Elliptic curve data - 5056.e1

Formats: - HTML - YAML - JSON - 2024-06-09T21:05:22.036846

• 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': '5056r', 'Clabel': '5056r2', 'Cnumber': 2, 'abc_quality': 1.0196212670962481, 'absD': 12906109962551296, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 3160, 'ainvs': [0, -1, 0, -1496321, 704984737], 'analytic_rank': 1, 'bad_primes': [2, 79], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 5056, 'degree': 46080, 'elladic_images': ['5.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1818303748471429637006804252', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 5, 'iso_nlabel': 4, 'isogeny_degrees': [1, 5], 'jinv': [1413378216646643521, 49232902384], 'lmfdb_iso': '5056.e', 'lmfdb_label': '5056.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -23380, -1385691], 'min_quad_twist_disc': -8, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '40.24.0-5.a.2.1', '316.2.0.?', '1580.24.1.?', '3160.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.69582193102277297250972684748', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1421096040072249995748322430', 'prec': 100}, 'szpiro_ratio': 6.363397957872993, '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, -1, 0, -1, 0, -3, 0, -2, 0, 2, 0, 1, 0, 1, 0, -2, 0, 0, 0], 'aplist': [0, -1, -1, -3, 2, 1, -2, 0, 6, 10, -2, 2, 2, 4, -3, -4, 5, -12, 8, 13, -6, 1, -6, -15, 13], 'class_deg': 5, 'class_size': 2, 'conductor': 5056, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '5056.e', 'trace_hash': 1395852588552426471}
• 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': '0.012731694688620154465245191848', 'prec': 107}, 'conductor': 5056, 'gens': [[699, 316, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.69582193102277297250972684748', 'prec': 103}], 'lmfdb_label': '5056.e1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.37307999426056913417062192103', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5959724203235427255082521949319200769', 'prec': 130}, 'tamagawa_product': 10, 'torsion_generators': [], 'xcoord_integral_points': [699]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '79': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '5056.e1'}
• ec_torsion_growth •

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

  
  
  • id: 265109
    {'degree': 3, 'field': [2, -4, -1, 1], 'lmfdb_label': '5056.e1', 'torsion': [2]}
  • id: 265110
    {'degree': 4, 'field': [20, 0, -10, 0, 1], 'lmfdb_label': '5056.e1', 'torsion': [5]}
  • id: 265111
    {'degree': 6, 'field': [8, -8, -34, 54, -17, -2, 1], 'lmfdb_label': '5056.e1', 'torsion': [2, 2]}
  • id: 265112
    {'degree': 8, 'field': [-12, 0, -14, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '5056.e1', 'torsion': [3]}
  • id: 265113
    {'degree': 10, 'field': [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '5056.e1', 'torsion': [5]}
  • id: 265114
    {'degree': 12, 'field': [316, 0, 416, 0, -2535, 0, 160, 0, -130, 0, 0, 0, 1], 'lmfdb_label': '5056.e1', 'torsion': [4]}
  • id: 265115
    {'degree': 12, 'field': [8000, 0, -17000, 0, 12025, 0, -3800, 0, 575, 0, -40, 0, 1], 'lmfdb_label': '5056.e1', 'torsion': [10]}
• 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: 98299
    {'conductor': 5056, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '5056.e1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 98300
    {'conductor': 5056, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '5056.e1', 'prime': 79, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1697032
    {'adelic_gens': [[3151, 10, 3150, 11], [797, 10, 1540, 101], [2194, 3155, 2385, 1584], [1579, 0, 0, 3159], [1, 0, 10, 1], [1, 10, 0, 1], [6, 5, 785, 1576], [1589, 3150, 1590, 3149], [6, 13, 3105, 3041], [3154, 3147, 1635, 1699]], 'adelic_image': '3160.48.1.?', 'conductor': 5056, 'lmfdb_label': '5056.e1', 'prime': 0}
  • id: 25165
    {'conductor': 5056, 'elladic_image': '5.12.0.2', 'lmfdb_label': '5056.e1', 'modell_image': '5B.4.2', 'prime': 5}
• ec_padic •

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

  
  
  • id: 186389
    {'lmfdb_iso': '5056.e', 'p': 5, 'prec': 20, 'unit': 16929411177354, 'val': 1}
  • id: 186390
    {'lmfdb_iso': '5056.e', 'p': 7, 'prec': 20, 'unit': 215608381074592, 'val': 2}
  • id: 186388
    {'lmfdb_iso': '5056.e', 'p': 11, 'prec': 20, 'unit': 13122483765153293779, 'val': 1}
  • id: 186395
    {'lmfdb_iso': '5056.e', 'p': 13, 'prec': 20, 'unit': 10865367125833268882257, 'val': -1}
  • id: 186397
    {'lmfdb_iso': '5056.e', 'p': 17, 'prec': 20, 'unit': 60840626812431956764136, 'val': 1}
  • id: 186401
    {'lmfdb_iso': '5056.e', 'p': 23, 'prec': 20, 'unit': 43994168085859397490931686, 'val': 1}
  • id: 186394
    {'lmfdb_iso': '5056.e', 'p': 29, 'prec': 20, 'unit': 2287435438962740400760962291, 'val': 1}
  • id: 186391
    {'lmfdb_iso': '5056.e', 'p': 31, 'prec': 20, 'unit': 2368047730467853298143576525, 'val': 1}
  • id: 186406
    {'lmfdb_iso': '5056.e', 'p': 37, 'prec': 20, 'unit': 576999656869889275403318249531, 'val': 1}
  • id: 186392
    {'lmfdb_iso': '5056.e', 'p': 41, 'prec': 20, 'unit': 4240969603272119826616396453092, 'val': 1}
  • id: 186393
    {'lmfdb_iso': '5056.e', 'p': 43, 'prec': 20, 'unit': 1003419480339742553135946393650, 'val': 1}
  • id: 186396
    {'lmfdb_iso': '5056.e', 'p': 47, 'prec': 20, 'unit': 43109456566677066040499455906586, 'val': 1}
  • id: 186399
    {'lmfdb_iso': '5056.e', 'p': 53, 'prec': 20, 'unit': 5671964105705320861859471272645, 'val': 2}
  • id: 186404
    {'lmfdb_iso': '5056.e', 'p': 59, 'prec': 20, 'unit': 888761201081718442344713679542069, 'val': 1}
  • id: 186405
    {'lmfdb_iso': '5056.e', 'p': 61, 'prec': 20, 'unit': 4084331290165252480789228736982462, 'val': 1}
  • id: 186398
    {'lmfdb_iso': '5056.e', 'p': 67, 'prec': 20, 'unit': 33352730991349691318944136830738893, 'val': 1}
  • id: 186403
    {'lmfdb_iso': '5056.e', 'p': 71, 'prec': 20, 'unit': 43144132591515727927298925160451857, 'val': 1}
  • id: 186400
    {'lmfdb_iso': '5056.e', 'p': 73, 'prec': 20, 'unit': 51553263263325739608399191426122256, 'val': 1}
  • id: 186387
    {'lmfdb_iso': '5056.e', 'p': 83, 'prec': 20, 'unit': 1309312507230173342422187599855620061, 'val': 1}
  • id: 186402
    {'lmfdb_iso': '5056.e', 'p': 89, 'prec': 20, 'unit': 3182978447564083234161490860988968813, 'val': 1}
  • id: 186386
    {'lmfdb_iso': '5056.e', 'p': 97, 'prec': 20, 'unit': 24647773637589170221869885933451753117, 'val': 1}