Elliptic curve data - 960.a7

Formats: - HTML - YAML - JSON - 2024-10-10T08:28:11.499170

• 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': '960i', 'Clabel': '960i1', 'Cnumber': 1, 'abc_quality': 1.1980768440515948, 'absD': 3932160, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [0, -1, 0, -1, -95], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 960, 'degree': 128, 'elladic_images': ['32.96.0.85'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436435', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-1, 15], 'lmfdb_iso': '960.a', 'lmfdb_label': '960.a7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 0, 0], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.9', '16.48.0-16.g.1.10', '24.48.0-24.bz.1.1', '30.6.0.a.1', '32.96.0-32.e.1.9', '40.48.0-40.cb.2.5', '48.96.0-48.bv.1.11', '60.12.0.g.1', '80.192.2.?', '96.192.1.?', '120.96.0.?', '160.384.5.?', '240.384.5.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 15], [3, 4, 320], [5, 6, 192]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0954247526427890968608286186', 'prec': 103}, 'szpiro_ratio': 3.2968804329692936, '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, 0, 0, 1, 0, -4, 0, 2, 0, 1, 0, 2, 0, 4, 0], 'aplist': [0, -1, -1, 0, -4, 2, 2, 4, 0, 2, 0, 10, 10, 4, -8, 10, -4, 2, 12, 8, 10, 0, 12, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 960, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '960.a', 'trace_hash': 539569839425448692}
• 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': '1.1178508563087645508833713911', 'prec': 100}, 'conductor': 960, 'gens': [], 'heights': [], 'lmfdb_label': '960.a7', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1287136996856674305331052614', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1287136996856674305331052614328305627', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[5, 0, 1]], 'xcoord_integral_points': [5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '960.a7'}
• ec_torsion_growth •

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

  
  
  • id: 46184
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [4]}
  • id: 46185
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [4]}
  • id: 46183
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '960.a7', 'torsion': [2, 2]}
  • id: 46187
    {'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [8]}
  • id: 46188
    {'degree': 4, 'field': [4, 0, 6, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [8]}
  • id: 46186
    {'degree': 4, 'field': [6, -12, 13, -2, 1], 'lmfdb_label': '960.a7', 'torsion': [2, 4]}
  • id: 46194
    {'degree': 8, 'field': [-48, 0, -56, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [6]}
  • id: 46191
    {'degree': 8, 'field': [16, 0, -24, 0, 32, 0, -6, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [2, 8]}
  • id: 46192
    {'degree': 8, 'field': [16, 0, -8, 0, 4, 0, -2, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [16]}
  • id: 46189
    {'degree': 8, 'field': [16, 0, 22, 0, 9, 0, -2, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [2, 4]}
  • id: 46190
    {'degree': 8, 'field': [121, 0, -272, 0, 39, 0, -8, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [8]}
  • id: 46193
    {'degree': 8, 'field': [241, -124, 124, -58, 24, 4, 1, -2, 1], 'lmfdb_label': '960.a7', 'torsion': [16]}
  • id: 46197
    {'degree': 16, 'field': [1, 0, -4, 0, 19, 0, -52, 0, 73, 0, -52, 0, 19, 0, -4, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [16]}
  • id: 46196
    {'degree': 16, 'field': [1, 0, 0, 0, 49, 0, 0, 0, 1056, 0, 0, 0, 49, 0, 0, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [2, 8]}
  • id: 46198
    {'degree': 16, 'field': [256, 0, 128, 0, 0, 0, -32, 0, -16, 0, -8, 0, 0, 0, 2, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [2, 16]}
  • id: 46202
    {'degree': 16, 'field': [256, 0, 1024, 0, 1024, 0, -288, 0, -384, 0, 72, 0, 4, 0, 4, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [12]}
  • id: 46199
    {'degree': 16, 'field': [256, 0, 3456, 0, 8512, 0, 1248, 0, -1200, 0, 192, 0, -8, 0, -6, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [32]}
  • id: 46195
    {'degree': 16, 'field': [2116, -4784, 5408, -5992, 4808, -1672, -24, 924, -1307, 732, -216, -4, 98, -76, 32, -8, 1], 'lmfdb_label': '960.a7', 'torsion': [4, 4]}
  • id: 46201
    {'degree': 16, 'field': [2304, 0, -82176, 0, -13760, 0, -5088, 0, 1920, 0, 152, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '960.a7', 'torsion': [12]}
  • id: 46200
    {'degree': 16, 'field': [2304, 0, -384, 0, 14080, 0, -192, 0, 480, 0, 8, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '960.a7', '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: 13136
    {'conductor': 960, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '960.a7', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 13137
    {'conductor': 960, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '960.a7', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 13138
    {'conductor': 960, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '960.a7', '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: 1670591
    {'adelic_gens': [[479, 448, 390, 449], [214, 3, 365, 268], [1, 0, 32, 1], [1, 32, 0, 1], [5, 28, 68, 381], [449, 32, 448, 33], [23, 18, 318, 395], [352, 29, 107, 162], [297, 478, 326, 17]], 'adelic_image': '480.768.13.?', 'conductor': 960, 'lmfdb_label': '960.a7', 'prime': 0}
  • id: 4443
    {'conductor': 960, 'elladic_image': '32.96.0.85', 'lmfdb_label': '960.a7', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 960.a does not appear in ec_padic