Elliptic curve data - 6240.a2

Formats: - HTML - YAML - JSON - 2024-04-25T04:23:58.271406

• 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': '6240b', 'Clabel': '6240b2', 'Cnumber': 2, 'abc_quality': 0.9081603122524584, 'absD': 658045440, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 520, 'ainvs': [0, -1, 0, -536, -4440], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6240, 'degree': 3072, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.45974667067911783794301842189', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [33324076232, 1285245], 'lmfdb_iso': '6240.a', 'lmfdb_label': '6240.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -536, -4440], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '20.12.0-4.c.1.1', '40.24.0-40.v.1.4', '104.24.0.?', '520.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.5148702646657485350579340720', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.060113714740841144119905669203', 'prec': 110}, 'szpiro_ratio': 3.4865308307367737, '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, -1, 0, -1, 0, -4, 0, 1, 0, -4, 0, -1, 0, 1, 0, 2, 0, 4, 0], 'aplist': [0, -1, -1, -4, -4, -1, 2, 4, 0, 6, 0, 10, 2, 4, -4, -6, 4, -2, 4, 8, -2, -16, -4, 10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 6240, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '6240.a', 'trace_hash': 1836904659296272476}
• 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': '0.39872100535973955609698126831', 'prec': 103}, 'conductor': 6240, 'gens': [[-11, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.5148702646657485350579340720', 'prec': 100}], 'lmfdb_label': '6240.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.99442338386852032986669808320', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5008457985792349742990511314975968619', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-15, 0, 1]], 'xcoord_integral_points': [-15, -11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [3, 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': '6240.a2'}
• ec_torsion_growth •

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

  
  
  • id: 324790
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [2, 2]}
  • id: 324792
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [4]}
  • id: 324791
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [4]}
  • id: 324793
    {'degree': 4, 'field': [9, 0, -4, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [2, 4]}
  • id: 324797
    {'degree': 8, 'field': [-1875, 0, -6200, 0, -150, 0, 0, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [6]}
  • id: 324796
    {'degree': 8, 'field': [484, 0, 9248, 0, 1644, 0, 80, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [8]}
  • id: 324794
    {'degree': 8, 'field': [7471, 1444, -1618, 352, -185, 8, 2, -4, 1], 'lmfdb_label': '6240.a2', 'torsion': [2, 4]}
  • id: 324795
    {'degree': 8, 'field': [8100, 0, 100, 0, 210, 0, 30, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [8]}
  • id: 324803
    {'degree': 16, 'field': [264196, 0, 409936, 0, 581152, 0, -57192, 0, -8580, 0, 1632, 0, -68, 0, 4, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [12]}
  • id: 324800
    {'degree': 16, 'field': [1143081, 854076, -508504, -609276, 113768, 191896, -6396, -41068, 833, 4896, 376, -708, 118, -28, 24, -8, 1], 'lmfdb_label': '6240.a2', 'torsion': [2, 8]}
  • id: 324798
    {'degree': 16, 'field': [4100625, 0, 0, 0, 0, 0, 0, 0, 68850, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [4, 4]}
  • id: 324802
    {'degree': 16, 'field': [15706270, 9321660, 12309616, 5141256, 3039184, -2618580, -599906, 148488, 485683, -22488, -1730, 5952, 1144, -276, -44, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [12]}
  • id: 324799
    {'degree': 16, 'field': [2892718656, 0, 666807552, 0, 120092544, 0, 5038848, 0, 175284, 0, 10368, 0, 972, 0, 0, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [2, 8]}
  • id: 324801
    {'degree': 16, 'field': [4743765625, 0, -2844800000, 0, 260252500, 0, 3270000, 0, -383250, 0, -74400, 0, 2500, 0, -80, 0, 1], 'lmfdb_label': '6240.a2', 'torsion': [2, 6]}
• 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: 124561
    {'conductor': 6240, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '6240.a2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 124562
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6240.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 124563
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6240.a2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 124564
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6240.a2', 'prime': 13, '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: 1704840
    {'adelic_gens': [[41, 8, 164, 33], [513, 8, 512, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [216, 3, 5, 2], [328, 73, 187, 174], [7, 6, 514, 515], [191, 192, 442, 185]], 'adelic_image': '520.48.0.?', 'conductor': 6240, 'lmfdb_label': '6240.a2', 'prime': 0}
  • id: 30612
    {'conductor': 6240, 'elladic_image': '8.12.0.7', 'lmfdb_label': '6240.a2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 243510
    {'lmfdb_iso': '6240.a', 'p': 7, 'prec': 20, 'unit': 5387190822486539, 'val': 1}
  • id: 243515
    {'lmfdb_iso': '6240.a', 'p': 11, 'prec': 20, 'unit': 31739519315394168717, 'val': 1}
  • id: 243516
    {'lmfdb_iso': '6240.a', 'p': 17, 'prec': 20, 'unit': 72357042551229769029493, 'val': 1}
  • id: 243517
    {'lmfdb_iso': '6240.a', 'p': 19, 'prec': 20, 'unit': 1334419316968025845908261, 'val': 1}
  • id: 243513
    {'lmfdb_iso': '6240.a', 'p': 29, 'prec': 20, 'unit': 4433757950572940368103421222, 'val': 1}
  • id: 243509
    {'lmfdb_iso': '6240.a', 'p': 37, 'prec': 20, 'unit': 282023443540574834557007710532, 'val': 1}
  • id: 243511
    {'lmfdb_iso': '6240.a', 'p': 41, 'prec': 20, 'unit': 1067611730885842580165881797817, 'val': 1}
  • id: 243512
    {'lmfdb_iso': '6240.a', 'p': 43, 'prec': 20, 'unit': 5527910520584388301071764214112, 'val': 1}
  • id: 243523
    {'lmfdb_iso': '6240.a', 'p': 47, 'prec': 20, 'unit': 2594661708779847458857415723557, 'val': 1}
  • id: 243518
    {'lmfdb_iso': '6240.a', 'p': 53, 'prec': 20, 'unit': 107288556995818715135515052410240, 'val': 1}
  • id: 243519
    {'lmfdb_iso': '6240.a', 'p': 59, 'prec': 20, 'unit': 549094156558585830859728689977761, 'val': 1}
  • id: 243524
    {'lmfdb_iso': '6240.a', 'p': 61, 'prec': 20, 'unit': 1906965272865211492578599332972812, 'val': 1}
  • id: 243508
    {'lmfdb_iso': '6240.a', 'p': 67, 'prec': 20, 'unit': 15330919282426992140619485607766984, 'val': 1}
  • id: 243522
    {'lmfdb_iso': '6240.a', 'p': 71, 'prec': 20, 'unit': 134672923640490236310282072383689754, 'val': 1}
  • id: 243520
    {'lmfdb_iso': '6240.a', 'p': 73, 'prec': 20, 'unit': 114075996413226768785745812564544289, 'val': 1}
  • id: 243514
    {'lmfdb_iso': '6240.a', 'p': 79, 'prec': 20, 'unit': 328545962247226637055510180700405539, 'val': 1}
  • id: 243507
    {'lmfdb_iso': '6240.a', 'p': 83, 'prec': 20, 'unit': 2093667539687101670125514078785474687, 'val': 1}
  • id: 243521
    {'lmfdb_iso': '6240.a', 'p': 89, 'prec': 20, 'unit': 10239162770042048212046140925681034352, 'val': 1}
  • id: 243506
    {'lmfdb_iso': '6240.a', 'p': 97, 'prec': 20, 'unit': 31395775274247314640502669799667567239, 'val': 1}