Elliptic curve data - 960.b2

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• 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': '960a', 'Clabel': '960a3', 'Cnumber': 3, 'abc_quality': 1.118508545588007, 'absD': 61440000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, -1, 0, -161, -639], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 960, 'degree': 256, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.22237616304910113557587277855', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [14172488, 1875], 'lmfdb_iso': '960.b', 'lmfdb_label': '960.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -40, 100], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '12.12.0-4.c.1.2', '24.24.0-24.s.1.3', '40.24.0-40.ba.1.3', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5173095078278007933230761484', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 3], [3, 4, 320], [5, 6, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.64405781265083050119566737327', 'prec': 107}, 'szpiro_ratio': 3.9120841537307003, '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, 0, 0, -2, 0, 1, 0, 6, 0, -4, 0], 'aplist': [0, -1, -1, 0, 0, -2, 6, -4, -8, 2, -4, -10, 2, -4, -8, 2, 8, 2, -12, -8, -14, 12, -4, -14, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 960, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '960.b', 'trace_hash': 373387439712671620}
• 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': '0.64098301113759041022743014227', 'prec': 103}, 'conductor': 960, 'gens': [[-5, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5173095078278007933230761484', 'prec': 100}], 'lmfdb_label': '960.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.3512866125547235579541795149', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0503200250297037421203944396850625894', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-9, 0, 1]], 'xcoord_integral_points': [-9, -5, 16]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '960.b2'}
• ec_torsion_growth •

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

  
  
  • id: 45591
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [2, 2]}
  • id: 45593
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '960.b2', 'torsion': [4]}
  • id: 45592
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [4]}
  • id: 45594
    {'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [2, 4]}
  • id: 45598
    {'degree': 8, 'field': [-243, 0, 144, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [6]}
  • id: 45596
    {'degree': 8, 'field': [6, 0, 28, -16, 34, -24, 16, -4, 1], 'lmfdb_label': '960.b2', 'torsion': [8]}
  • id: 45595
    {'degree': 8, 'field': [9, 0, 36, 0, 12, 0, -12, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [2, 4]}
  • id: 45597
    {'degree': 8, 'field': [36, 0, 72, 0, 138, 0, 12, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [8]}
  • id: 45603
    {'degree': 16, 'field': [25, 0, 100, 0, 100, 0, 132, 0, 162, 0, -12, 0, 4, 0, 4, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [12]}
  • id: 45600
    {'degree': 16, 'field': [36, 0, -168, 192, 580, -592, -504, 776, 318, -416, 24, -128, 126, -16, 0, -4, 1], 'lmfdb_label': '960.b2', 'torsion': [2, 8]}
  • id: 45599
    {'degree': 16, 'field': [81, 0, -324, 0, 648, 0, -864, 0, 711, 0, -288, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [4, 4]}
  • id: 45602
    {'degree': 16, 'field': [225, 0, -2124, 0, 1660, 0, -12, 0, 42, 0, -220, 0, 60, 0, -12, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [2, 6]}
  • id: 45604
    {'degree': 16, 'field': [11664, 0, 18144, 0, 24336, 0, 6048, 0, 1404, 0, 336, 0, 36, 0, 0, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [12]}
  • id: 45601
    {'degree': 16, 'field': [467856, 0, 562464, 0, 227448, 0, 22896, 0, -5472, 0, -1368, 0, -18, 0, 12, 0, 1], 'lmfdb_label': '960.b2', 'torsion': [2, 8]}
• 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: 13016
    {'conductor': 960, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '960.b2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 13017
    {'conductor': 960, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '960.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 13018
    {'conductor': 960, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '960.b2', 'prime': 5, '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: 1670594
    {'adelic_gens': [[113, 8, 112, 9], [7, 6, 114, 115], [72, 7, 53, 66], [1, 0, 8, 1], [97, 8, 28, 33], [1, 4, 4, 17], [72, 7, 23, 36], [44, 1, 103, 6], [1, 8, 0, 1]], 'adelic_image': '120.48.0.?', 'conductor': 960, 'lmfdb_label': '960.b2', 'prime': 0}
  • id: 4446
    {'conductor': 960, 'elladic_image': '8.12.0.7', 'lmfdb_label': '960.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 21246
    {'lmfdb_iso': '960.b', 'p': 13, 'prec': 20, 'unit': 101256926435832116155, 'val': 1}
  • id: 21248
    {'lmfdb_iso': '960.b', 'p': 17, 'prec': 20, 'unit': 90861672501140194283864, 'val': 1}
  • id: 21249
    {'lmfdb_iso': '960.b', 'p': 19, 'prec': 20, 'unit': 660931944102401579010804, 'val': 1}
  • id: 21253
    {'lmfdb_iso': '960.b', 'p': 23, 'prec': 20, 'unit': 48997246115248284019224957, 'val': 1}
  • id: 21245
    {'lmfdb_iso': '960.b', 'p': 29, 'prec': 20, 'unit': 53682143695721405750841739, 'val': 1}
  • id: 21257
    {'lmfdb_iso': '960.b', 'p': 31, 'prec': 20, 'unit': 8430707571024140945971697723, 'val': 1}
  • id: 21241
    {'lmfdb_iso': '960.b', 'p': 37, 'prec': 20, 'unit': 149036805213845420036277867499, 'val': 1}
  • id: 21243
    {'lmfdb_iso': '960.b', 'p': 41, 'prec': 20, 'unit': 4167900220117622682808234672321, 'val': 1}
  • id: 21244
    {'lmfdb_iso': '960.b', 'p': 43, 'prec': 20, 'unit': 10642951547048969504474773189019, 'val': 1}
  • id: 21255
    {'lmfdb_iso': '960.b', 'p': 47, 'prec': 20, 'unit': 6373614234094153656912494842439, 'val': 1}
  • id: 21250
    {'lmfdb_iso': '960.b', 'p': 53, 'prec': 20, 'unit': 350087936695372690148010139631104, 'val': 1}
  • id: 21251
    {'lmfdb_iso': '960.b', 'p': 59, 'prec': 20, 'unit': 1193335751707724877765357908628123, 'val': 1}
  • id: 21256
    {'lmfdb_iso': '960.b', 'p': 61, 'prec': 20, 'unit': 5143617103246695945968645029226536, 'val': 1}
  • id: 21240
    {'lmfdb_iso': '960.b', 'p': 67, 'prec': 20, 'unit': 6421014999584847129814849855748517, 'val': 1}
  • id: 21242
    {'lmfdb_iso': '960.b', 'p': 71, 'prec': 20, 'unit': 29220864536272076128933039327943969, 'val': 1}
  • id: 21252
    {'lmfdb_iso': '960.b', 'p': 73, 'prec': 20, 'unit': 136250978381632517814143283735635924, 'val': 1}
  • id: 21247
    {'lmfdb_iso': '960.b', 'p': 79, 'prec': 20, 'unit': 581554237466443243469068819211655581, 'val': 1}
  • id: 21239
    {'lmfdb_iso': '960.b', 'p': 83, 'prec': 20, 'unit': 106928212277089337918167795300965594, 'val': 1}
  • id: 21254
    {'lmfdb_iso': '960.b', 'p': 89, 'prec': 20, 'unit': 2176828358333886789197089931167920487, 'val': 1}
  • id: 21238
    {'lmfdb_iso': '960.b', 'p': 97, 'prec': 20, 'unit': 28941730021655654331727435162083435754, 'val': 1}