Elliptic curve data - 206910.ej2

Formats: - HTML - YAML - JSON - 2025-10-19T08:11:40.980740

• 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': '206910j', 'Clabel': '206910j2', 'Cnumber': 2, 'abc_quality': 1.0425519890633115, 'absD': 1144839861671616000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 12540, 'ainvs': [1, -1, 1, -451925222, 3697951492469], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 206910, 'degree': 49766400, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4653070574848057578703858541', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 113, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [7903870428425797297009, 886464000000], 'lmfdb_iso': '206910.ej', 'lmfdb_label': '206910.ej2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -414991, 102863225], 'min_quad_twist_disc': 33, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '33.8.0-3.a.1.1', '60.24.0.t.1', '66.24.0-6.a.1.1', '76.6.0.?', '228.24.0.?', '660.48.0.?', '1140.48.1.?', '2508.48.0.?', '12540.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 10, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.71787865348964417250128907089', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 20691], [3, 2, 2299], [5, 6, 41382], [11, 62, 1710], [19, 20, 10890]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7170532767515656401417914467', 'prec': 100}, 'szpiro_ratio': 5.833370608604099, '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, 0, 1, 1, 0, -2, 1, 0, 1, 0, 0, 4, -2, 0, 1, -6, 0, -1, 1], 'aplist': [1, 0, 1, -2, 0, 4, -6, -1, 0, 0, 8, 8, -12, -2, 0, 6, 12, -2, -16, 0, 10, -8, 0, 12, 8], 'class_deg': 6, 'class_size': 4, 'conductor': 206910, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '206910.ej', 'trace_hash': 1116454411698960685}
• 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': '0.00097740044780432618063076747416', 'prec': 113}, 'conductor': 206910, 'gens': [[12777, 90811, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.71787865348964417250128907089', 'prec': 103}], 'lmfdb_label': '206910.ej2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.11939870386554560231017413689', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.342784429354557549380117570892533760', 'prec': 130}, 'tamagawa_product': 576, 'torsion_generators': [[49083, -49087, 2]], 'xcoord_integral_points': [-24483, 11817, 12277, 12777, 5290777]}
• lmfdb_label 206910.ej2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9050026
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '206910.ej2', 'torsion': [2, 2]}
  • id: 9050027
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '206910.ej2', 'torsion': [6]}
  • id: 9050029
    {'degree': 4, 'field': [102, 54, -53, -2, 1], 'lmfdb_label': '206910.ej2', 'torsion': [2, 6]}
  • id: 9050028
    {'degree': 4, 'field': [529, 43, 38, -1, 1], 'lmfdb_label': '206910.ej2', 'torsion': [4]}
  • id: 9050030
    {'degree': 6, 'field': [495, -429, 48, 31, -4, -1, 1], 'lmfdb_label': '206910.ej2', 'torsion': [6]}
  • id: 9050033
    {'degree': 8, 'field': [576, 576, 456, 84, 178, -78, 29, -3, 1], 'lmfdb_label': '206910.ej2', 'torsion': [12]}
  • id: 9050032
    {'degree': 8, 'field': [51984, 0, -797088, 0, 5605, 0, -152, 0, 1], 'lmfdb_label': '206910.ej2', 'torsion': [2, 4]}
  • id: 9050031
    {'degree': 8, 'field': [2608225, 0, -24795, 0, 4196, 0, -27, 0, 1], 'lmfdb_label': '206910.ej2', 'torsion': [2, 4]}
  • id: 9050034
    {'degree': 12, 'field': [144, -1548, 5847, -3225, 580, 111, -325, 108, 21, 21, -4, -3, 1], 'lmfdb_label': '206910.ej2', 'torsion': [3, 6]}
  • id: 9050035
    {'degree': 12, 'field': [900, 2076, 678, -6010, 4395, -2064, 1403, -726, 330, -110, 33, -6, 1], 'lmfdb_label': '206910.ej2', 'torsion': [2, 6]}
  • id: 9050038
    {'degree': 16, 'field': [-22236012, -38391552, 56301600, -2392632, -42860936, 36316448, 485488, -2971068, 463453, -72884, -69920, 11020, 4330, -228, -112, 0, 1], 'lmfdb_label': '206910.ej2', 'torsion': [2, 12]}
  • id: 9050037
    {'degree': 16, 'field': [13124884, 6191404, 21442406, 166402, 4223541, -5316626, 249840, 795064, -3509, -22432, 5454, 938, 267, 38, -4, -4, 1], 'lmfdb_label': '206910.ej2', 'torsion': [2, 12]}
  • id: 9050036
    {'degree': 16, 'field': [15863552860, -5286963760, 1126042680, -42759200, 70360791, -22737840, 34217887, -17440574, 6051549, -1288636, 219604, -6528, -2073, 188, -51, -2, 1], 'lmfdb_label': '206910.ej2', 'torsion': [8]}
  • id: 9050039
    {'degree': 18, 'field': [-22053039, 34576776, -8553645, -23470746, 28650402, -21498858, 16112182, -8178594, 1649676, 157942, -146628, 58482, -19650, 4914, -774, 10, 3, -6, 1], 'lmfdb_label': '206910.ej2', '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: 5124972
    {'conductor': 206910, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '206910.ej2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 5124973
    {'conductor': 206910, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '206910.ej2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5124974
    {'conductor': 206910, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '206910.ej2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 5124975
    {'conductor': 206910, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '206910.ej2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5124976
    {'conductor': 206910, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '206910.ej2', 'prime': 19, '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: 2988385
    {'adelic_gens': [[1, 6, 6, 37], [1, 12, 0, 1], [5226, 4477, 5225, 1046], [3419, 0, 0, 12539], [1891, 5698, 3036, 12539], [12529, 12, 12528, 13], [5017, 3432, 462, 8053], [11, 2, 12490, 12531], [4390, 10263, 3993, 6832], [1, 0, 12, 1]], 'adelic_image': '12540.96.1.?', 'conductor': 206910, 'lmfdb_label': '206910.ej2', 'prime': 0}
  • id: 764468
    {'conductor': 206910, 'elladic_image': '2.3.0.1', 'lmfdb_label': '206910.ej2', 'modell_image': '2B', 'prime': 2}
  • id: 764469
    {'conductor': 206910, 'elladic_image': '3.4.0.1', 'lmfdb_label': '206910.ej2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 206910.ej does not appear in ec_padic