Elliptic curve data - 210.d6

Formats: - HTML - YAML - JSON - 2024-04-30T14:46:24.695451

• 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': '210a', 'Clabel': '210a5', 'Cnumber': 5, 'abc_quality': 1.1620070102954823, 'absD': 18600435000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 840, 'ainvs': [1, 0, 0, -81, 6561], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 210, 'degree': 192, 'elladic_images': ['8.12.0.7', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.64971986870186991312831998223', 'prec': 103}, 'faltings_index': 4, 'faltings_ratio': 4, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [-58818484369, 18600435000], 'lmfdb_iso': '210.d', 'lmfdb_label': '210.d6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -81, 6561], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '4.6.0.c.1', '6.24.0-6.a.1.4', '8.12.0-4.c.1.3', '12.48.0-12.g.1.12', '24.96.0-24.bu.1.30', '28.12.0-4.c.1.1', '56.24.0-56.v.1.2', '84.96.0.?', '120.192.1.?', '168.192.1.?', '840.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.64971986870186991312831998223', 'prec': 103}, 'szpiro_ratio': 5.816789523218608, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
• 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, 0, 1, 2, 1, -1, 1, -6, 1, -4, -1], 'aplist': [1, 1, -1, 1, 0, 2, -6, -4, 0, -6, -4, 2, 6, 8, -12, 6, -12, 2, 8, 0, 14, -16, 12, 6, 14], 'class_deg': 12, 'class_size': 8, 'conductor': 210, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '210.d', 'trace_hash': 850949398862613817}
• 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': '0.27268452518500185779761107129', 'prec': 103}, 'conductor': 210, 'gens': [], 'heights': [], 'lmfdb_label': '210.d6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.99521243017777446939912563315', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9904248603555489387982512662981887046', 'prec': 130}, 'tamagawa_product': 72, 'torsion_generators': [[36, 207, 1]], 'xcoord_integral_points': [0, 36]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': [1, 0], '5': [0, 0], '7': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '210.d6'}
• ec_torsion_growth •

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

  
  
  • id: 8613
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [12]}
  • id: 8614
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [12]}
  • id: 8612
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [2, 6]}
  • id: 8615
    {'degree': 4, 'field': [9, 0, 8, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [2, 12]}
  • id: 8616
    {'degree': 6, 'field': [48, 0, -23, 0, 1, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [3, 6]}
  • id: 8617
    {'degree': 8, 'field': [226, 248, -196, -112, 77, -28, 14, -4, 1], 'lmfdb_label': '210.d6', 'torsion': [2, 12]}
  • id: 8618
    {'degree': 8, 'field': [900, 0, -795, 0, 19, 0, 19, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [24]}
  • id: 8619
    {'degree': 8, 'field': [7056, 0, -2688, 0, 298, 0, -8, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [24]}
  • id: 8620
    {'degree': 9, 'field': [256, -192, -1872, 2876, -1032, 12, 71, -9, -3, 1], 'lmfdb_label': '210.d6', 'torsion': [18]}
  • id: 8623
    {'degree': 12, 'field': [1548, -4536, 1392, 6120, -2537, -930, 857, -558, 258, -90, 29, -6, 1], 'lmfdb_label': '210.d6', 'torsion': [3, 12]}
  • id: 8622
    {'degree': 12, 'field': [7056, 0, -11172, 0, 17101, 0, -763, 0, -84, 0, -7, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [3, 12]}
  • id: 8621
    {'degree': 12, 'field': [451584, 0, 357504, 0, 273616, 0, 6104, 0, -336, 0, 14, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [6, 6]}
  • id: 8624
    {'degree': 16, 'field': [2401, 0, 0, 0, 0, 0, 0, 0, 1666, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [4, 12]}
  • id: 8626
    {'degree': 16, 'field': [12996, 0, 27984, 0, 11428, 0, 6096, 0, 14133, 0, -5588, 0, 492, 0, 12, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [2, 24]}
  • id: 8625
    {'degree': 16, 'field': [104976, 0, -3888, 0, -4716, 0, 59568, 0, 45904, 0, 1928, 0, -363, 0, -10, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [2, 24]}
  • id: 8628
    {'degree': 18, 'field': [-40769244, 11887560, 56536056, -45386640, 5050782, 5649102, 2316897, -6908562, 5188554, -2490430, 860433, -204084, 18224, 6486, -3003, 526, -36, -6, 1], 'lmfdb_label': '210.d6', 'torsion': [36]}
  • id: 8629
    {'degree': 18, 'field': [93312, 0, -404352, 0, 508896, 0, -158144, 0, 47352, 0, 71880, 0, 16618, 0, 1572, 0, 66, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [36]}
  • id: 8627
    {'degree': 18, 'field': [25092716544, 0, -7169347584, 0, 960180480, 0, -126831600, 0, 4773384, 0, 1049580, 0, -23338, 0, -1428, 0, 42, 0, 1], 'lmfdb_label': '210.d6', 'torsion': [2, 18]}
• 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: 1764
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '210.d6', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1765
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '210.d6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 1766
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '210.d6', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1767
    {'conductor': 210, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '210.d6', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1666665
    {'adelic_gens': [[246, 409, 35, 176], [1, 12, 12, 145], [337, 24, 684, 289], [15, 106, 374, 11], [631, 24, 642, 289], [421, 24, 572, 149], [817, 24, 816, 25], [496, 21, 195, 466], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '840.384.5.?', 'conductor': 210, 'lmfdb_label': '210.d6', 'prime': 0}
  • id: 895
    {'conductor': 210, 'elladic_image': '8.12.0.7', 'lmfdb_label': '210.d6', 'modell_image': '2B', 'prime': 2}
  • id: 896
    {'conductor': 210, 'elladic_image': '3.8.0.1', 'lmfdb_label': '210.d6', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 210.d does not appear in ec_padic