Number field data - 5.1.6571389.1

Formats: - HTML - YAML - JSON - 2024-05-20T23:07:11.679314

• 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

  
  {'class_group': [11], 'class_number': 11, 'cm': False, 'coeffs': [-1, 8, -9, 8, -1, 1], 'conductor': 0, 'degree': 5, 'dirichlet_group': [], 'disc_abs': 6571389, 'disc_rad': 597399, 'disc_sign': 1, 'frobs': [[2, [[4, 1], [1, 1]]], [3, [0]], [5, [[2, 2], [1, 1]]], [7, [[4, 1], [1, 1]]], [11, [0]], [13, [[3, 1], [2, 1]]], [17, [[4, 1], [1, 1]]], [19, [[3, 1], [1, 2]]], [23, [[5, 1]]], [29, [[4, 1], [1, 1]]], [31, [[5, 1]]], [37, [[5, 1]]], [41, [[5, 1]]], [43, [0]], [47, [[5, 1]]], [53, [[5, 1]]], [59, [[3, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [60, 80, 60, 60], 'galois_label': '5T5', 'galt': 5, 'grd': 1152.650633160811, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.1.6571389.1', 'local_algs': ['3.2.1.1', '3.3.0.1', '11.1.0.1', '11.1.0.1', '11.3.2.1', '43.1.0.1', '43.2.1.2', '43.2.0.1', 'm421.2.1.1', 'm421.1.3.0'], 'monogenic': 1, 'num_ram': 4, 'r2': 2, 'ramps': [3, 11, 43, 421], 'rd': 23.0957162528, 'regulator': {'__RealLiteral__': 0, 'data': '7.19937117811', 'prec': 44}, 'res': {'sib': ['-113,-147,676,-1040,907,-546,277,-85,30,-4,1', '-1327136,-162221,40077,1854,-574,-1,1', '-1353512046275,-14060676885,5566342987,-617480754,165063219,-4056427,786682,-8450,1441,-4,1', '-4913249,7507115,-6456538,5328869,-2340786,-363904,315825,-361296,176711,6550,-17996,1711,574,-81,-6,1', '1046386246269073990116715360,473627632332262835897239824,-225833482775929200955099312,245233786645161086513243020,-72918869570719978740172212,25253226794683415046173343,-4955180264232684447226175,1042017190193163745085991,-166583068307877878803982,29576704629900466071966,-4796952764239950890456,763267840961303687355,-103058734722875527274,12784552601718913380,-1469681410226659013,141370156034443354,-12186537935883713,797354793416533,-40890317208187,-1108101080786,443413342665,-60123543683,7059069532,-606526186,47755795,-3187579,223940,-7710,711,-6,1', '126713390651044427895322076325,12939978488124391311825374445,66247915914405368182099443249,289926702103276162328296505220,-12222595260779010181653981978,-21660834918008858389588769409,122438519902956978963408100716,-82249381121437147729334240061,56750685133279991069884722561,-25395230338382289597801077736,10779964032570670050531497079,-3745753286382781894212352866,1177436216191493574401468431,-339117442703288657600835464,86635901603933502021859682,-21117858069962853000309805,4682177924266042068224257,-962863842675449540079328,193830612662094547676105,-33219036969266603896892,6249823344927047890783,-880774415876237639791,157697369921457465249,-18057894542598971077,3111624802266738536,-286473626610890474,47812938516186750,-3502198668119563,567573286685402,-32660123023620,5135441008664,-227925482368,34654442683,-1151139755,168346352,-3966788,554385,-8324,1104,-8,1', '2011209169281408000,-4274702512370334720,2715775030958473728,-4892999449205814912,-1223756798616813120,573885621148368672,789281571445176208,-229793154146980584,3633945844276824,9118331388707116,-3747631912330995,852180672586140,4548246456044,-48716700100194,13670896296804,-1842676485474,-146431258200,107339610780,-22574418566,2019992976,306964839,-142862984,21504480,-1014750,-363456,85686,-7644,68,120,-12,1', '2470614256,-14893956088,-90279079440,-262206200812,-442198287703,-558677188465,-519941576910,-454216886319,-353557874096,-275389327513,-188989406589,-115301894173,-63685076098,-32463226747,-15482660169,-6745652584,-2626216260,-902877301,-271532847,-71858875,-16304167,-2814575,-177333,106979,48933,9549,407,-276,-60,0,1', '2496400,0,-3171229,0,936576,0,-147480,0,7052,0,-140,0,1', '451871901295541060647,-353397120241371881370,114475582674396435465,-8165393028207633575,852370563917870095,-333330618539818721,74542267135737852,-1018979422306347,-988974112051885,188387564372462,-4578472910245,4388950956625,-460092652071,-157641143521,3241695357,366278854,426348605,-30117564,1792584,-353994,12584,-2195,200,-6,1', '4669840181455527,-9695694222816098,8351460545677942,-3843685572727188,1230532671715288,-331715968293400,74038282099440,-13996012688170,2535239982178,-412868371374,58769315777,-7983418908,949953582,-100320742,9742398,-827610,67194,-3364,370,-2,1', '500191667101202117308,100547316571952606876,-19635472375999254855,3305804320825483255,-194850746748092458,-46521039149044919,38303143437181899,-3979964185874147,-791943625149649,113647219923959,4221817330852,-1206942218429,22565213906,6008353515,-280815801,-15744946,970742,19344,-1545,-8,1', '6571389,0,17361443,0,25683350,0,19490030,0,8368887,0,2206632,0,365481,0,37621,0,2306,0,76,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{4} + 7 a^{2} - 2 a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4']}