Elliptic curve data - 57960.bd4

Formats: - HTML - YAML - JSON - 2024-04-30T19:56:51.599977

• 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': '57960s', 'Clabel': '57960s1', 'Cnumber': 1, 'abc_quality': 0.8752374537980175, 'absD': 3220605360, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 19320, 'ainvs': [0, 0, 0, 198, -2511], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 57960, 'degree': 20480, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.50722933698159535623042968700', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 29, 'isogeny_degrees': [1, 2, 4], 'jinv': [73598976, 276115], 'lmfdb_iso': '57960.bd', 'lmfdb_label': '57960.bd4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 22, 93], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '60.12.0-4.c.1.2', '168.12.0.?', '230.6.0.?', '276.12.0.?', '280.12.0.?', '460.12.0.?', '840.24.0.?', '1288.12.0.?', '1380.24.0.?', '3864.24.0.?', '6440.24.0.?', '19320.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.9045461906305399736597502787', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27312586753910792593960363861', 'prec': 107}, 'szpiro_ratio': 2.660587728878265, '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, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, 1, -1, 0, 2, 2, 4, -1, 2, 0, 2, -2, 4, -12, -2, 12, -6, -4, 0, -10, -4, 12, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 57960, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '57960.bd', 'trace_hash': 1766724637883625983}
• 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': '0.36259866081123876183280676762', 'prec': 103}, 'conductor': 57960, 'gens': [[865, 25676, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '4.9045461906305399736597502787', 'prec': 100}], 'lmfdb_label': '57960.bd4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.71967308718630338295377355509', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.0593397965178094529762478732458785000', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[9, 0, 1]], 'xcoord_integral_points': [9]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [4, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '57960.bd4'}
• ec_torsion_growth •

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

  
  
  • id: 2790595
    {'degree': 2, 'field': [-17, -1, 1], 'lmfdb_label': '57960.bd4', 'torsion': [4]}
  • id: 2790596
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '57960.bd4', 'torsion': [4]}
  • id: 2790594
    {'degree': 2, 'field': [29, -1, 1], 'lmfdb_label': '57960.bd4', 'torsion': [2, 2]}
  • id: 2790597
    {'degree': 4, 'field': [139, -47, 8, -1, 1], 'lmfdb_label': '57960.bd4', 'torsion': [2, 4]}
  • id: 2790601
    {'degree': 8, 'field': [-64827, 0, 0, 0, 882, 0, 36, 0, 1], 'lmfdb_label': '57960.bd4', 'torsion': [6]}
  • id: 2790598
    {'degree': 8, 'field': [8581, 21274, 21982, 10102, 1815, 38, -8, -4, 1], 'lmfdb_label': '57960.bd4', 'torsion': [2, 4]}
  • id: 2790600
    {'degree': 8, 'field': [211600, 0, 4600, 0, 1205, 0, -10, 0, 1], 'lmfdb_label': '57960.bd4', 'torsion': [8]}
  • id: 2790599
    {'degree': 8, 'field': [3728005, 37530, -40324, 5654, -2991, 194, -60, -4, 1], 'lmfdb_label': '57960.bd4', 'torsion': [8]}
  • id: 2790602
    {'degree': 16, 'field': [154654096, -11839072, 453152, 3697824, 11966296, -1269392, 106320, 118112, -9591, 20186, -1710, -434, 451, -18, 8, -4, 1], 'lmfdb_label': '57960.bd4', 'torsion': [4, 4]}
  • id: 2790603
    {'degree': 16, 'field': [1475789056, 0, 208675712, 0, -5404112, 0, 13987624, 0, 4856625, 0, -84706, 0, 2563, 0, -38, 0, 1], 'lmfdb_label': '57960.bd4', 'torsion': [2, 8]}
  • id: 2790606
    {'degree': 16, 'field': [4202539929, 0, -7890483132, 0, 1066533804, 0, -139407156, 0, 7951230, 0, -475524, 0, 14652, 0, -204, 0, 1], 'lmfdb_label': '57960.bd4', 'torsion': [12]}
  • id: 2790607
    {'degree': 16, 'field': [13282101504, 0, -813189888, 0, -38031840, 0, -8297856, 0, 1260525, 0, -19404, 0, 2058, 0, 0, 0, 1], 'lmfdb_label': '57960.bd4', 'torsion': [12]}
  • id: 2790605
    {'degree': 16, 'field': [23148101025, 0, 0, 0, 314940150, 0, -18331920, 0, 1772955, 0, -74520, 0, 2394, 0, -36, 0, 1], 'lmfdb_label': '57960.bd4', 'torsion': [2, 6]}
  • id: 2790604
    {'degree': 16, 'field': [355393227421, 148171249236, 34380126492, 5459594576, 1427563138, 275592316, 59422416, 9094508, 1252203, 277756, 22824, 11500, 638, 72, 68, -4, 1], 'lmfdb_label': '57960.bd4', 'torsion': [2, 8]}
• 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: 1394769
    {'conductor': 57960, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '57960.bd4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1394770
    {'conductor': 57960, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '57960.bd4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1394771
    {'conductor': 57960, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57960.bd4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1394772
    {'conductor': 57960, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '57960.bd4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1394773
    {'conductor': 57960, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57960.bd4', 'prime': 23, '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: 2048786
    {'adelic_gens': [[4033, 16908, 10470, 13687], [1, 8, 0, 1], [3868, 6441, 1311, 12886], [1, 0, 8, 1], [2761, 12888, 17484, 12913], [2419, 2418, 13698, 16915], [6439, 0, 0, 19319], [1, 4, 4, 17], [7, 6, 19314, 19315], [2248, 3, 7845, 6442], [19313, 8, 19312, 9]], 'adelic_image': '19320.48.0.?', 'conductor': 57960, 'lmfdb_label': '57960.bd4', 'prime': 0}
  • id: 245816
    {'conductor': 57960, 'elladic_image': '4.6.0.1', 'lmfdb_label': '57960.bd4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2938880
    {'lmfdb_iso': '57960.bd', 'p': 13, 'prec': 20, 'unit': 790695102541821899493, 'val': 1}
  • id: 2938882
    {'lmfdb_iso': '57960.bd', 'p': 17, 'prec': 20, 'unit': 211637704302485433837892, 'val': 1}
  • id: 2938883
    {'lmfdb_iso': '57960.bd', 'p': 19, 'prec': 20, 'unit': 473086302330920745985150, 'val': 1}
  • id: 2938879
    {'lmfdb_iso': '57960.bd', 'p': 29, 'prec': 20, 'unit': 4754558458577908219607397769, 'val': 1}
  • id: 2938876
    {'lmfdb_iso': '57960.bd', 'p': 37, 'prec': 20, 'unit': 528062206071528688148039179458, 'val': 1}
  • id: 2938877
    {'lmfdb_iso': '57960.bd', 'p': 41, 'prec': 20, 'unit': 2403462185126037218609349536549, 'val': 1}
  • id: 2938878
    {'lmfdb_iso': '57960.bd', 'p': 43, 'prec': 20, 'unit': 10759703003617353245766428381538, 'val': 1}
  • id: 2938888
    {'lmfdb_iso': '57960.bd', 'p': 47, 'prec': 20, 'unit': 45373912013510731779959787763081, 'val': 1}
  • id: 2938884
    {'lmfdb_iso': '57960.bd', 'p': 53, 'prec': 20, 'unit': 533074627933299451858960069211941, 'val': 1}
  • id: 2938885
    {'lmfdb_iso': '57960.bd', 'p': 59, 'prec': 20, 'unit': 2234039981584068904698927444626938, 'val': 1}
  • id: 2938889
    {'lmfdb_iso': '57960.bd', 'p': 61, 'prec': 20, 'unit': 7171618785304464343480152395141122, 'val': 1}
  • id: 2938875
    {'lmfdb_iso': '57960.bd', 'p': 67, 'prec': 20, 'unit': 38251410354919671355921827685859539, 'val': 1}
  • id: 2938886
    {'lmfdb_iso': '57960.bd', 'p': 73, 'prec': 20, 'unit': 240817179514184327726756494351901789, 'val': 1}
  • id: 2938881
    {'lmfdb_iso': '57960.bd', 'p': 79, 'prec': 20, 'unit': 258993069485374165266032239562217697, 'val': 1}
  • id: 2938874
    {'lmfdb_iso': '57960.bd', 'p': 83, 'prec': 20, 'unit': 1249348253718595813216699901248416821, 'val': 1}
  • id: 2938887
    {'lmfdb_iso': '57960.bd', 'p': 89, 'prec': 20, 'unit': 5619844151021596216810623656151473056, 'val': 1}
  • id: 2938873
    {'lmfdb_iso': '57960.bd', 'p': 97, 'prec': 20, 'unit': 3979565838337044884562887332016903176, 'val': 1}