Elliptic curve data - 99099.bk2

Formats: - HTML - YAML - JSON - 2024-05-06T09:12:43.691296

• 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': '99099q', 'Clabel': '99099q1', 'Cnumber': 1, 'abc_quality': 0.8714055948137694, 'absD': 117523585179, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 18018, 'ainvs': [0, 0, 1, -7986, 275184], 'analytic_rank': 1, 'bad_primes': [3, 7, 11, 13], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 99099, 'degree': 138240, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0097453336815730801334298859', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 36, 'isogeny_degrees': [1, 3, 9], 'jinv': [-43614208, 91], 'lmfdb_iso': '99099.bk', 'lmfdb_label': '99099.bk2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -7, 5], 'min_quad_twist_disc': 33, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '33.8.0-3.a.1.1', '99.24.0.?', '117.36.0.?', '182.2.0.?', '546.8.0.?', '1287.72.0.?', '1638.72.3.?', '6006.16.0.?', '18018.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4745532074991647694970239791', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.73850844705166703759516452154', 'prec': 107}, 'szpiro_ratio': 3.353090944111825, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, -2, 3, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 4, -6, 0, 7, -6], 'aplist': [0, 0, 3, -1, 0, -1, -6, 7, -3, -9, 5, 2, -6, 1, -3, 9, 0, 10, 14, 6, -11, 1, 3, -15, -1], 'class_deg': 9, 'class_size': 3, 'conductor': 99099, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '99099.bk', 'trace_hash': 37469425927844504}
• 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': '0.13272304804758853569480337235', 'prec': 103}, 'conductor': 99099, 'gens': [[-88, 544, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4745532074991647694970239791', 'prec': 100}], 'lmfdb_label': '99099.bk2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0513405298354723639642981233', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.2010302017710684395265186213456822749', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-88, 372]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [20, 5, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '99099.bk2'}
• ec_torsion_growth •

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

  
  
  • id: 4603127
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '99099.bk2', 'torsion': [3]}
  • id: 4603128
    {'degree': 3, 'field': [-2, 4, 0, 1], 'lmfdb_label': '99099.bk2', 'torsion': [2]}
  • id: 4603132
    {'degree': 6, 'field': [-1122, -330, 202, 27, -13, -3, 1], 'lmfdb_label': '99099.bk2', 'torsion': [6]}
  • id: 4603131
    {'degree': 6, 'field': [-131, 25, 215, 27, -33, -1, 1], 'lmfdb_label': '99099.bk2', 'torsion': [9]}
  • id: 4603129
    {'degree': 6, 'field': [9, -33, 44, -23, 14, -3, 1], 'lmfdb_label': '99099.bk2', 'torsion': [2, 2]}
  • id: 4603130
    {'degree': 6, 'field': [9036, -1392, -237, 163, 12, -3, 1], 'lmfdb_label': '99099.bk2', 'torsion': [3]}
  • id: 4603133
    {'degree': 12, 'field': [-456491042, 5527304, -251374608, -56818244, -18056204, -272352, -1346540, 22272, -11280, -298, 4, 0, 1], 'lmfdb_label': '99099.bk2', 'torsion': [4]}
  • id: 4603134
    {'degree': 12, 'field': [138384, -199764, 114351, -26313, 13060, -1089, -949, 852, 45, 21, -4, -3, 1], 'lmfdb_label': '99099.bk2', 'torsion': [3, 3]}
  • id: 4603135
    {'degree': 12, 'field': [168631, -250097, 143959, -16681, -21716, 10691, -666, -748, 164, 28, -5, -2, 1], 'lmfdb_label': '99099.bk2', 'torsion': [9]}
  • id: 4603136
    {'degree': 12, 'field': [2217121, 0, -672665, 0, 94190, 0, -9509, 0, 674, 0, -29, 0, 1], 'lmfdb_label': '99099.bk2', 'torsion': [2, 6]}
  • id: 4603137
    {'degree': 18, 'field': [73779588, -120742116, 113130684, -64228436, 26749564, -7614656, 1576449, 35757, -47801, -40416, 55133, -17659, 2492, 287, 165, -90, 29, -3, 1], 'lmfdb_label': '99099.bk2', 'torsion': [6]}
  • id: 4603138
    {'degree': 18, 'field': [293129719, -393552837, -145759236, 304062390, 11541615, -100820079, 8204406, 18737757, -2821934, -2164591, 433518, 165117, -38742, -8607, 2121, 294, -68, -5, 1], 'lmfdb_label': '99099.bk2', '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: 2431357
    {'conductor': 99099, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '99099.bk2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2431358
    {'conductor': 99099, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '99099.bk2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2431359
    {'conductor': 99099, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '99099.bk2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2431360
    {'conductor': 99099, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '99099.bk2', 'prime': 13, '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: 2315472
    {'adelic_gens': [[1637, 0, 0, 18017], [18001, 18, 18000, 19], [1, 18, 0, 1], [1, 0, 18, 1], [10, 9, 81, 73], [15445, 11484, 9603, 13267], [4291, 11484, 14355, 6205], [1627, 6534, 13266, 5543], [1, 18, 10, 181]], 'adelic_image': '18018.144.3.?', 'conductor': 99099, 'lmfdb_label': '99099.bk2', 'prime': 0}
  • id: 398572
    {'conductor': 99099, 'elladic_image': '9.12.0.1', 'lmfdb_label': '99099.bk2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 5155112
    {'lmfdb_iso': '99099.bk', 'p': 5, 'prec': 20, 'unit': 14864445323353, 'val': 1}
  • id: 5155119
    {'lmfdb_iso': '99099.bk', 'p': 17, 'prec': 20, 'unit': 175393375899186785823198, 'val': 1}
  • id: 5155109
    {'lmfdb_iso': '99099.bk', 'p': 19, 'prec': 20, 'unit': 411897054290378716189002, 'val': 1}
  • id: 5155123
    {'lmfdb_iso': '99099.bk', 'p': 23, 'prec': 20, 'unit': 27766113650316048959208331, 'val': 1}
  • id: 5155117
    {'lmfdb_iso': '99099.bk', 'p': 29, 'prec': 20, 'unit': 3676444787047970151465695172, 'val': 1}
  • id: 5155114
    {'lmfdb_iso': '99099.bk', 'p': 31, 'prec': 20, 'unit': 19477305389283736711945192774, 'val': 1}
  • id: 5155127
    {'lmfdb_iso': '99099.bk', 'p': 37, 'prec': 20, 'unit': 296197099529139212176337869205, 'val': 1}
  • id: 5155115
    {'lmfdb_iso': '99099.bk', 'p': 41, 'prec': 20, 'unit': 1507311026147803498103797351510, 'val': 1}
  • id: 5155116
    {'lmfdb_iso': '99099.bk', 'p': 43, 'prec': 20, 'unit': 10913523945909332388920564663484, 'val': -1}
  • id: 5155118
    {'lmfdb_iso': '99099.bk', 'p': 47, 'prec': 20, 'unit': 45813888669150537804704681477508, 'val': 1}
  • id: 5155121
    {'lmfdb_iso': '99099.bk', 'p': 53, 'prec': 20, 'unit': 427281716275917910084351061522798, 'val': 1}
  • id: 5155126
    {'lmfdb_iso': '99099.bk', 'p': 61, 'prec': 20, 'unit': 6844001689350619858521309694327912, 'val': 1}
  • id: 5155111
    {'lmfdb_iso': '99099.bk', 'p': 67, 'prec': 20, 'unit': 36368382601100184923221720919142907, 'val': 1}
  • id: 5155113
    {'lmfdb_iso': '99099.bk', 'p': 71, 'prec': 20, 'unit': 97310706191775999151941906857245945, 'val': 1}
  • id: 5155122
    {'lmfdb_iso': '99099.bk', 'p': 73, 'prec': 20, 'unit': 29649152266999437978821921334945675, 'val': 1}
  • id: 5155125
    {'lmfdb_iso': '99099.bk', 'p': 79, 'prec': 20, 'unit': 35531349834222963583667344397192670725, 'val': -1}
  • id: 5155120
    {'lmfdb_iso': '99099.bk', 'p': 83, 'prec': 20, 'unit': 995026459029514947899657438197310923, 'val': 1}
  • id: 5155124
    {'lmfdb_iso': '99099.bk', 'p': 89, 'prec': 20, 'unit': 10147037551490639633916034126726470341, 'val': 1}
  • id: 5155110
    {'lmfdb_iso': '99099.bk', 'p': 97, 'prec': 20, 'unit': 53867772298584434343333048150657285665, 'val': 1}