.0.?', '312.96.0.?', '1144.96.0.?', '3432.192.1.?'], '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, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.54109563890691482136975761516', 'prec': 103}, 'szpiro_ratio': 4.72013709712213, '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, 0, -1, 0, 2, 0, 0, 0, 1, 0, -1, 0, 0, 0, -2, 0, -6, 0, -4, 0], 'aplist': [0, -1, 2, 0, -1, 0, -6, -4, 8, -10, 0, -6, -10, -4, 8, -10, -12, 14, -12, 0, 6, -8, 12, -2, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 89232, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '89232.z', 'trace_hash': 1626315184931307192}
• 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': '0.0065163883120455832348604271088', 'prec': 110}, 'conductor': 89232, 'gens': [], 'heights': [], 'lmfdb_label': '89232.z3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14547327974974701240507135653', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.58189311899898804962028542611909508835', 'prec': 133}, 'tamagawa_product': 64, 'torsion_generators': [[-316, 0, 1], [1257, 0, 1]], 'xcoord_integral_points': [-940, -316, 1257]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '11': [0, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '89232.z3'}
• ec_torsion_growth •

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

  
  
  • id: 4174070
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '89232.z3', 'torsion': [2, 4]}
  • id: 4174071
    {'degree': 4, 'field': [16, 0, 5, 0, 1], 'lmfdb_label': '89232.z3', 'torsion': [2, 4]}
  • id: 4174072
    {'degree': 4, 'field': [169, 0, -13, 0, 1], 'lmfdb_label': '89232.z3', 'torsion': [2, 4]}
  • id: 4174076
    {'degree': 8, 'field': [-85683, 0, -7592, 0, -1014, 0, 0, 0, 1], 'lmfdb_label': '89232.z3', 'torsion': [2, 6]}
  • id: 4174073
    {'degree': 8, 'field': [81, 0, -63, 0, 40, 0, -7, 0, 1], 'lmfdb_label': '89232.z3', 'torsion': [4, 4]}
  • id: 4174074
    {'degree': 8, 'field': [1444, 0, 764, 0, 101, 0, -10, 0, 1], 'lmfdb_label': '89232.z3', 'torsion': [2, 8]}
  • id: 4174075
    {'degree': 8, 'field': [3793, 6928, -5498, -2780, 1191, 236, -74, -4, 1], 'lmfdb_label': '89232.z3', 'torsion': [2, 8]}
  • id: 4174077
    {'degree': 16, 'field': [22932, 58968, 42156, 24840, 47982, 25704, 12018, 10008, 6697, 492, 2158, -96, 336, -12, 28, 0, 1], 'lmfdb_label': '89232.z3', 'torsion': [4, 8]}
  • id: 4174079
    {'degree': 16, 'field': [59049, 0, -49113, 0, -2097, 0, 181278, 0, -35517, 0, 2662, 0, -186, 0, 0, 0, 1], 'lmfdb_label': '89232.z3', 'torsion': [2, 12]}
  • id: 4174078
    {'degree': 16, 'field': [36321652, 427440, -7511640, -3910608, -462146, 1358760, 308340, -229710, -31161, 25974, -5508, -1326, 1261, 0, -60, 0, 1], 'lmfdb_label': '89232.z3', 'torsion': [2, 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: 2180840
    {'conductor': 89232, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '89232.z3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2180841
    {'conductor': 89232, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '89232.z3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2180842
    {'conductor': 89232, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '89232.z3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2180843
    {'conductor': 89232, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '89232.z3', 'prime': 13, '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: 2251645
    {'adelic_gens': [[1151, 6, 3426, 3427], [3425, 8, 3424, 9], [791, 3428, 0, 3431], [937, 8, 316, 33], [1, 0, 8, 1], [1, 8, 0, 1], [3431, 2566, 0, 857], [5, 4, 3428, 3429], [1721, 860, 880, 1725]], 'adelic_image': '3432.192.1.?', 'conductor': 89232, 'lmfdb_label': '89232.z3', 'prime': 0}
  • id: 362836
    {'conductor': 89232, 'elladic_image': '8.24.0.11', 'lmfdb_label': '89232.z3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 89232.z does not appear in ec_padic