Number field data - 8.2.2693955999488.1

Formats: - HTML - YAML - JSON - 2025-01-30T02:15:55.069385

• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-5, -6, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 2693955999488, 'disc_rad': 21046531246, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[4, 2]]], [5, [[6, 1], [1, 2]]], [7, [[7, 1], [1, 1]]], [11, [[4, 2]]], [13, [0]], [17, [[6, 1], [2, 1]]], [19, [[7, 1], [1, 1]]], [23, [[5, 1], [1, 3]]], [29, [[4, 1], [2, 2]]], [31, [[7, 1], [1, 1]]], [37, [[6, 1], [1, 2]]], [41, [[4, 1], [2, 1], [1, 2]]], [43, [[7, 1], [1, 1]]], [47, [[3, 2], [2, 1]]], [53, [[4, 1], [2, 2]]], [59, [[3, 2], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [44640, 20160, 20160, 20160], 'galois_label': '8T50', 'galt': 50, 'grd': 220982.8019336467, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.2.2693955999488.1', 'local_algs': ['2.8.8.13', '13.1.0.1', '13.2.1.1', '13.5.0.1', 'm20173.2.1.1', 'm20173.1.3.0', 'm20173.1.3.0', 'm40127.1.1.0', 'm40127.1.1.0', 'm40127.2.1.1', 'm40127.1.4.0'], 'monogenic': 1, 'num_ram': 4, 'r2': 3, 'ramps': [2, 13, 20173, 40127], 'rd': 35.793058667, 'regulator': {'__RealLiteral__': 0, 'data': '2815.70995221', 'prec': 44}, 'res': {'sib': ['-2805852840062976,13408428275712000,-17992466496000000,12060533076480000,-15400735027200000,13621926583342080,-7644909703680000,7514509529537280,-4229793312768000,2431723460000000,-1821276779212800,679754409600000,-502536083281920,196138153760000,-90621887823360,49297832096000,-11102508000000,9374022790400,-944589600000,1309113985280,-55961280000,135056796160,-2267676000,10364000000,-59972400,590800000,-933120,24700000,-6480,736000,0,14800,0,180,0,1', '-78125,0,0,0,-15625,-22500,-32400,-46656,9375,9000,6480,0,1875,3600,3888,0,-375,-360,0,0,-75,-108,0,0,5,0,0,0,1', '144342784368495820800000000,-66220919653260749045760000,463751651175398637601554432,-185941197721887904235520000,77106443092833910784000000,-20470496730373414777651200,9717726426466703769600000,-2457952748448467021660160,769311890582531645440000,-123887332237932079681536,38711858005108879360000,-3253117355550720000000,1251844568085951795200,-50645466224640000000,26895250031962726400,-494166201338880000,396506608963933952,-3052250159616000,4098814720000000,-11561817657600,29964390400000,-24395696640,153996640000,-21781872,543200000,0,1248800,0,1680,0,1', '82886427316106808740627088417529288914455897118232236331,-15217383878205113571226719508344448644412587505918,8475106761968538250215897503280807038944428210920,-634641880939995835144612279264274079102740,140283552661944867687335870323899696487590,78105053225391960735357455195915736,-9662943957340671968506261277906488,71097745510732278119724065504,-18204798488532513342643580660,-9076141568550690414206,68762152277905245680,30599338274764,-7367918617086,-2352364,388992,-8,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{7} + a^{5} + a^{4} + a^{3} + 3 a^{2} + a - 1 \\)', '\\( a^{7} - 2 a^{6} + 3 a^{5} - 3 a^{4} + a^{3} + 2 a^{2} - 4 a - 1 \\)', '\\( 2 a^{7} - 2 a^{6} + 2 a^{5} - a^{4} - a^{2} + 3 a - 14 \\)', '\\( 23 a^{7} - 13 a^{6} - 36 a^{5} + 36 a^{4} + 48 a^{3} - 79 a^{2} - 55 a + 17 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7']}