Elliptic curve data - 116160.ex1

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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': '116160id', 'Clabel': '116160id4', 'Cnumber': 4, 'abc_quality': 1.07876989573691, 'absD': 6871931397048655872000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 440, 'ainvs': [0, 1, 0, -15255841, -22590827041], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 116160, 'degree': 11796480, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9866996438701091538694030539', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 127, 'isogeny_degrees': [1, 2, 4], 'jinv': [3382175663521924, 59189241375], 'lmfdb_iso': '116160.ex', 'lmfdb_label': '116160.ex1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -31520, -2131632], 'min_quad_twist_disc': 88, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '40.24.0-40.z.1.14', '88.24.0.?', '220.12.0.?', '440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 605], [3, 4, 7744], [5, 6, 23232], [11, 72, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.86355576672433013594878843631', 'prec': 103}, 'szpiro_ratio': 5.250490623184189, '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, -6, 0, -1, 0, 2, 0, 4, 0], 'aplist': [0, 1, -1, -4, 0, -6, 2, 4, 8, 6, 0, 2, -2, 8, 0, 2, 4, -10, 12, 16, -6, 8, 16, 10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 116160, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '116160.ex', 'trace_hash': 837552943489798857}
• 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': '0.0025455735580750728864421798479', 'prec': 110}, 'conductor': 116160, 'gens': [], 'heights': [], 'lmfdb_label': '116160.ex1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.076471862819154717838296103518', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4470996102129509708254753125615057585', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-2479, 0, 1]], 'xcoord_integral_points': [-2479]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [0, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '116160.ex1'}
• ec_torsion_growth •

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

  
  
  • id: 5328534
    {'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [2, 2]}
  • id: 5328535
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [4]}
  • id: 5328536
    {'degree': 2, 'field': [110, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [4]}
  • id: 5328537
    {'degree': 4, 'field': [729, 0, 56, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [2, 4]}
  • id: 5328541
    {'degree': 8, 'field': [-9075, 0, -3718, 0, -330, 0, 0, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [6]}
  • id: 5328539
    {'degree': 8, 'field': [729, 0, 206, 0, 30, 0, 6, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [8]}
  • id: 5328538
    {'degree': 8, 'field': [2401, 0, -1372, 0, 239, 0, -28, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [2, 4]}
  • id: 5328540
    {'degree': 8, 'field': [9801, 0, 1188, 0, 199, 0, 2, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [8]}
  • id: 5328542
    {'degree': 16, 'field': [93636, -117504, 73728, -62952, 49648, -17712, 4296, 124, -3947, 2612, -856, 236, 58, -76, 32, -8, 1], 'lmfdb_label': '116160.ex1', 'torsion': [4, 4]}
  • id: 5328546
    {'degree': 16, 'field': [149769, 0, 507384, 0, 556740, 0, 20228, 0, -9490, 0, 1448, 0, 40, 0, 4, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [12]}
  • id: 5328544
    {'degree': 16, 'field': [289161, 189696, 102076, -415016, -139782, 224456, 202184, -155088, -53957, 46456, 5176, -6768, 218, 392, -36, -8, 1], 'lmfdb_label': '116160.ex1', 'torsion': [2, 8]}
  • id: 5328545
    {'degree': 16, 'field': [944784, 0, 559872, 0, -2764368, 0, -62208, 0, -666120, 0, -14656, 0, 2856, 0, 0, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [2, 6]}
  • id: 5328543
    {'degree': 16, 'field': [2624400, 0, 1075680, 0, 381744, 0, 79232, 0, 7820, 0, 1520, 0, 220, 0, -8, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [2, 8]}
  • id: 5328547
    {'degree': 16, 'field': [684628686, -332408448, 336224196, -291017016, 198148158, -96362124, 31068300, -5934068, 697836, -61320, -1246, 2340, 180, -52, -24, 0, 1], 'lmfdb_label': '116160.ex1', 'torsion': [12]}
• 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: 2858771
    {'conductor': 116160, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '116160.ex1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2858772
    {'conductor': 116160, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '116160.ex1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 2858773
    {'conductor': 116160, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '116160.ex1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2858774
    {'conductor': 116160, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '116160.ex1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2423374
    {'adelic_gens': [[96, 3, 5, 2], [1, 0, 8, 1], [433, 8, 432, 9], [1, 8, 0, 1], [1, 4, 4, 17], [384, 157, 381, 352], [381, 382, 262, 45], [7, 6, 434, 435], [36, 439, 97, 434]], 'adelic_image': '440.48.0.?', 'conductor': 116160, 'lmfdb_label': '116160.ex1', 'prime': 0}
  • id: 458349
    {'conductor': 116160, 'elladic_image': '8.12.0.7', 'lmfdb_label': '116160.ex1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 116160.ex does not appear in ec_padic