Elliptic curve data - 210.e8

Formats: - HTML - YAML - JSON - 2024-05-01T10:49:31.294052

• 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': '210e', 'Clabel': '210e6', 'Cnumber': 6, 'abc_quality': 1.1083142308531486, 'absD': 269165039062500, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [1, 0, 0, 1270, -789048], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 210, 'degree': 1024, 'elladic_images': ['16.96.0.25'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4478558266155903922444221867', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [226523624554079, 269165039062500], 'lmfdb_iso': '210.e', 'lmfdb_label': '210.e8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1270, -789048], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.1', '8.48.0-8.q.1.2', '16.96.0-16.j.1.2', '24.96.0-24.be.1.9', '48.192.1-48.bf.2.2', '56.96.0-56.bd.1.2', '84.48.0.?', '112.192.1.?', '160.192.2.?', '168.192.1.?', '336.384.5.?', '480.384.5.?', '1120.384.5.?', '3360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4478558266155903922444221867', 'prec': 100}, 'szpiro_ratio': 7.607959706757792, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 1, 1, 1, 1, -1, 1, 1, 1, -4, 1, -2, -1, 1, 1, 2, 1, 4, 1], 'aplist': [1, 1, 1, -1, -4, -2, 2, 4, -8, -2, 0, 6, -6, -4, 0, -10, 12, 14, -12, -8, 10, 16, -12, 10, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 210, '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': '210.e', 'trace_hash': 2192440699906191649}
• 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': '0.055259685364584924396892213395', 'prec': 107}, 'conductor': 210, 'gens': [], 'heights': [], 'lmfdb_label': '210.e8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.25648325250488331579192829714', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0518660200390665263354263771371387657', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[244, 3628, 1]], 'xcoord_integral_points': [244]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 2], '3': [5, 0], '5': [1, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '210.e8'}
• ec_torsion_growth •

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

  
  
  • id: 9081
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [8]}
  • id: 9080
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [2, 4]}
  • id: 9082
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [8]}
  • id: 9086
    {'degree': 4, 'field': [-1176, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [16]}
  • id: 9084
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [2, 8]}
  • id: 9087
    {'degree': 4, 'field': [24, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [16]}
  • id: 9083
    {'degree': 4, 'field': [25, 0, 11, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [4, 4]}
  • id: 9085
    {'degree': 4, 'field': [49, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [2, 8]}
  • id: 9088
    {'degree': 8, 'field': [1, 0, 0, 0, 23, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [4, 8]}
  • id: 9090
    {'degree': 8, 'field': [25, 0, 76, 0, -6, 0, 4, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [2, 16]}
  • id: 9091
    {'degree': 8, 'field': [320, -520, 65, -216, -3, -6, 1, -2, 1], 'lmfdb_label': '210.e8', 'torsion': [12]}
  • id: 9089
    {'degree': 8, 'field': [87025, 0, -3524, 0, 594, 0, 4, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [2, 16]}
  • id: 9093
    {'degree': 16, 'field': [2500, 0, 7952, 0, 7256, 0, 1232, 0, 104, 0, -280, 0, 4, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [2, 16]}
  • id: 9095
    {'degree': 16, 'field': [30625, 0, 0, 8400, -12974, -2952, 1152, -1248, 2391, 1416, 288, 288, 22, -24, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [4, 16]}
  • id: 9098
    {'degree': 16, 'field': [102400, 0, 228800, 0, -222335, 0, 52646, 0, -3893, 0, 776, 0, -29, 0, 2, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [2, 12]}
  • id: 9099
    {'degree': 16, 'field': [291600, 0, -1312200, 0, -140940, 0, -96984, 0, 4644, 0, -684, 0, 328, 0, -20, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [24]}
  • id: 9100
    {'degree': 16, 'field': [291600, 0, 1312200, 0, -140940, 0, 96984, 0, 4644, 0, 684, 0, 328, 0, 20, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [24]}
  • id: 9097
    {'degree': 16, 'field': [1382976, 0, 0, 0, -2145024, 0, 0, 0, 1698096, 0, 0, 0, -1824, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [32]}
  • id: 9092
    {'degree': 16, 'field': [3111696, 0, 0, 0, 0, 0, 0, 0, -1764, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [4, 8]}
  • id: 9094
    {'degree': 16, 'field': [15760900, 0, 5998608, 0, 587416, 0, 11088, 0, 7944, 0, -2520, 0, 4, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [2, 16]}
  • id: 9096
    {'degree': 16, 'field': [112021056, 0, 0, 0, 9936089856, 0, 0, 0, -71446704, 0, 0, 0, 2016, 0, 0, 0, 1], 'lmfdb_label': '210.e8', 'torsion': [32]}
• 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: 1872
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '210.e8', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1873
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '210.e8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1874
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '210.e8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 1875
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '210.e8', 'prime': 7, '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: 1666675
    {'adelic_gens': [[2017, 16, 0, 1], [1, 8, 0, 421], [1, 0, 32, 1], [25, 16, 1624, 2249], [2269, 24, 126, 2885], [1, 32, 0, 1], [7, 16, 2775, 793], [985, 16, 1974, 2473], [3329, 32, 3328, 33], [1, 32, 4, 129]], 'adelic_image': '3360.768.13.?', 'conductor': 210, 'lmfdb_label': '210.e8', 'prime': 0}
  • id: 908
    {'conductor': 210, 'elladic_image': '16.96.0.25', 'lmfdb_label': '210.e8', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 210.e does not appear in ec_padic