Elliptic curve data - 1680.e1

Formats: - HTML - YAML - JSON - 2024-04-29T22:37:13.660225

• 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': '1680c', 'Clabel': '1680c3', 'Cnumber': 3, 'abc_quality': 0.971018922966229, 'absD': 331914240, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, -1, 0, -2896, -59024], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1680, 'degree': 1536, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.65828348483183690391253584137', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [2624033547076, 324135], 'lmfdb_iso': '1680.e', 'lmfdb_label': '1680.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -2896, 59024], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0-4.c.1.2', '20.12.0-4.c.1.1', '56.12.0-4.c.1.5', '60.24.0-60.h.1.2', '168.24.0.?', '280.24.0.?', '840.48.0.?'], '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, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.080660834365215812731509073488', 'prec': 107}, 'szpiro_ratio': 4.783810788954864, '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, 1, 0, 1, 0, 4, 0, -6, 0, 1, 0, -2, 0, 8, 0], 'aplist': [0, -1, -1, 1, 4, -6, -2, 8, -4, 6, -4, -2, -2, 12, 0, 2, 4, 6, 4, -8, 6, 16, 4, -18, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 1680, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1680.e', 'trace_hash': 1240056197982986267}
• 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': '0.26805396155226377661530597680', 'prec': 103}, 'conductor': 1680, 'gens': [], 'heights': [], 'lmfdb_label': '1680.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.65078965102496103354030722817', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3015793020499220670806144563440103170', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-31, 0, 1]], 'xcoord_integral_points': [-31]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1680.e1'}
• ec_torsion_growth •

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

  
  
  • id: 84064
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '1680.e1', 'torsion': [2, 2]}
  • id: 84066
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '1680.e1', 'torsion': [4]}
  • id: 84065
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '1680.e1', 'torsion': [4]}
  • id: 84067
    {'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '1680.e1', 'torsion': [2, 4]}
  • id: 84071
    {'degree': 8, 'field': [-108, 0, 36, 0, 36, 0, 0, 0, 1], 'lmfdb_label': '1680.e1', 'torsion': [6]}
  • id: 84068
    {'degree': 8, 'field': [1, 38, -44, 14, -11, 2, 4, -4, 1], 'lmfdb_label': '1680.e1', 'torsion': [2, 4]}
  • id: 84069
    {'degree': 8, 'field': [1521, 0, 1542, 0, 439, 0, 18, 0, 1], 'lmfdb_label': '1680.e1', 'torsion': [8]}
  • id: 84070
    {'degree': 8, 'field': [3600, 0, 1080, 0, 264, 0, 18, 0, 1], 'lmfdb_label': '1680.e1', 'torsion': [8]}
  • id: 84072
    {'degree': 16, 'field': [1, -6, 18, -36, 37, 0, -18, 42, -60, 42, -18, 0, 37, -36, 18, -6, 1], 'lmfdb_label': '1680.e1', 'torsion': [4, 4]}
  • id: 84077
    {'degree': 16, 'field': [11664, 0, 3888, 0, 5184, 0, -1296, 0, 1404, 0, 72, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '1680.e1', 'torsion': [12]}
  • id: 84075
    {'degree': 16, 'field': [20506, 97504, -59364, -15820, -7942, 38664, -88838, 36100, -22680, 3820, 358, -1638, 488, -220, 54, -8, 1], 'lmfdb_label': '1680.e1', 'torsion': [2, 6]}
  • id: 84073
    {'degree': 16, 'field': [275625, 0, -262500, 0, 1493125, 0, -817500, 0, 198600, 0, -25300, 0, 1725, 0, -60, 0, 1], 'lmfdb_label': '1680.e1', 'torsion': [2, 8]}
  • id: 84074
    {'degree': 16, 'field': [962361, 0, -1465452, 0, 778653, 0, -103140, 0, 1656, 0, 180, 0, -27, 0, 12, 0, 1], 'lmfdb_label': '1680.e1', 'torsion': [2, 8]}
  • id: 84076
    {'degree': 16, 'field': [8463525, 4971540, -2245754, -1743700, 925456, 442704, -174366, -75948, 27010, 9332, -2102, -1452, 264, 120, -26, -4, 1], 'lmfdb_label': '1680.e1', '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: 26417
    {'conductor': 1680, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '1680.e1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 26418
    {'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '1680.e1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 26419
    {'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1680.e1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 26420
    {'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1680.e1', 'prime': 7, 'reduction_type': 1, '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: 1674980
    {'adelic_gens': [[176, 3, 5, 2], [312, 727, 287, 240], [833, 8, 832, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [241, 8, 124, 33], [7, 6, 834, 835], [739, 738, 538, 115], [284, 1, 583, 6]], 'adelic_image': '840.48.0.?', 'conductor': 1680, 'lmfdb_label': '1680.e1', 'prime': 0}
  • id: 8160
    {'conductor': 1680, 'elladic_image': '4.6.0.1', 'lmfdb_label': '1680.e1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1680.e does not appear in ec_padic