Elliptic curve data - 210210.dk1

Formats: - HTML - YAML - JSON - 2025-10-18T08:15:18.245460

• 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': '210210cd', 'Clabel': '210210cd4', 'Cnumber': 4, 'abc_quality': 1.0625410991773636, 'absD': 22315620179138275489500000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 24024, 'ainvs': [1, 1, 1, -173916788340, 27916389331186005], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 210210, 'degree': 696729600, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.8040769926140472749587688483', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 88, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4944928228995290413834018379264689, 189679641808585500000], 'lmfdb_iso': '210210.dk', 'lmfdb_label': '210210.dk1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3549322211, -81389397224415], 'min_quad_twist_disc': -7, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '21.8.0-3.a.1.2', '42.24.0-6.a.1.4', '88.6.0.?', '156.24.0.?', '264.24.0.?', '1092.48.0.?', '1848.48.0.?', '3432.48.1.?', '24024.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 6, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 539], [3, 4, 98], [5, 6, 7007], [7, 26, 4290], [11, 12, 19110], [13, 14, 16170]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.8311219180863906224060924766', 'prec': 100}, 'szpiro_ratio': 7.282974396765504, '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, 1, -1, 1, 1, -1, 0, 1, 1, 1, -1, -1, -1, 0, -1, 1, 0, 1, -2, 1], 'aplist': [1, -1, 1, 0, -1, -1, 0, -2, 6, 6, -2, -4, 6, 8, 0, 0, 12, -2, 8, 12, -8, 8, -12, -6, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 210210, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '210210.dk', 'trace_hash': 1121601332412582536}
• 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': '0.000067178722823066097917524594219', 'prec': 117}, 'conductor': 210210, 'gens': [], 'heights': [], 'lmfdb_label': '210210.dk1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.036347752007778252436848562332', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3617302409333902924218274798168058592', 'prec': 130}, 'tamagawa_product': 480, 'torsion_generators': [[963091, -963095, 2]], 'xcoord_integral_points': []}
• lmfdb_label 210210.dk1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9187159
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '210210.dk1', 'torsion': [2, 2]}
  • id: 9187160
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '210210.dk1', 'torsion': [6]}
  • id: 9187162
    {'degree': 4, 'field': [267, 54, -53, -2, 1], 'lmfdb_label': '210210.dk1', 'torsion': [2, 6]}
  • id: 9187161
    {'degree': 4, 'field': [1078, 0, -49, 0, 1], 'lmfdb_label': '210210.dk1', 'torsion': [4]}
  • id: 9187163
    {'degree': 6, 'field': [212, -120, -18, 11, 9, -3, 1], 'lmfdb_label': '210210.dk1', 'torsion': [6]}
  • id: 9187166
    {'degree': 8, 'field': [484, 0, -770, 0, 555, 0, -35, 0, 1], 'lmfdb_label': '210210.dk1', 'torsion': [12]}
  • id: 9187165
    {'degree': 8, 'field': [234256, 0, 78144, 0, 9617, 0, -186, 0, 1], 'lmfdb_label': '210210.dk1', 'torsion': [2, 4]}
  • id: 9187164
    {'degree': 8, 'field': [220522500, 0, -17182000, 0, 126500, 0, -440, 0, 1], 'lmfdb_label': '210210.dk1', 'torsion': [2, 4]}
  • id: 9187167
    {'degree': 12, 'field': [316, -984, 612, 560, 240, -804, 605, -366, 195, -80, 27, -6, 1], 'lmfdb_label': '210210.dk1', 'torsion': [3, 6]}
  • id: 9187168
    {'degree': 12, 'field': [161572856, 50357712, -22795860, -11544944, 2534442, 768984, -157419, -25086, 5493, 532, -105, -6, 1], 'lmfdb_label': '210210.dk1', 'torsion': [2, 6]}
  • id: 9187171
    {'degree': 16, 'field': [2258377081, 1238318004, -73078504, 185489128, 148061515, 4541900, -5640682, -4295984, 1027372, 131516, -5116, -7832, 2779, -220, -58, 0, 1], 'lmfdb_label': '210210.dk1', 'torsion': [2, 12]}
  • id: 9187170
    {'degree': 16, 'field': [13478370417801, 9107256920904, -11191137729420, 4238896290720, -2294820850526, 203549050664, -56355654128, -9845703880, 2452635131, 7244264, -2833568, 756568, -127126, 448, -44, -8, 1], 'lmfdb_label': '210210.dk1', 'torsion': [2, 12]}
  • id: 9187169
    {'degree': 16, 'field': [155257281811984, 0, 7908716603040, 0, 360195596200, 0, 4653339768, 0, 43979697, 0, -8032584, 0, 98278, 0, -384, 0, 1], 'lmfdb_label': '210210.dk1', 'torsion': [8]}
  • id: 9187172
    {'degree': 18, 'field': [70573698949245025, 102433960227977550, 59543740162678050, 17341552293856035, 2548929513440565, 162628124412150, 3784223863956, 46154632311, -149225770242, -23066636737, -872981217, -114158601, -8756733, 468099, -15507, 858, 333, -9, 1], 'lmfdb_label': '210210.dk1', 'torsion': [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: 5209154
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '210210.dk1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 5209155
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '210210.dk1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5209156
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '210210.dk1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 5209157
    {'conductor': 210210, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '210210.dk1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5209158
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '210210.dk1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5209159
    {'conductor': 210210, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '210210.dk1', 'prime': 13, '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: 3008990
    {'adelic_gens': [[20591, 0, 0, 24023], [1, 0, 12, 1], [1002, 8449, 13013, 17018], [24013, 12, 24012, 13], [8009, 3444, 9730, 20665], [1, 6, 6, 37], [20602, 6867, 22281, 3424], [1, 12, 0, 1], [12937, 3444, 19278, 20665], [11, 2, 23974, 24015], [16234, 6867, 12453, 3424]], 'adelic_image': '24024.96.1.?', 'conductor': 210210, 'lmfdb_label': '210210.dk1', 'prime': 0}
  • id: 775636
    {'conductor': 210210, 'elladic_image': '2.3.0.1', 'lmfdb_label': '210210.dk1', 'modell_image': '2B', 'prime': 2}
  • id: 775637
    {'conductor': 210210, 'elladic_image': '3.4.0.1', 'lmfdb_label': '210210.dk1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 210210.dk does not appear in ec_padic