Elliptic curve data - 3528.x2

Formats: - HTML - YAML - JSON - 2024-05-18T13:48:49.485025

• 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': '3528k', 'Clabel': '3528k3', 'Cnumber': 3, 'abc_quality': 1.1170620055320515, 'absD': 421733286955008, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 0, 0, -26019, -1278018], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3528, 'degree': 12288, 'elladic_images': ['8.12.0.15'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5202283920631240099037554532', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2, 4], 'jinv': [11090466, 2401], 'lmfdb_iso': '3528.x', 'lmfdb_label': '3528.x2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -59, -138], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.k.1', '24.24.0-8.k.1.3', '56.24.0.v.1', '84.12.0.?', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.1764888079323694142251416279', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.63741774231187068864567298166', 'prec': 107}, 'szpiro_ratio': 5.155587931502616, '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, 4, 0, -2, 0, 0, 0, -6, 0, -8, 0], 'aplist': [0, 0, 2, 0, 4, -2, -6, -8, 0, -6, -8, -2, 2, -4, -8, -6, 0, 6, -4, 8, -10, 16, 8, -6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 3528, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3528.x', 'trace_hash': 2015772246107615184}
• 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': '0.047813044265653245371781248640', 'prec': 107}, 'conductor': 3528, 'gens': [[-279, 3555, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '5.1764888079323694142251416279', 'prec': 100}], 'lmfdb_label': '3528.x2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.38168417606324512688755929852', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9515677311125527501716782778930001239', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-126, 0, 1]], 'xcoord_integral_points': [-126]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '3528.x2'}
• ec_torsion_growth •

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

  
  
  • id: 183697
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [2, 2]}
  • id: 183698
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [4]}
  • id: 183699
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [4]}
  • id: 183700
    {'degree': 4, 'field': [121, 0, 20, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [2, 4]}
  • id: 183704
    {'degree': 8, 'field': [-14, -56, -62, 10, 58, 34, 4, -2, 1], 'lmfdb_label': '3528.x2', 'torsion': [6]}
  • id: 183702
    {'degree': 8, 'field': [4, 0, -7, 0, 11, 0, 7, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [8]}
  • id: 183703
    {'degree': 8, 'field': [4, 0, 16, 0, 62, 0, 8, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [8]}
  • id: 183701
    {'degree': 8, 'field': [487, 628, -482, -272, 87, 56, -14, -4, 1], 'lmfdb_label': '3528.x2', 'torsion': [2, 4]}
  • id: 183707
    {'degree': 16, 'field': [1, 0, 12, 0, 120, 0, 264, 0, 431, 0, 264, 0, 120, 0, 12, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [2, 8]}
  • id: 183709
    {'degree': 16, 'field': [1, 0, 20, 0, 28, 0, 56, 0, -14, 0, 56, 0, 28, 0, 20, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [12]}
  • id: 183706
    {'degree': 16, 'field': [4, 0, -8, 40, 48, -152, 280, -332, 341, -344, 338, -256, 146, -56, 18, -4, 1], 'lmfdb_label': '3528.x2', 'torsion': [2, 8]}
  • id: 183708
    {'degree': 16, 'field': [289, 0, 1256, 0, 11200, 0, -14812, 0, 6286, 0, -112, 0, -140, 0, -4, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [2, 6]}
  • id: 183710
    {'degree': 16, 'field': [1849, 0, 3040, 0, 6736, 0, 3004, 0, 1222, 0, 520, 0, 148, 0, 28, 0, 1], 'lmfdb_label': '3528.x2', 'torsion': [12]}
  • id: 183705
    {'degree': 16, 'field': [99817, 132392, 34384, -210616, -155584, 192056, 111480, -100912, -30367, 27640, 3228, -3944, -10, 280, -20, -8, 1], 'lmfdb_label': '3528.x2', 'torsion': [4, 4]}
• 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: 64640
    {'conductor': 3528, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '3528.x2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 64641
    {'conductor': 3528, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '3528.x2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 64642
    {'conductor': 3528, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '3528.x2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1686941
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [136, 57, 27, 70], [7, 6, 162, 163], [161, 8, 160, 9], [43, 36, 138, 13], [1, 4, 4, 17], [55, 0, 0, 167], [95, 48, 156, 23]], 'adelic_image': '168.48.0.?', 'conductor': 3528, 'lmfdb_label': '3528.x2', 'prime': 0}
  • id: 17616
    {'conductor': 3528, 'elladic_image': '8.12.0.15', 'lmfdb_label': '3528.x2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 119057
    {'lmfdb_iso': '3528.x', 'p': 5, 'prec': 20, 'unit': 12797866911266, 'val': 1}
  • id: 119056
    {'lmfdb_iso': '3528.x', 'p': 11, 'prec': 20, 'unit': 56442424324742830819, 'val': 1}
  • id: 119063
    {'lmfdb_iso': '3528.x', 'p': 13, 'prec': 20, 'unit': 214901807977624062393, 'val': 1}
  • id: 119065
    {'lmfdb_iso': '3528.x', 'p': 17, 'prec': 20, 'unit': 160608048136966578498400, 'val': 1}
  • id: 119066
    {'lmfdb_iso': '3528.x', 'p': 19, 'prec': 20, 'unit': 711279961265674641821505, 'val': 1}
  • id: 119062
    {'lmfdb_iso': '3528.x', 'p': 29, 'prec': 20, 'unit': 3949205488684222789054985903, 'val': 1}
  • id: 119059
    {'lmfdb_iso': '3528.x', 'p': 31, 'prec': 20, 'unit': 9372414214477513231297254620, 'val': 1}
  • id: 119073
    {'lmfdb_iso': '3528.x', 'p': 37, 'prec': 20, 'unit': 551754480380039200706370434173, 'val': 1}
  • id: 119060
    {'lmfdb_iso': '3528.x', 'p': 41, 'prec': 20, 'unit': 2759859287873701282376865685606, 'val': 1}
  • id: 119061
    {'lmfdb_iso': '3528.x', 'p': 43, 'prec': 20, 'unit': 4508047039761050011206679958495, 'val': 1}
  • id: 119064
    {'lmfdb_iso': '3528.x', 'p': 47, 'prec': 20, 'unit': 2602538379772340623904959030909, 'val': 1}
  • id: 119067
    {'lmfdb_iso': '3528.x', 'p': 53, 'prec': 20, 'unit': 344114172457146943773326220731786, 'val': 1}
  • id: 119072
    {'lmfdb_iso': '3528.x', 'p': 61, 'prec': 20, 'unit': 5790883053880039557563558172133568, 'val': 1}
  • id: 119055
    {'lmfdb_iso': '3528.x', 'p': 67, 'prec': 20, 'unit': 48606447274549322613399432340943613, 'val': 1}
  • id: 119058
    {'lmfdb_iso': '3528.x', 'p': 71, 'prec': 20, 'unit': 96850591388624091012446116210258752, 'val': 1}
  • id: 119068
    {'lmfdb_iso': '3528.x', 'p': 73, 'prec': 20, 'unit': 175449107693067142309294887610423869, 'val': 1}
  • id: 119071
    {'lmfdb_iso': '3528.x', 'p': 79, 'prec': 20, 'unit': 835213457342219239720584196147999240, 'val': 1}
  • id: 119069
    {'lmfdb_iso': '3528.x', 'p': 83, 'prec': 20, 'unit': 2518152557644710949832175760297750931, 'val': 1}
  • id: 119070
    {'lmfdb_iso': '3528.x', 'p': 89, 'prec': 20, 'unit': 291880637113364684448626434572230690, 'val': 1}
  • id: 119054
    {'lmfdb_iso': '3528.x', 'p': 97, 'prec': 20, 'unit': 50754505931745153855744718185175315719, 'val': 1}