Elliptic curve data - 210.e6

Formats: - HTML - YAML - JSON - 2024-09-11T12:49:13.436220

• 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': '210e', 'Clabel': '210e2', 'Cnumber': 2, 'abc_quality': 1.0190986885579905, 'absD': 51438240000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 1680, 'ainvs': [1, 0, 0, -1070, 7812], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 210, 'degree': 256, 'elladic_images': ['8.96.0.40'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.75470864605564508282719006522', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [135487869158881, 51438240000], 'lmfdb_iso': '210.e', 'lmfdb_label': '210.e6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1070, 7812], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '8.96.0-8.l.2.2', '28.48.0-28.c.1.1', '48.192.1-48.f.2.3', '56.192.1-56.cd.2.5', '80.192.2.?', '240.384.5.?', '336.384.5.?', '560.384.5.?', '1680.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 14, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 70], [5, 6, 42], [7, 8, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.75470864605564508282719006522', 'prec': 103}, 'szpiro_ratio': 6.085515026358872, 'torsion': 16, 'torsion_primes': [2], 'torsion_structure': [2, 8]}
• 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': '0.22103874145833969758756885358', 'prec': 103}, 'conductor': 210, 'gens': [], 'heights': [], 'lmfdb_label': '210.e6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0259330100195332631677131886', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0518660200390665263354263771371387657', 'prec': 130}, 'tamagawa_product': 512, 'torsion_generators': [[-36, 18, 1], [4, 58, 1]], 'xcoord_integral_points': [-36, -26, -8, 4, 28, 34, 64, 244]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [5, 0], '5': [1, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '210.e6'}
• ec_torsion_growth •

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

  
  
  • id: 9020
    {'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '210.e6', 'torsion': [4, 8]}
  • id: 9021
    {'degree': 4, 'field': [16, 0, -2, 0, 1], 'lmfdb_label': '210.e6', 'torsion': [2, 16]}
  • id: 9022
    {'degree': 4, 'field': [256, 0, -38, 0, 1], 'lmfdb_label': '210.e6', 'torsion': [2, 16]}
  • id: 9023
    {'degree': 8, 'field': [320, -520, 65, -216, -3, -6, 1, -2, 1], 'lmfdb_label': '210.e6', 'torsion': [2, 24]}
  • id: 9025
    {'degree': 16, 'field': [1, -2, 2, -12, 13, 8, 30, -26, -12, -26, 30, 8, 13, -12, 2, -2, 1], 'lmfdb_label': '210.e6', 'torsion': [4, 16]}
  • id: 9028
    {'degree': 16, 'field': [256, 0, -872960, 0, 424910656, 0, -87293120, 0, 8136196, 0, -426800, 0, 12916, 0, -200, 0, 1], 'lmfdb_label': '210.e6', 'torsion': [2, 32]}
  • id: 9026
    {'degree': 16, 'field': [576, -5184, 17712, -28560, 25018, -18900, 17850, -13276, 8321, -4684, 2534, -1204, 504, -168, 44, -8, 1], 'lmfdb_label': '210.e6', 'torsion': [4, 16]}
  • id: 9024
    {'degree': 16, 'field': [87616, 0, -63424, 0, 42772, 0, -11940, 0, 3561, 0, -360, 0, 22, 0, -4, 0, 1], 'lmfdb_label': '210.e6', 'torsion': [8, 8]}
  • id: 9027
    {'degree': 16, 'field': [3594816, 0, 2723328, 0, 1286328, 0, 442656, 0, 77020, 0, 3296, 0, -102, 0, 8, 0, 1], 'lmfdb_label': '210.e6', 'torsion': [2, 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: 1856
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '210.e6', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 1857
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '210.e6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 1858
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '210.e6', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1859
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '210.e6', '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: 1666673
    {'adelic_gens': [[15, 16, 74, 289], [1121, 8, 0, 1], [1, 16, 0, 1], [1353, 16, 1076, 121], [13, 8, 320, 617], [241, 16, 1446, 97], [1, 0, 16, 1], [1, 16, 4, 65], [1665, 16, 1664, 17]], 'adelic_image': '1680.768.13.?', 'conductor': 210, 'lmfdb_label': '210.e6', 'prime': 0}
  • id: 906
    {'conductor': 210, 'elladic_image': '8.96.0.40', 'lmfdb_label': '210.e6', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 210.e does not appear in ec_padic