Elliptic curve data - 85291.a1

Formats: - HTML - YAML - JSON - 2024-06-04T10:44:31.530610

• 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': '85291a', 'Clabel': '85291a3', 'Cnumber': 3, 'abc_quality': 1.104947099482495, 'absD': 1718709261211, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 68742, 'ainvs': [0, -1, 1, -3453537, 2471420737], 'analytic_rank': 1, 'bad_primes': [19, 67], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 85291, 'degree': 912384, 'elladic_images': ['27.36.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1357854666868008333551308818', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9], 'jinv': [-50357871050752, 19], 'lmfdb_iso': '85291.a', 'lmfdb_label': '85291.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -769, -8470], 'min_quad_twist_disc': -67, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '27.36.0.a.1', '38.2.0.a.1', '114.8.0.?', '171.36.0.?', '201.8.0.?', '342.72.3.?', '513.324.16.?', '603.24.0.?', '1026.648.43.?', '1809.72.0.?', '7638.16.0.?', '11457.72.0.?', '22914.144.3.?', '34371.648.16.?', '68742.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.6189532928564484771374511095', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.033439156991317803520094883618', 'prec': 107}, 'szpiro_ratio': 5.000811240044095, '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, 2, -2, -3, 0, 1, 0, 1, 0, -3, -4, 4, 0, -6, 4, -3, 0, 1, 6], 'aplist': [0, 2, -3, 1, -3, 4, -3, 1, 0, 6, 4, 2, 6, 1, -3, -12, -6, 1, 0, 6, -7, -8, 12, 12, -8], 'class_deg': 9, 'class_size': 3, 'conductor': 85291, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '85291.a', 'trace_hash': 1934132040798618685}
• 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': '0.013959835946873308799821799323', 'prec': 107}, 'conductor': 85291, 'gens': [[-7367, 1860677, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '5.6189532928564484771374511095', 'prec': 100}], 'lmfdb_label': '85291.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.50420458430323004953966431594', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6662040184879025229728857085581367155', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 5, 0], '3': [3, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [4, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '67': 'a'}, 'iwp0': 0, 'lmfdb_label': '85291.a1'}
• ec_torsion_growth •

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

  
  
  • id: 3998280
    {'degree': 2, 'field': [-50, -1, 1], 'lmfdb_label': '85291.a1', 'torsion': [3]}
  • id: 3998281
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '85291.a1', 'torsion': [2]}
  • id: 3998285
    {'degree': 6, 'field': [-140502, -2502, 7558, 97, -145, -1, 1], 'lmfdb_label': '85291.a1', 'torsion': [6]}
  • id: 3998282
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '85291.a1', 'torsion': [2, 2]}
  • id: 3998284
    {'degree': 6, 'field': [2547, -14283, 10485, 489, -261, -3, 1], 'lmfdb_label': '85291.a1', 'torsion': [9]}
  • id: 3998283
    {'degree': 6, 'field': [9413, -1885, 874, 3, 38, -1, 1], 'lmfdb_label': '85291.a1', 'torsion': [3]}
  • id: 3998286
    {'degree': 12, 'field': [-28095693347, 4206966670, 936584684, -54085038, -11013397, -2673372, 835592, 25004, -16913, 598, 12, -6, 1], 'lmfdb_label': '85291.a1', 'torsion': [4]}
  • id: 3998287
    {'degree': 12, 'field': [20340100, 0, 8146703, 0, 1204743, 0, 95143, 0, 4221, 0, 101, 0, 1], 'lmfdb_label': '85291.a1', 'torsion': [3, 3]}
  • id: 3998288
    {'degree': 12, 'field': [24250249, -9206781, 10035447, -2668560, 1550988, -315690, 124799, -18348, 5361, -528, 117, -6, 1], 'lmfdb_label': '85291.a1', 'torsion': [9]}
  • id: 3998289
    {'degree': 12, 'field': [16294777801, 0, -1929195301, 0, 95631606, 0, -2534093, 0, 37806, 0, -301, 0, 1], 'lmfdb_label': '85291.a1', 'torsion': [2, 6]}
  • id: 3998291
    {'degree': 18, 'field': [-99499598909559, -95561136041895, 28642397127948, 19675520254002, 240400323675, -3820567650375, 336447521446, 214090370781, -26738741160, -5798328587, 827408970, 90037797, -13236490, -834123, 115545, 4238, -528, -9, 1], 'lmfdb_label': '85291.a1', 'torsion': [18]}
  • id: 3998290
    {'degree': 18, 'field': [112368513604, -11239533608, 57360521356, -6506116820, 13418984530, -1593905374, 1882527801, -210000223, 172347213, -16498882, 10500853, -806143, 420602, -24209, 10641, -410, 155, -3, 1], 'lmfdb_label': '85291.a1', 'torsion': [6]}
• 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: 2079825
    {'conductor': 85291, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '85291.a1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2079826
    {'conductor': 85291, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '85291.a1', 'prime': 67, 'reduction_type': 0, '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: 2225802
    {'adelic_gens': [[52325, 0, 0, 68741], [33769, 6231, 19095, 18560], [8845, 48240, 65995, 23719], [1, 54, 0, 1], [28, 27, 729, 703], [68689, 54, 68688, 55], [1, 0, 54, 1], [31, 36, 62920, 61981]], 'adelic_image': '68742.1296.43.?', 'conductor': 85291, 'lmfdb_label': '85291.a1', 'prime': 0}
  • id: 348055
    {'conductor': 85291, 'elladic_image': '27.36.0.1', 'lmfdb_label': '85291.a1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 4402893
    {'lmfdb_iso': '85291.a', 'p': 5, 'prec': 20, 'unit': 4038829066382, 'val': 1}
  • id: 4402894
    {'lmfdb_iso': '85291.a', 'p': 7, 'prec': 20, 'unit': 40527248787776082, 'val': -1}
  • id: 4402892
    {'lmfdb_iso': '85291.a', 'p': 11, 'prec': 20, 'unit': 4012122199738637073, 'val': 1}
  • id: 4402899
    {'lmfdb_iso': '85291.a', 'p': 13, 'prec': 20, 'unit': 981947235184547694825, 'val': 1}
  • id: 4402901
    {'lmfdb_iso': '85291.a', 'p': 17, 'prec': 20, 'unit': 110223140454629094976991, 'val': 1}
  • id: 4402898
    {'lmfdb_iso': '85291.a', 'p': 29, 'prec': 20, 'unit': 817281932198031701487253391, 'val': 1}
  • id: 4402895
    {'lmfdb_iso': '85291.a', 'p': 31, 'prec': 20, 'unit': 9600481619462789925261414212, 'val': 1}
  • id: 4402910
    {'lmfdb_iso': '85291.a', 'p': 37, 'prec': 20, 'unit': 555303041317817238291905388660, 'val': 1}
  • id: 4402896
    {'lmfdb_iso': '85291.a', 'p': 41, 'prec': 20, 'unit': 2909443194994677304408446251628, 'val': 1}
  • id: 4402897
    {'lmfdb_iso': '85291.a', 'p': 43, 'prec': 20, 'unit': 390686296267039427698421953336142, 'val': -1}
  • id: 4402908
    {'lmfdb_iso': '85291.a', 'p': 47, 'prec': 20, 'unit': 25850997756350538064024124473505, 'val': 1}
  • id: 4402903
    {'lmfdb_iso': '85291.a', 'p': 53, 'prec': 20, 'unit': 137425091787065103627363763824896, 'val': 1}
  • id: 4402904
    {'lmfdb_iso': '85291.a', 'p': 59, 'prec': 20, 'unit': 4077142423296798533510848013942684, 'val': 1}
  • id: 4402909
    {'lmfdb_iso': '85291.a', 'p': 61, 'prec': 20, 'unit': 116480261116814196845734075080323193, 'val': -1}
  • id: 4402907
    {'lmfdb_iso': '85291.a', 'p': 71, 'prec': 20, 'unit': 78830110398397403861329054570068353, 'val': 1}
  • id: 4402905
    {'lmfdb_iso': '85291.a', 'p': 73, 'prec': 20, 'unit': 294141769540576069478015247465323, 'val': 2}
  • id: 4402900
    {'lmfdb_iso': '85291.a', 'p': 79, 'prec': 20, 'unit': 153507563322324858316277452518035453, 'val': 1}
  • id: 4402902
    {'lmfdb_iso': '85291.a', 'p': 83, 'prec': 20, 'unit': 223813959687794796334331340313566479, 'val': 1}
  • id: 4402906
    {'lmfdb_iso': '85291.a', 'p': 89, 'prec': 20, 'unit': 4330542562856443545587022645838044748, 'val': 1}
  • id: 4402891
    {'lmfdb_iso': '85291.a', 'p': 97, 'prec': 20, 'unit': 31904226277239560280487964744912134252, 'val': 1}