Elliptic curve data - 960.p3

Formats: - HTML - YAML - JSON - 2025-03-07T04:35:53.405388

• 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': '960o', 'Clabel': '960o6', 'Cnumber': 6, 'abc_quality': 1.0522127879225598, 'absD': 2359296000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, 1, 0, -21345, 1190943], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 960, 'degree': 2304, 'elladic_images': ['4.12.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2573131657762969897064744430', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 6, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4102915888729, 9000000], 'lmfdb_iso': '960.p', 'lmfdb_label': '960.p3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -334, -2368], 'min_quad_twist_disc': -8, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '4.12.0-2.a.1.1', '6.24.0.a.1', '12.96.0-12.a.1.13', '24.192.1-24.cp.2.1', '40.24.0-40.a.1.1', '60.192.1-60.h.3.16', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 64], [5, 6, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.21759239493637902558062626081', 'prec': 103}, 'szpiro_ratio': 6.0462751798187755, '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, 1, 0, 4, 0, 1, 0, 0, 0, -2, 0, 1, 0, 6, 0, -4, 0], 'aplist': [0, 1, 1, 4, 0, -2, 6, -4, 0, 6, -8, -2, -6, -4, 0, 6, 0, 10, -4, 0, 2, -8, 12, 18, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 960, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '960.p', 'trace_hash': 2118015427448264448}
• 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': '0.080893133771631653978989586801', 'prec': 107}, 'conductor': 960, 'gens': [], 'heights': [], 'lmfdb_label': '960.p3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.81910691718318947792851914759', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4573207515495684337855574427775219318', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[81, 0, 1], [87, 0, 1]], 'xcoord_integral_points': [-169, 81, 87]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '960.p3'}
• ec_torsion_growth •

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

  
  
  • id: 46693
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [2, 12]}
  • id: 46695
    {'degree': 4, 'field': [16, 0, -2, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [2, 4]}
  • id: 46694
    {'degree': 4, 'field': [25, 0, 0, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [2, 4]}
  • id: 46696
    {'degree': 6, 'field': [17, 36, 12, -6, 6, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [2, 6]}
  • id: 46697
    {'degree': 8, 'field': [16, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [4, 12]}
  • id: 46698
    {'degree': 8, 'field': [256, 0, -256, 0, 90, 0, -16, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [2, 24]}
  • id: 46699
    {'degree': 12, 'field': [25, -180, 372, 432, 186, 72, -50, -72, 24, 0, -6, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [6, 12]}
  • id: 46701
    {'degree': 16, 'field': [36, 0, 180, 0, 201, 0, -150, 0, -104, 0, 50, 0, 36, 0, -10, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [2, 8]}
  • id: 46700
    {'degree': 16, 'field': [256, 0, 0, 0, 576, 0, 0, 0, -284, 0, 0, 0, 36, 0, 0, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [2, 8]}
  • id: 46702
    {'degree': 18, 'field': [-864, 0, 9072, 0, -20520, 0, 40068, 0, -57456, 0, 35244, 0, -8172, 0, 900, 0, -48, 0, 1], 'lmfdb_label': '960.p3', 'torsion': [2, 36]}
• 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: 13241
    {'conductor': 960, 'conductor_valuation': 6, 'discriminant_valuation': 24, 'j_denominator_valuation': 6, 'kodaira_symbol': -18, 'lmfdb_label': '960.p3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 13242
    {'conductor': 960, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '960.p3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 13243
    {'conductor': 960, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '960.p3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

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

  
  
  • id: 1670663
    {'adelic_gens': [[1, 12, 0, 1], [59, 108, 114, 47], [47, 6, 94, 115], [109, 12, 108, 13], [9, 4, 104, 113], [97, 6, 0, 1], [23, 108, 6, 113], [1, 0, 12, 1]], 'adelic_image': '120.384.5.?', 'conductor': 960, 'lmfdb_label': '960.p3', 'prime': 0}
  • id: 4525
    {'conductor': 960, 'elladic_image': '4.12.0.1', 'lmfdb_label': '960.p3', 'modell_image': '2Cs', 'prime': 2}
  • id: 4526
    {'conductor': 960, 'elladic_image': '3.4.0.1', 'lmfdb_label': '960.p3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 960.p does not appear in ec_padic