Elliptic curve data - 720.c6

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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': '720h', 'Clabel': '720h2', 'Cnumber': 2, 'abc_quality': 0.9622954410890624, 'absD': 671846400, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 240, 'ainvs': [0, 0, 0, -723, 7378], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 720, 'degree': 256, 'elladic_images': ['16.96.0.33'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.49360216253118371296264218203', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [13997521, 225], 'lmfdb_iso': '720.c', 'lmfdb_label': '720.c6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5, 2], 'min_quad_twist_disc': 12, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.i.1.6', '12.24.0-4.b.1.1', '16.96.0-16.d.2.4', '20.24.0-4.b.1.2', '24.96.0-24.bb.2.6', '40.96.0-40.bd.1.9', '48.192.1-48.n.1.4', '60.48.0-60.c.1.5', '80.384.5.?', '120.192.1.?', '240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 15, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.65015642199656306277411657149', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 80], [5, 6, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.74885116236281644215221255789', 'prec': 107}, 'szpiro_ratio': 4.767082102283438, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, -1, 0, -4, -2, -2, -4, 0, 2, 0, -10, -10, -4, 8, 10, -4, -2, -12, -8, 10, 0, 12, 6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 720, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '720.c', 'trace_hash': 4452916081343144}
• 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': '0.37261695210292151696112379702', 'prec': 103}, 'conductor': 720, 'gens': [[9, 40, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.65015642199656306277411657149', 'prec': 103}], 'lmfdb_label': '720.c6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.6172770870370731764583619466', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1029661685700951958666744095510211554', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[14, 0, 1], [17, 0, 1]], 'xcoord_integral_points': [-31, -1, 9, 14, 17, 18, 23, 41, 161]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 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': '720.c6'}
• ec_torsion_growth •

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

  
  
  • id: 33503
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 4]}
  • id: 33506
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 8]}
  • id: 33505
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 4]}
  • id: 33507
    {'degree': 4, 'field': [1, 8, -7, -2, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 8]}
  • id: 33504
    {'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 4]}
  • id: 33510
    {'degree': 8, 'field': [-27, 0, 0, 0, 18, 0, -7, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 6]}
  • id: 33509
    {'degree': 8, 'field': [1, 0, -8, 0, 14, 0, -7, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 16]}
  • id: 33508
    {'degree': 8, 'field': [1, 0, -3, 0, 8, 0, -3, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [4, 8]}
  • id: 33514
    {'degree': 16, 'field': [1, 0, -4, 0, 19, 0, -52, 0, 73, 0, -52, 0, 19, 0, -4, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 16]}
  • id: 33513
    {'degree': 16, 'field': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [4, 16]}
  • id: 33511
    {'degree': 16, 'field': [1, 0, 4, 0, 25, 0, -44, 0, 64, 0, -44, 0, 25, 0, 4, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 8]}
  • id: 33515
    {'degree': 16, 'field': [9, 0, -207, 0, -72, 0, -111, 0, -75, 0, -21, 0, 7, 0, -2, 0, 1], 'lmfdb_label': '720.c6', 'torsion': [2, 12]}
  • id: 33512
    {'degree': 16, 'field': [256, 0, -352, 0, 340, 0, -262, 0, 109, 0, 62, 0, -5, 0, 2, 0, 1], 'lmfdb_label': '720.c6', '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: 9037
    {'conductor': 720, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '720.c6', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9038
    {'conductor': 720, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '720.c6', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9039
    {'conductor': 720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '720.c6', 'prime': 5, '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: 1669216
    {'adelic_gens': [[1, 0, 16, 1], [1, 16, 0, 1], [5, 16, 4, 193], [79, 224, 234, 143], [61, 8, 170, 197], [1, 16, 4, 65], [225, 16, 224, 17], [225, 232, 32, 31]], 'adelic_image': '240.768.13.?', 'conductor': 720, 'lmfdb_label': '720.c6', 'prime': 0}
  • id: 3244
    {'conductor': 720, 'elladic_image': '16.96.0.33', 'lmfdb_label': '720.c6', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 13727
    {'lmfdb_iso': '720.c', 'p': 11, 'prec': 20, 'unit': 43906525018167855924, 'val': 1}
  • id: 13733
    {'lmfdb_iso': '720.c', 'p': 13, 'prec': 20, 'unit': 1050216521060315950416, 'val': 1}
  • id: 13735
    {'lmfdb_iso': '720.c', 'p': 17, 'prec': 20, 'unit': 146974378396802910006343, 'val': 1}
  • id: 13736
    {'lmfdb_iso': '720.c', 'p': 19, 'prec': 20, 'unit': 645610779401273589096835, 'val': 1}
  • id: 13732
    {'lmfdb_iso': '720.c', 'p': 29, 'prec': 20, 'unit': 635502968018070440704760311, 'val': 1}
  • id: 13728
    {'lmfdb_iso': '720.c', 'p': 37, 'prec': 20, 'unit': 427881884625212267800043957160, 'val': 1}
  • id: 13730
    {'lmfdb_iso': '720.c', 'p': 41, 'prec': 20, 'unit': 3609352190954947843956766182626, 'val': 1}
  • id: 13731
    {'lmfdb_iso': '720.c', 'p': 43, 'prec': 20, 'unit': 1193721172049375777434313971501, 'val': 1}
  • id: 13734
    {'lmfdb_iso': '720.c', 'p': 47, 'prec': 20, 'unit': 46603194439184679613680173114932, 'val': 1}
  • id: 13737
    {'lmfdb_iso': '720.c', 'p': 53, 'prec': 20, 'unit': 153092985733952845781749568941485, 'val': 1}
  • id: 13741
    {'lmfdb_iso': '720.c', 'p': 59, 'prec': 20, 'unit': 3397981198819534724675723237320607, 'val': 1}
  • id: 13742
    {'lmfdb_iso': '720.c', 'p': 61, 'prec': 20, 'unit': 1227328655682497316346359354975315, 'val': 1}
  • id: 13726
    {'lmfdb_iso': '720.c', 'p': 67, 'prec': 20, 'unit': 44972203484216404298387080491173082, 'val': 1}
  • id: 13729
    {'lmfdb_iso': '720.c', 'p': 71, 'prec': 20, 'unit': 14526522180241375913254122419835034, 'val': 1}
  • id: 13738
    {'lmfdb_iso': '720.c', 'p': 73, 'prec': 20, 'unit': 108602073314063531770790775126697761, 'val': 1}
  • id: 13739
    {'lmfdb_iso': '720.c', 'p': 83, 'prec': 20, 'unit': 335670270648972733548818610740980245, 'val': 1}
  • id: 13740
    {'lmfdb_iso': '720.c', 'p': 89, 'prec': 20, 'unit': 4959470568886811811169105190804729727, 'val': 1}
  • id: 13725
    {'lmfdb_iso': '720.c', 'p': 97, 'prec': 20, 'unit': 25652459188021153382165473745798913797, 'val': 1}