Elliptic curve data - 576.c1

Formats: - HTML - YAML - JSON - 2023-12-02T04:40:08.423486

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '576h', 'Clabel': '576h3', 'Cnumber': 3, 'absD': 23887872, 'ainvs': [0, 0, 0, -396, -3024], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 4, 'class_size': 4, 'cm': -16, 'conductor': 576, 'degree': 128, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.27849398926246329157119571734', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [287496, 1], 'lmfdb_iso': '576.c', 'lmfdb_label': '576.c1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -11, -14], 'min_quad_twist_disc': 24, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7772517496792384795883746700', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1372461307715231908979670529', 'prec': 103}, '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, -2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, -2, 0, 0, -6, -2, 0, 0, -10, 0, 2, -10, 0, 0, 14, 0, 10, 0, 0, -6, 0, 0, -10, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 576, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '576.c', 'trace_hash': 1086616701052248176}
• 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': '0.57293215150169773562417464832', 'prec': 103}, 'conductor': 576, 'gens': [[-11, 1, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7772517496792384795883746700', 'prec': 100}], 'lmfdb_label': '576.c1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0704505140376155993171555258', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9024600490183925553056020003914001736', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-12, 0, 1]], 'xcoord_integral_points': [-12, -11, 24]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [1, 1, 0], '11': [1, 3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '576.c1'}
• ec_torsion_growth •

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

  
  
  • id: 26424
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [2, 2]}
  • id: 26426
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '576.c1', 'torsion': [4]}
  • id: 26425
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [4]}
  • id: 26427
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [2, 4]}
  • id: 26431
    {'degree': 8, 'field': [-3, 0, 0, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [6]}
  • id: 26428
    {'degree': 8, 'field': [1, 0, -4, 0, -12, 0, -4, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [2, 4]}
  • id: 26430
    {'degree': 8, 'field': [4, 0, 8, 0, 14, 0, 4, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [2, 8]}
  • id: 26429
    {'degree': 8, 'field': [10, -32, 52, -64, 54, -32, 16, -4, 1], 'lmfdb_label': '576.c1', 'torsion': [8]}
  • id: 26432
    {'degree': 8, 'field': [106, -160, 124, -108, 64, -8, -6, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [10]}
  • id: 26436
    {'degree': 16, 'field': [-2084, -8960, 10624, 18992, -22136, -9344, 17472, -2792, -4118, 2024, 116, -356, 68, 20, -2, -4, 1], 'lmfdb_label': '576.c1', 'torsion': [10]}
  • id: 26433
    {'degree': 16, 'field': [1, 0, -4, 0, 8, 0, -24, 0, 47, 0, -24, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [4, 4]}
  • id: 26434
    {'degree': 16, 'field': [1, 0, 0, 0, -6, 0, 0, 0, 35, 0, 0, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [2, 8]}
  • id: 26437
    {'degree': 16, 'field': [4, 0, -16, 0, 16, 0, 8, 0, -20, 0, -16, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [2, 6]}
  • id: 26439
    {'degree': 16, 'field': [4, 0, 16, 0, 16, 0, -8, 0, -20, 0, 16, 0, 4, 0, 4, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [12]}
  • id: 26435
    {'degree': 16, 'field': [9, 0, 0, 0, -18, 0, 0, 0, 39, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [3, 12]}
  • id: 26441
    {'degree': 16, 'field': [25, 0, 0, 0, -10, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 1], 'lmfdb_label': '576.c1', 'torsion': [20]}
  • id: 26438
    {'degree': 16, 'field': [34, -232, 964, -2592, 5036, -7240, 8260, -7720, 6076, -4060, 2332, -1136, 474, -160, 44, -8, 1], 'lmfdb_label': '576.c1', 'torsion': [2, 10]}
  • id: 26440
    {'degree': 16, 'field': [145, -140, 0, 380, -538, 560, -32, -412, 788, -748, 592, -324, 162, -56, 20, -4, 1], 'lmfdb_label': '576.c1', 'torsion': [20]}
• 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: 6776
    {'conductor': 576, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '576.c1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6777
    {'conductor': 576, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '576.c1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 576.c1 does not appear in ec_galrep
• ec_padic •

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

  
  
  • id: 9504
    {'lmfdb_iso': '576.c', 'p': 5, 'prec': 20, 'unit': 378286143012, 'val': 2}
  • id: 9497
    {'lmfdb_iso': '576.c', 'p': 13, 'prec': 20, 'unit': 796883871780699603273, 'val': 1}
  • id: 9499
    {'lmfdb_iso': '576.c', 'p': 17, 'prec': 20, 'unit': 186487849336496595755471, 'val': 1}
  • id: 9498
    {'lmfdb_iso': '576.c', 'p': 29, 'prec': 20, 'unit': 158764665994758718868162246, 'val': 1}
  • id: 9495
    {'lmfdb_iso': '576.c', 'p': 37, 'prec': 20, 'unit': 293881860179848758926965716969, 'val': 1}
  • id: 9496
    {'lmfdb_iso': '576.c', 'p': 41, 'prec': 20, 'unit': 4138364432459298220591877641682, 'val': 1}
  • id: 9500
    {'lmfdb_iso': '576.c', 'p': 53, 'prec': 20, 'unit': 383213405820380721703622649590136, 'val': 1}
  • id: 9503
    {'lmfdb_iso': '576.c', 'p': 61, 'prec': 20, 'unit': 2491145086919888397255214061347000, 'val': 1}
  • id: 9501
    {'lmfdb_iso': '576.c', 'p': 73, 'prec': 20, 'unit': 116633071478965807592241351369010343, 'val': 1}
  • id: 9502
    {'lmfdb_iso': '576.c', 'p': 89, 'prec': 20, 'unit': 1150859138397852057215409756289342382, 'val': 1}
  • id: 9494
    {'lmfdb_iso': '576.c', 'p': 97, 'prec': 20, 'unit': 36253603171097553392385091938952432115, 'val': 1}