Elliptic curve data - 768.c2

Formats: - HTML - YAML - JSON - 2024-06-11T10:52:28.329462

• 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': '768e', 'Clabel': '768e1', 'Cnumber': 1, 'abc_quality': 1.2424379096229237, 'absD': 41472, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 24, 'ainvs': [0, -1, 0, -3, -9], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 768, 'degree': 64, 'elladic_images': ['8.48.0.206'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.43171442438310503261991559624', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2], 'jinv': [-8000, 81], 'lmfdb_iso': '768.c', 'lmfdb_label': '768.c2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -13, 85], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.f.1', '8.48.0-8.n.1.4', '24.96.1-24.cm.1.3'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.95157480980306401468283968733', 'prec': 107}, 'szpiro_ratio': 2.7308323512513817, '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, 0, 0, 4, 0, 1, 0, 4, 0, -4, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, -1, 0, 4, 4, -4, -2, -4, 8, 8, 4, 4, 6, 4, 8, 8, -12, -12, 12, -8, -6, 4, -4, -6, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 768, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '768.c', 'trace_hash': 746677868745359343}
• 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': '2.3712775220707629205649158807', 'prec': 100}, 'conductor': 768, 'gens': [], 'heights': [], 'lmfdb_label': '768.c2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.5362999083141049711545057211', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5362999083141049711545057210919411181', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[3, 0, 1]], 'xcoord_integral_points': [3]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '768.c2'}
• ec_torsion_growth •

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

  
  
  • id: 35573
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '768.c2', 'torsion': [2, 2]}
  • id: 35574
    {'degree': 4, 'field': [-2, 0, 0, 0, 1], 'lmfdb_label': '768.c2', 'torsion': [4]}
  • id: 35575
    {'degree': 4, 'field': [2, 0, 0, 0, 1], 'lmfdb_label': '768.c2', 'torsion': [2, 4]}
  • id: 35577
    {'degree': 8, 'field': [-12, 0, 64, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '768.c2', 'torsion': [6]}
  • id: 35576
    {'degree': 8, 'field': [1, 0, -4, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '768.c2', 'torsion': [4, 4]}
  • id: 35579
    {'degree': 16, 'field': [1, 0, 0, 0, -12, 0, 0, 0, 166, 0, 0, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '768.c2', 'torsion': [4, 8]}
  • id: 35578
    {'degree': 16, 'field': [4, 0, 16, 0, -88, 0, 96, 0, -64, 0, -24, 0, 20, 0, -8, 0, 1], 'lmfdb_label': '768.c2', 'torsion': [8]}
  • id: 35580
    {'degree': 16, 'field': [729, 0, 864, 0, 900, 0, 864, 0, 366, 0, 64, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '768.c2', '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: 9687
    {'conductor': 768, 'conductor_valuation': 8, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '768.c2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9688
    {'conductor': 768, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '768.c2', 'prime': 3, '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: 1669464
    {'adelic_gens': [[22, 11, 15, 22], [1, 0, 8, 1], [17, 8, 20, 9], [1, 4, 4, 17], [10, 23, 1, 18], [3, 8, 16, 3], [1, 8, 0, 1], [17, 8, 16, 9]], 'adelic_image': '24.96.1.?', 'conductor': 768, 'lmfdb_label': '768.c2', 'prime': 0}
  • id: 3461
    {'conductor': 768, 'elladic_image': '8.48.0.206', 'lmfdb_label': '768.c2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 768.c does not appear in ec_padic