Elliptic curve data - 539.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
  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': '539d', 'Clabel': '539d3', 'Cnumber': 3, 'abc_quality': 1.0929566831983986, 'absD': 1294139, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 3850, 'ainvs': [0, 1, 1, -383196, 91174234], 'analytic_rank': 1, 'bad_primes': [7, 11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 539, 'degree': 1800, 'elladic_images': ['25.60.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4696641896263037751640417769', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 25, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5, 25], 'jinv': [-52893159101157376, 11], 'lmfdb_iso': '539.a', 'lmfdb_label': '539.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -7820, -263580], 'min_quad_twist_disc': -7, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '22.2.0.a.1', '25.60.0.a.2', '35.24.0-5.a.2.2', '110.24.1.?', '175.120.0.?', '275.300.12.?', '550.600.37.?', '770.48.1.?', '1925.600.12.?', '3850.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.55568073570994009832121611548', 'prec': 103}, 'semistable': False, 'serre_invariants': [[7, 26, 11], [11, 12, 49]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540518', 'prec': 103}, 'szpiro_ratio': 7.978502483369696, '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, 1, 2, -1, -2, 0, 0, -2, 2, 1, 2, -4, 0, -1, -4, 2, 4, 0, -2], 'aplist': [-2, 1, -1, 0, 1, -4, 2, 0, -1, 0, -7, 3, 8, -6, -8, -6, -5, -12, -7, -3, -4, -10, 6, -15, 7], 'class_deg': 25, 'class_size': 3, 'conductor': 539, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '539.a', 'trace_hash': 1927269313374205969}
• 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': '0.052901246384455980505943048909', 'prec': 107}, 'conductor': 539, 'gens': [[1429, 45, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '0.55568073570994009832121611548', 'prec': 103}], 'lmfdb_label': '539.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.1027617076765241103117353267', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2255668740688816300719797533452071914', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 5, 0], '3': [1, 0], '5': [1, 0], '7': 'a', '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '539.a1'}
• ec_torsion_growth •

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

  
  
  • id: 24240
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '539.a1', 'torsion': [2]}
  • id: 24241
    {'degree': 4, 'field': [11, 9, -9, -1, 1], 'lmfdb_label': '539.a1', 'torsion': [5]}
  • id: 24242
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '539.a1', 'torsion': [2, 2]}
  • id: 24243
    {'degree': 8, 'field': [-223, -136, 50, 27, -33, 21, -2, -2, 1], 'lmfdb_label': '539.a1', 'torsion': [3]}
  • id: 24244
    {'degree': 10, 'field': [32, -25, 710, -530, 155, -139, 105, -50, 20, -5, 1], 'lmfdb_label': '539.a1', 'torsion': [5]}
  • id: 24245
    {'degree': 12, 'field': [-6137, 10412, 3562, -12930, 4123, 808, 148, 64, -57, -32, 6, -2, 1], 'lmfdb_label': '539.a1', 'torsion': [4]}
  • id: 24246
    {'degree': 12, 'field': [2321, -10032, -7868, 3113, 4009, -896, -1317, 78, 265, 13, -25, -1, 1], 'lmfdb_label': '539.a1', 'torsion': [10]}
  • id: 24247
    {'degree': 20, 'field': [21517195051, -174870664265, -373712335590, -47943036735, 234282460390, 67165539948, -61917017090, -18111848990, 9055215240, 2245529115, -796174676, -149800505, 42910045, 5595605, -1395645, -114998, 26105, 1205, -255, -5, 1], 'lmfdb_label': '539.a1', 'torsion': [25]}
• 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: 6065
    {'conductor': 539, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '539.a1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6066
    {'conductor': 539, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '539.a1', 'prime': 11, '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: 1668214
    {'adelic_gens': [[38, 41, 1291, 1089], [2640, 1659, 2877, 1863], [1, 0, 50, 1], [3801, 50, 3800, 51], [1, 50, 0, 1], [1649, 0, 0, 3849], [1436, 2345, 3815, 2416]], 'adelic_image': '3850.1200.37.?', 'conductor': 539, 'lmfdb_label': '539.a1', 'prime': 0}
  • id: 2399
    {'conductor': 539, 'elladic_image': '25.60.0.2', 'lmfdb_label': '539.a1', 'modell_image': '5B.4.2', 'prime': 5}
• ec_padic •

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

  
  
  • id: 8468
    {'lmfdb_iso': '539.a', 'p': 5, 'prec': 20, 'unit': 264952672167, 'val': 1}
  • id: 8457
    {'lmfdb_iso': '539.a', 'p': 13, 'prec': 20, 'unit': 1067669773423140915552, 'val': 1}
  • id: 8459
    {'lmfdb_iso': '539.a', 'p': 17, 'prec': 20, 'unit': 71086006927802192949427, 'val': 1}
  • id: 8464
    {'lmfdb_iso': '539.a', 'p': 23, 'prec': 20, 'unit': 34321044534982678778470727, 'val': 1}
  • id: 8454
    {'lmfdb_iso': '539.a', 'p': 31, 'prec': 20, 'unit': 15992286111164374044569251101, 'val': 1}
  • id: 8452
    {'lmfdb_iso': '539.a', 'p': 37, 'prec': 20, 'unit': 90196076061819242153125943039, 'val': 1}
  • id: 8455
    {'lmfdb_iso': '539.a', 'p': 41, 'prec': 20, 'unit': 898292920451293361071452525786, 'val': 1}
  • id: 8456
    {'lmfdb_iso': '539.a', 'p': 43, 'prec': 20, 'unit': 3713720966817360365330213847412, 'val': 1}
  • id: 8466
    {'lmfdb_iso': '539.a', 'p': 47, 'prec': 20, 'unit': 4781402636582204374125095949697, 'val': 1}
  • id: 8461
    {'lmfdb_iso': '539.a', 'p': 53, 'prec': 20, 'unit': 95395268935801589401674205729347, 'val': 1}
  • id: 8462
    {'lmfdb_iso': '539.a', 'p': 59, 'prec': 20, 'unit': 1879145228636950143684072522092300, 'val': 1}
  • id: 8467
    {'lmfdb_iso': '539.a', 'p': 61, 'prec': 20, 'unit': 1397273035557073440948648061239485, 'val': 1}
  • id: 8451
    {'lmfdb_iso': '539.a', 'p': 67, 'prec': 20, 'unit': 8317015838455921588347642278952169, 'val': 1}
  • id: 8453
    {'lmfdb_iso': '539.a', 'p': 71, 'prec': 20, 'unit': 104055768873292146252770890166659679, 'val': 1}
  • id: 8463
    {'lmfdb_iso': '539.a', 'p': 73, 'prec': 20, 'unit': 154107145694377275459703268283574069, 'val': 1}
  • id: 8458
    {'lmfdb_iso': '539.a', 'p': 79, 'prec': 20, 'unit': 344185832423707715371648439939621732, 'val': 1}
  • id: 8460
    {'lmfdb_iso': '539.a', 'p': 83, 'prec': 20, 'unit': 2330875980292686351903385064451608629, 'val': 1}
  • id: 8465
    {'lmfdb_iso': '539.a', 'p': 89, 'prec': 20, 'unit': 6301526548189294814539182074490912292, 'val': 1}
  • id: 8450
    {'lmfdb_iso': '539.a', 'p': 97, 'prec': 20, 'unit': 10166429216194628953680572424592665145, 'val': 1}