Elliptic curve data - 9768.q2

Formats: - HTML - YAML - JSON - 2025-10-24T10:26:47.526632

• 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': '9768k', 'Clabel': '9768k2', 'Cnumber': 2, 'abc_quality': 1.030665642117994, 'absD': 88192414100289970944, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1628, 'ainvs': [0, 1, 0, -58989892, 174368087600], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 9768, 'degree': 1118208, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0403169119587337091686978569', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2], 'jinv': [-88678136326676754811067728, 344501617579257699], 'lmfdb_iso': '9768.q', 'lmfdb_label': '9768.q2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -58989892, 174368087600], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '22.6.0.a.1', '148.6.0.?', '1628.12.0.?'], '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, 11], [3, 4, 3256], [7, 2, 3256], [11, 12, 888], [37, 38, 264]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.5782187915854368362238764426', 'prec': 100}, 'szpiro_ratio': 7.107127995423468, '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, 4, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 6, 0], 'aplist': [0, 1, 2, 4, 1, 0, 0, 6, 8, 8, 4, 1, -10, 10, 8, -14, 0, -8, -12, -16, -14, -14, -12, 2, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 9768, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '9768.q', 'trace_hash': 2043756471181705620}
• 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': '0.0022867268113528259206736990489', 'prec': 110}, 'conductor': 9768, 'gens': [], 'heights': [], 'lmfdb_label': '9768.q2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16790716254040634720958350493', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7014005511313777218683381379477793112', 'prec': 130}, 'tamagawa_product': 112, 'torsion_generators': [[-8869, 0, 1]], 'xcoord_integral_points': [-8869]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [7, 0], '5': [0, 0], '7': [2, 0], '11': [1, 0], '37': [1, 0]}, 'iwp0': 11, 'lmfdb_label': '9768.q2'}
• ec_torsion_growth •

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

  
  
  • id: 507059
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '9768.q2', 'torsion': [2, 2]}
  • id: 507060
    {'degree': 4, 'field': [-11, 0, -17, 0, 1], 'lmfdb_label': '9768.q2', 'torsion': [4]}
  • id: 507063
    {'degree': 8, 'field': [-98283, 0, -8200, 0, -1086, 0, 0, 0, 1], 'lmfdb_label': '9768.q2', 'torsion': [6]}
  • id: 507061
    {'degree': 8, 'field': [144, 0, -184, 0, 117, 0, 3, 0, 1], 'lmfdb_label': '9768.q2', 'torsion': [2, 4]}
  • id: 507062
    {'degree': 8, 'field': [333, 48, 269, 100, -37, 14, 1, -2, 1], 'lmfdb_label': '9768.q2', 'torsion': [2, 4]}
  • id: 507064
    {'degree': 16, 'field': [13417569, 0, 0, 0, -3728934, 0, 1494504, 0, -202457, 0, -21352, 0, 3606, 0, -136, 0, 1], 'lmfdb_label': '9768.q2', 'torsion': [8]}
  • id: 507065
    {'degree': 16, 'field': [15178486401, 0, 6731866908, 0, 1045089378, 0, 66288456, 0, 1237587, 0, -53776, 0, -2418, 0, 0, 0, 1], 'lmfdb_label': '9768.q2', '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: 205896
    {'conductor': 9768, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '9768.q2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 205897
    {'conductor': 9768, 'conductor_valuation': 1, 'discriminant_valuation': 28, 'j_denominator_valuation': 28, 'kodaira_symbol': 32, 'lmfdb_label': '9768.q2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 28}
  • id: 205898
    {'conductor': 9768, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9768.q2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 205899
    {'conductor': 9768, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '9768.q2', 'prime': 37, 'reduction_type': 1, '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: 1728509
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [705, 4, 1410, 9], [1, 4, 0, 1], [409, 1222, 1220, 407], [1625, 4, 1624, 5], [1038, 1, 295, 0]], 'adelic_image': '1628.12.0.?', 'conductor': 9768, 'lmfdb_label': '9768.q2', 'prime': 0}
  • id: 47239
    {'conductor': 9768, 'elladic_image': '2.3.0.1', 'lmfdb_label': '9768.q2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 9768.q does not appear in ec_padic