Elliptic curve data - 8349.a1

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• 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': '8349d', 'Clabel': '8349d2', 'Cnumber': 2, 'abc_quality': 0.9246304097924353, 'absD': 2811467307, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 276, 'ainvs': [1, 0, 0, -1878, 31065], 'analytic_rank': 1, 'bad_primes': [3, 11, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 8349, 'degree': 5120, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.67155408812751617810995733329', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [413493625, 1587], 'lmfdb_iso': '8349.a', 'lmfdb_label': '8349.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -16, -25], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '92.6.0.?', '276.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2623255114076569274274055070', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.52739354827166909392101445569', 'prec': 107}, 'szpiro_ratio': 3.79046672422401, '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, 0, -1, 2, 3, 1, 0, 0, -1, 6, -2, 0, -1, -4, -1, -2, 0], 'aplist': [-1, 1, 0, 2, 0, 6, -4, -2, -1, -2, 4, 2, -2, -10, 0, -12, -12, 6, -10, 8, 14, -10, -12, -16, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 8349, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '8349.a', 'trace_hash': 1347708721485568697}
• 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': '0.26103306959538999109684425446', 'prec': 103}, 'conductor': 8349, 'gens': [[-1, 182, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2623255114076569274274055070', 'prec': 100}], 'lmfdb_label': '8349.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.4393977338382216658851826058', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6339769609727112264844885557007797497', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[95, -95, 2]], 'xcoord_integral_points': [-1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [2, 0], '5': [1, 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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '8349.a1'}
• ec_torsion_growth •

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

  
  
  • id: 436138
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '8349.a1', 'torsion': [2, 2]}
  • id: 436139
    {'degree': 4, 'field': [82, -40, 17, -1, 1], 'lmfdb_label': '8349.a1', 'torsion': [4]}
  • id: 436142
    {'degree': 8, 'field': [-16125, 25275, -14955, 3467, -49, -52, 1, -2, 1], 'lmfdb_label': '8349.a1', 'torsion': [6]}
  • id: 436141
    {'degree': 8, 'field': [5184, 0, -3024, 0, 429, 0, -24, 0, 1], 'lmfdb_label': '8349.a1', 'torsion': [2, 4]}
  • id: 436140
    {'degree': 8, 'field': [14617, -2048, 5219, -1854, 476, -96, 23, -2, 1], 'lmfdb_label': '8349.a1', 'torsion': [2, 4]}
  • id: 436143
    {'degree': 16, 'field': [102348544, -89522176, -41364352, 38575744, 3657920, -3086912, 6067968, -2489472, 1275052, -326040, 86034, -13826, 2849, -374, 56, -4, 1], 'lmfdb_label': '8349.a1', 'torsion': [8]}
  • id: 436144
    {'degree': 16, 'field': [227979801, 0, -171540, 0, -4456422, 0, -880305, 0, 65049, 0, -15675, 0, 2173, 0, -85, 0, 1], 'lmfdb_label': '8349.a1', 'torsion': [2, 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: 173624
    {'conductor': 8349, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8349.a1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 173625
    {'conductor': 8349, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '8349.a1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 173626
    {'conductor': 8349, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8349.a1', 'prime': 23, '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: 1719130
    {'adelic_gens': [[1, 2, 2, 5], [1, 4, 0, 1], [97, 4, 194, 9], [273, 4, 272, 5], [208, 73, 69, 208], [1, 0, 4, 1], [3, 4, 8, 11], [94, 1, 91, 0]], 'adelic_image': '276.12.0.?', 'conductor': 8349, 'lmfdb_label': '8349.a1', 'prime': 0}
  • id: 40838
    {'conductor': 8349, 'elladic_image': '2.3.0.1', 'lmfdb_label': '8349.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 345085
    {'lmfdb_iso': '8349.a', 'p': 7, 'prec': 20, 'unit': 6157336652435937, 'val': 1}
  • id: 345089
    {'lmfdb_iso': '8349.a', 'p': 13, 'prec': 20, 'unit': 132329683715742516708, 'val': 1}
  • id: 345091
    {'lmfdb_iso': '8349.a', 'p': 17, 'prec': 20, 'unit': 162725579323178635578208, 'val': 1}
  • id: 345081
    {'lmfdb_iso': '8349.a', 'p': 19, 'prec': 20, 'unit': 1512306904700987235460955, 'val': 1}
  • id: 345088
    {'lmfdb_iso': '8349.a', 'p': 29, 'prec': 20, 'unit': 2788878024236959633860197799, 'val': 1}
  • id: 345099
    {'lmfdb_iso': '8349.a', 'p': 31, 'prec': 20, 'unit': 21335094594936270645641772868, 'val': 1}
  • id: 345084
    {'lmfdb_iso': '8349.a', 'p': 37, 'prec': 20, 'unit': 593174726680475338838616768167, 'val': 1}
  • id: 345086
    {'lmfdb_iso': '8349.a', 'p': 41, 'prec': 20, 'unit': 2572778191303941496351027798085, 'val': 1}
  • id: 345087
    {'lmfdb_iso': '8349.a', 'p': 43, 'prec': 20, 'unit': 1142328575546657175159380101386, 'val': 1}
  • id: 345093
    {'lmfdb_iso': '8349.a', 'p': 53, 'prec': 20, 'unit': 365489567899776708317241761954304, 'val': 1}
  • id: 345097
    {'lmfdb_iso': '8349.a', 'p': 59, 'prec': 20, 'unit': 3985185615120227211616766619117613, 'val': 1}
  • id: 345098
    {'lmfdb_iso': '8349.a', 'p': 61, 'prec': 20, 'unit': 1670327765135340980864910387848098, 'val': 1}
  • id: 345083
    {'lmfdb_iso': '8349.a', 'p': 67, 'prec': 20, 'unit': 47029179109171613376570732634540728, 'val': 1}
  • id: 345096
    {'lmfdb_iso': '8349.a', 'p': 71, 'prec': 20, 'unit': 94844011206856985482507234807493086, 'val': 1}
  • id: 345094
    {'lmfdb_iso': '8349.a', 'p': 73, 'prec': 20, 'unit': 11188781890896252833037633226267433, 'val': 1}
  • id: 345090
    {'lmfdb_iso': '8349.a', 'p': 79, 'prec': 20, 'unit': 37835365483826894285699943082772917, 'val': 1}
  • id: 345092
    {'lmfdb_iso': '8349.a', 'p': 83, 'prec': 20, 'unit': 2636122614931865091287800505674328537, 'val': 1}
  • id: 345095
    {'lmfdb_iso': '8349.a', 'p': 89, 'prec': 20, 'unit': 3838473255885708592577058992413372319, 'val': 1}
  • id: 345082
    {'lmfdb_iso': '8349.a', 'p': 97, 'prec': 20, 'unit': 9146889227002653715369829278407191184, 'val': 1}