Number field data - 8.0.3172352108695376607450650959096645338500694016.1

Formats: - HTML - YAML - JSON - 2024-04-24T10:19:41.452003

• 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
  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

  
  {'cm': False, 'coeffs': [210825220, -6144, -8960, -7168, -3360, -896, -112, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 3172352108695376607450650959096645338500694016, 'disc_rad': 9583046, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[5, 1], [3, 1]]], [5, [[7, 1], [1, 1]]], [7, [[3, 2], [1, 2]]], [11, [0]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[7, 1], [1, 1]]], [23, [[7, 1], [1, 1]]], [29, [[6, 1], [2, 1]]], [31, [[6, 1], [2, 1]]], [37, [[4, 1], [2, 1], [1, 2]]], [41, [[5, 1], [3, 1]]], [43, [[5, 1], [3, 1]]], [47, [[3, 1], [2, 2], [1, 1]]], [53, [[7, 1], [1, 1]]], [59, [[6, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [55440, 17280, 17280], 'galois_label': '8T49', 'galt': 49, 'grd': 3580574.3571707755, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.3172352108695376607450650959096645338500694016.1', 'local_algs': ['2.4.9.3', '2.4.9.3', '11.1.0.1', '11.7.6.1', 'm435593.1.1.0', 'm435593.7.1.6'], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [2, 11, 435593], 'rd': 487161.179294, 'res': {'sib': ['-200718463216114003952814398432,-50747486840808853281733968096,27230452144446951228021543456,1287983122533914430202690144,2012149206326526335626419568,1142554896723296486602850000,-528972861655744832520560224,-17308741992185080591650560,21804318925436672520094108,-10032075306558736942182324,2355461271323788043790380,168490663951028917884348,-232426657494195674505044,38504162795586667004332,1524442185356115256084,-1218535026395548030604,175909000997769673147,-18593488609019584949,2667105247348520665,-249699150167291903,-27771338981366636,12205048878474292,-1799718473085700,168044684753596,-15640873131418,1669467875702,-92404398614,-7424129110,1397611704,-36256584,-5452216,314888,10171,-917,-7,1', '-256299984968,-43553877128,95942827800,29672467720,3733251676,1515515876,231018856,-79327760,-32931093,-3941681,-45913,23547,3101,161,-3,1', '-256386290636,-43617019564,95909239548,29663992428,3734202452,1516471964,231310672,-79282472,-32930505,-3942405,-46053,23535,3101,161,-3,1', '194029440410240750836514816,101263273295239119657500672,10517708374747659087380480,-2587945078551390191616000,-384233385314462346510336,65013293505130618945536,12398658144851886866432,-645894369256689893376,-603376630228504350720,-133577981202068150272,1321983765205336192,4174511161520255008,79041875726273409,-108049203057262592,-4466644618813440,1906922630651904,109700380750336,-23087015555584,-1508714758816,224156418784,17431055454,-1381761024,-139575296,3440640,539392,-3584,-1120,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/4*a^4 - 1/2*a^2 - 1/2', '1/44*a^5 + 5/44*a^4 - 1/2*a^3 - 9/22*a^2 - 7/22*a + 9/22', '1/88*a^6 + 1/11*a^4 - 5/11*a^3 - 17/44*a^2 + 5/22', '1/88*a^7 + 1/11*a^4 - 17/44*a^3 - 4/11*a^2 - 1/2*a + 4/11']}