Elliptic curve data - 9408.q2

Formats: - HTML - YAML - JSON - 2025-10-30T01:28:10.667864

• 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': '9408bp', 'Clabel': '9408bp1', 'Cnumber': 1, 'abc_quality': 1.1169180726528216, 'absD': 9067247960064, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 168, 'ainvs': [0, -1, 0, -3201, -159711], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 9408, 'degree': 16128, 'elladic_images': ['7.24.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1741973343265719349885618884', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 16, 'isogeny_degrees': [1, 7], 'jinv': [-2401, 6], 'lmfdb_iso': '9408.q', 'lmfdb_label': '9408.q2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1, -1], 'min_quad_twist_disc': 56, 'modell_images': ['7B.6.3'], 'modm_images': ['7.24.0.a.2', '24.2.0.b.1', '56.48.0-7.a.2.4', '84.48.0.?', '168.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 147], [3, 4, 3136], [7, 26, 192]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1627968692168882325408547894', 'prec': 103}, 'szpiro_ratio': 4.098525773062428, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 0, 0, 0, 1, 0, 5, 0, 0, 0, 1, 0, -4, 0, 8, 0], 'aplist': [0, -1, -1, 0, 5, 0, -4, 8, 4, 5, -3, 4, 0, 2, 6, 9, -11, 6, -2, -2, 10, -3, -7, -6, 7], 'class_deg': 7, 'class_size': 2, 'conductor': 9408, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '9408.q', 'trace_hash': 1592648311532022641}
• 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': '0.095522384274359097541632078620', 'prec': 107}, 'conductor': 9408, 'gens': [], 'heights': [], 'lmfdb_label': '9408.q2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29559960551556992132338382939', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7735976330934195279403029763146198960', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [0, 0], '7': 'a', '11': [0, 0], '13': [0, 0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '9408.q2'}
• ec_torsion_growth •

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

  
  
  • id: 489811
    {'degree': 3, 'field': [-6, -2, -1, 1], 'lmfdb_label': '9408.q2', 'torsion': [2]}
  • id: 489812
    {'degree': 6, 'field': [6, 0, 13, 0, 16, 0, 1], 'lmfdb_label': '9408.q2', 'torsion': [2, 2]}
  • id: 489813
    {'degree': 6, 'field': [8, 0, 24, 0, 10, 0, 1], 'lmfdb_label': '9408.q2', 'torsion': [7]}
  • id: 489814
    {'degree': 8, 'field': [-48, 0, -62, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '9408.q2', 'torsion': [3]}
  • id: 489815
    {'degree': 12, 'field': [36, 60, 144, -68, -264, -116, 112, 156, 53, -9, -12, -1, 1], 'lmfdb_label': '9408.q2', 'torsion': [4]}
  • id: 489816
    {'degree': 14, 'field': [-224, 0, 64, 0, 768, 0, 704, 0, 272, 0, 72, 0, 10, 0, 1], 'lmfdb_label': '9408.q2', 'torsion': [7]}
  • id: 489817
    {'degree': 18, 'field': [1, -2, 13, 18, 6, -16, 29, 20, -31, 98, 151, -274, 135, -74, 54, -18, 6, -4, 1], 'lmfdb_label': '9408.q2', 'torsion': [14]}
• 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: 197950
    {'conductor': 9408, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '9408.q2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 197951
    {'conductor': 9408, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9408.q2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 197952
    {'conductor': 9408, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '9408.q2', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1726278
    {'adelic_gens': [[160, 161, 91, 6], [1, 0, 14, 1], [64, 7, 49, 162], [8, 5, 91, 57], [155, 14, 154, 15], [41, 154, 0, 167], [1, 14, 0, 1], [39, 88, 98, 55]], 'adelic_image': '168.96.2.?', 'conductor': 9408, 'lmfdb_label': '9408.q2', 'prime': 0}
  • id: 45732
    {'conductor': 9408, 'elladic_image': '7.24.0.2', 'lmfdb_label': '9408.q2', 'modell_image': '7B.6.3', 'prime': 7}
• lmfdb_iso 9408.q does not appear in ec_padic