Elliptic curve data - 441.a2

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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
  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': '441f', 'Clabel': '441f1', 'Cnumber': 1, 'abc_quality': 0.9123874511245065, 'absD': 107163, 'adelic_genus': 9, 'adelic_index': 336, 'adelic_level': 546, 'ainvs': [0, 0, 1, -21, 40], 'analytic_rank': 1, 'bad_primes': [3, 7], 'class_deg': 13, 'class_size': 2, 'cm': 0, 'conductor': 441, 'degree': 48, 'elladic_images': ['13.28.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.29578137208499745632736253347', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 13], 'jinv': [-28672, 3], 'lmfdb_iso': '441.a', 'lmfdb_label': '441.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -2, -1], 'min_quad_twist_disc': -3, 'modell_images': ['13B.4.1'], 'modm_images': ['6.2.0.a.1', '13.28.0.a.1', '78.56.1.?', '91.84.2.?', '182.168.2.?', '273.168.2.?', '546.336.9.?'], 'nonmax_primes': [13], 'nonmax_rad': 13, 'num_bad_primes': 2, 'num_int_pts': 10, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.076270034394571012613674763318', 'prec': 107}, 'semistable': False, 'serre_invariants': [[3, 8, 49], [7, 14, 9]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1694058745949378528758772758', 'prec': 103}, 'szpiro_ratio': 3.434588835051495, '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, -2, 0, 2, -2, 0, 0, 0, 0, 4, 2, 0, -1, 0, 0, -4, 0, 0, -1, -4], 'aplist': [-2, 0, -2, 0, 2, -1, 0, -1, 0, -4, -9, 3, -10, 5, -6, -12, -12, -10, -5, 6, 3, -1, 6, 16, 6], 'class_deg': 13, 'class_size': 2, 'conductor': 441, 'isogeny_matrix': [[1, 13], [13, 1]], 'lmfdb_iso': '441.a', 'trace_hash': 804677887719655042}
• 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': '1.8068097917472891421714666268', 'prec': 100}, 'conductor': 441, 'gens': [[4, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.076270034394571012613674763318', 'prec': 107}], 'lmfdb_label': '441.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '3.2597903746182327614046723214', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999999', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '0.99449729596489655501469818656666866663', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-5, 1, 2, 4, 46]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '441.a2'}
• ec_torsion_growth •

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

  
  
  • id: 19536
    {'degree': 3, 'field': [1, 5, -1, 1], 'lmfdb_label': '441.a2', 'torsion': [2]}
  • id: 19538
    {'degree': 6, 'field': [1, -8, 8, 6, -6, -1, 1], 'lmfdb_label': '441.a2', 'torsion': [13]}
  • id: 19537
    {'degree': 6, 'field': [27, 9, -8, -3, 4, -3, 1], 'lmfdb_label': '441.a2', 'torsion': [2, 2]}
  • id: 19539
    {'degree': 8, 'field': [-13, 7, 22, -23, -10, -1, 2, -2, 1], 'lmfdb_label': '441.a2', 'torsion': [3]}
  • id: 19540
    {'degree': 12, 'field': [-69, 202, -232, 108, -141, 212, -140, 4, -25, -18, 12, -4, 1], 'lmfdb_label': '441.a2', 'torsion': [4]}
  • id: 19541
    {'degree': 18, 'field': [1, -1, -7, 20, -11, -23, 15, 3, 42, -40, -15, 27, -23, 19, -7, -1, 5, -4, 1], 'lmfdb_label': '441.a2', 'torsion': [26]}
• 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: 4693
    {'conductor': 441, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '441.a2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4694
    {'conductor': 441, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '441.a2', 'prime': 7, 'reduction_type': 0, '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: 1667718
    {'adelic_gens': [[335, 26, 78, 251], [14, 23, 325, 339], [1, 26, 0, 379], [181, 520, 169, 207], [1, 0, 26, 1], [1, 26, 0, 1], [521, 26, 520, 27]], 'adelic_image': '546.336.9.?', 'conductor': 441, 'lmfdb_label': '441.a2', 'prime': 0}
  • id: 1904
    {'conductor': 441, 'elladic_image': '13.28.0.1', 'lmfdb_label': '441.a2', 'modell_image': '13B.4.1', 'prime': 13}
• ec_padic •

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

  
  
  • id: 6312
    {'lmfdb_iso': '441.a', 'p': 5, 'prec': 20, 'unit': 6280386554909, 'val': 1}
  • id: 6311
    {'lmfdb_iso': '441.a', 'p': 11, 'prec': 20, 'unit': 53739065549507670294, 'val': 1}
  • id: 6318
    {'lmfdb_iso': '441.a', 'p': 13, 'prec': 20, 'unit': 1285627191372639069623, 'val': 1}
  • id: 6321
    {'lmfdb_iso': '441.a', 'p': 19, 'prec': 20, 'unit': 525652093479540379739961, 'val': 1}
  • id: 6317
    {'lmfdb_iso': '441.a', 'p': 29, 'prec': 20, 'unit': 865934663226013758488736710, 'val': 1}
  • id: 6314
    {'lmfdb_iso': '441.a', 'p': 31, 'prec': 20, 'unit': 17182214333058966088762829057, 'val': 1}
  • id: 6328
    {'lmfdb_iso': '441.a', 'p': 37, 'prec': 20, 'unit': 217944218256213674646777057178, 'val': 1}
  • id: 6315
    {'lmfdb_iso': '441.a', 'p': 41, 'prec': 20, 'unit': 2678341172136841905963574753376, 'val': 1}
  • id: 6316
    {'lmfdb_iso': '441.a', 'p': 43, 'prec': 20, 'unit': 1801253231088128638675844464564, 'val': 1}
  • id: 6326
    {'lmfdb_iso': '441.a', 'p': 47, 'prec': 20, 'unit': 23339481314316687381512722036917, 'val': 1}
  • id: 6322
    {'lmfdb_iso': '441.a', 'p': 53, 'prec': 20, 'unit': 108439520998770730002776406326629, 'val': 1}
  • id: 6320
    {'lmfdb_iso': '441.a', 'p': 59, 'prec': 20, 'unit': 2189223130024117220774018941724657, 'val': 1}
  • id: 6327
    {'lmfdb_iso': '441.a', 'p': 61, 'prec': 20, 'unit': 5219405691233192413418405380774935, 'val': 1}
  • id: 6310
    {'lmfdb_iso': '441.a', 'p': 67, 'prec': 20, 'unit': 27113560174589515176162361491314199, 'val': 1}
  • id: 6313
    {'lmfdb_iso': '441.a', 'p': 71, 'prec': 20, 'unit': 90620652462627546466826162262239650, 'val': 1}
  • id: 6323
    {'lmfdb_iso': '441.a', 'p': 73, 'prec': 20, 'unit': 14932250733424247079026532094408103, 'val': 1}
  • id: 6319
    {'lmfdb_iso': '441.a', 'p': 79, 'prec': 20, 'unit': 668055939478824372066526898848548276, 'val': 1}
  • id: 6324
    {'lmfdb_iso': '441.a', 'p': 83, 'prec': 20, 'unit': 312564298663924021114920798413150121, 'val': 1}
  • id: 6325
    {'lmfdb_iso': '441.a', 'p': 89, 'prec': 20, 'unit': 1617072768581196175650240684742628867, 'val': 1}
  • id: 6309
    {'lmfdb_iso': '441.a', 'p': 97, 'prec': 20, 'unit': 1874927584493962146191472499878332933, 'val': 1}