Elliptic curve data - 960.p8

Formats: - HTML - YAML - JSON - 2024-04-25T00:10:27.768970

• 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': '960o', 'Clabel': '960o1', 'Cnumber': 1, 'abc_quality': 0.9968917246282063, 'absD': 566231040, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, 1, 0, 95, -1057], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 960, 'degree': 384, 'elladic_images': ['8.12.0.6', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.36143343116226948930023576383', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [357911, 2160], 'lmfdb_iso': '960.p', 'lmfdb_label': '960.p8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 1, 2], 'min_quad_twist_disc': -8, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '8.12.0-4.c.1.5', '12.48.0.c.2', '24.192.1-24.dh.3.10', '30.24.0.b.1', '40.24.0-40.bb.1.13', '60.96.1.n.4', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, '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': '-0.67828733967764847482561241836', 'prec': 107}, 'szpiro_ratio': 4.005926121745469, '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, 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': '0.48535880262978992387393752081', 'prec': 103}, 'conductor': 960, 'gens': [], 'heights': [], 'lmfdb_label': '960.p8', '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': 12, 'torsion_generators': [[7, 0, 1]], 'xcoord_integral_points': [7]}
• 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.p8'}
• ec_torsion_growth •

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

  
  
  • id: 46595
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [4]}
  • id: 46597
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [6]}
  • id: 46594
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 2]}
  • id: 46596
    {'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [4]}
  • id: 46599
    {'degree': 4, 'field': [-2, 4, -3, -2, 1], 'lmfdb_label': '960.p8', 'torsion': [8]}
  • id: 46601
    {'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [12]}
  • id: 46602
    {'degree': 4, 'field': [4, 0, 6, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [12]}
  • id: 46600
    {'degree': 4, 'field': [6, -12, 13, -2, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 6]}
  • id: 46598
    {'degree': 4, 'field': [16, 0, 2, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 4]}
  • id: 46603
    {'degree': 6, 'field': [-24, 0, 28, 0, -2, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [12]}
  • id: 46608
    {'degree': 8, 'field': [3, -12, 12, 0, 1, -4, 6, -4, 1], 'lmfdb_label': '960.p8', 'torsion': [24]}
  • id: 46607
    {'degree': 8, 'field': [16, 0, -24, 0, 32, 0, -6, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 12]}
  • id: 46606
    {'degree': 8, 'field': [16, 0, -14, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 8]}
  • id: 46605
    {'degree': 8, 'field': [36, -48, 32, -40, 16, 0, 8, -4, 1], 'lmfdb_label': '960.p8', 'torsion': [8]}
  • id: 46604
    {'degree': 8, 'field': [256, 0, -136, 0, 81, 0, -16, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 4]}
  • id: 46609
    {'degree': 12, 'field': [4, 0, -24, 0, 156, 0, 76, 0, 24, 0, 6, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [3, 12]}
  • id: 46610
    {'degree': 12, 'field': [16, 0, 56, 0, 60, 0, 10, 0, 0, 0, -4, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 12]}
  • id: 46611
    {'degree': 12, 'field': [108, 216, -252, 36, -204, 228, -9, -6, -23, -8, 9, -2, 1], 'lmfdb_label': '960.p8', 'torsion': [24]}
  • id: 46614
    {'degree': 16, 'field': [-240, 3840, -10800, 22080, -33228, 30432, -18432, 9456, -5312, 3608, -2216, 848, -113, -28, 22, -4, 1], 'lmfdb_label': '960.p8', 'torsion': [16]}
  • id: 46616
    {'degree': 16, 'field': [36, -144, 288, -312, 208, -72, -24, 124, -107, -28, 104, -124, 118, -76, 32, -8, 1], 'lmfdb_label': '960.p8', 'torsion': [24]}
  • id: 46615
    {'degree': 16, 'field': [36, 0, -396, 0, 1137, 0, -288, 0, 160, 0, 68, 0, 12, 0, -4, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 12]}
  • id: 46617
    {'degree': 16, 'field': [36, 0, 54, 0, 75, 18, -63, 30, -44, 42, 25, -78, 72, -42, 19, -6, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 24]}
  • id: 46612
    {'degree': 16, 'field': [256, 0, 0, 0, 16, 0, 0, 0, 216, 0, 0, 0, 1, 0, 0, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [4, 4]}
  • id: 46613
    {'degree': 16, 'field': [256, 0, 0, 0, 41, 0, 0, 0, 51, 0, 0, 0, 11, 0, 0, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [2, 8]}
  • id: 46618
    {'degree': 18, 'field': [2592, 0, 42768, 0, -1296, 0, 9684, 0, 0, 0, 576, 0, 422, 0, 48, 0, 6, 0, 1], 'lmfdb_label': '960.p8', 'torsion': [18]}
• 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: 13226
    {'conductor': 960, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '960.p8', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 13227
    {'conductor': 960, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '960.p8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 13228
    {'conductor': 960, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '960.p8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1670668
    {'adelic_gens': [[1, 12, 12, 25], [112, 21, 75, 106], [97, 24, 96, 25], [23, 96, 18, 113], [1, 0, 24, 1], [111, 92, 100, 91], [1, 24, 0, 1], [16, 63, 41, 74], [15, 106, 14, 11]], 'adelic_image': '120.384.5.?', 'conductor': 960, 'lmfdb_label': '960.p8', 'prime': 0}
  • id: 4535
    {'conductor': 960, 'elladic_image': '8.12.0.6', 'lmfdb_label': '960.p8', 'modell_image': '2B', 'prime': 2}
  • id: 4536
    {'conductor': 960, 'elladic_image': '3.4.0.1', 'lmfdb_label': '960.p8', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 960.p does not appear in ec_padic