Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (1-50 of 53 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
13.1.73343569978705405.1	$x^{13} + 2 x - 1$	$13$	[1,6]	$5\cdot 2441\cdot 2671\cdot 2249833471$	$4$	$19.8305857267$	$270820180.1541115$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$2894.42759466$
13.1.948413657113415680.1	$x^{13} - 2 x^{12} + 8 x^{9} - 12 x^{6} + 8 x^{3} - 2$	$13$	[1,6]	$2^{12}\cdot 5\cdot 11\cdot 4093\cdot 1028568967$	$5$	$24.1460438256$	$28853119.054754354$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$14759.3341822$
13.1.131...440.1	$x^{13} + 2 x - 2$	$13$	[1,6]	$2^{12}\cdot 5\cdot 291331\cdot 220166963$	$4$	$24.7587303274$	$33956918.31996527$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$12524.5893502$
13.3.142...435.1	$x^{13} - 3 x - 1$	$13$	[3,5]	$-\,5\cdot 226169\cdot 12570105664223$	$3$	$29.7363628145$	$3770257436.814926$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$45375.9232824$
13.1.146...885.1	$x^{13} - 3 x - 3$	$13$	[1,6]	$3^{12}\cdot 5\cdot 354451\cdot 155805347$	$4$	$35.5855862532$	$45811435.84232925$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$103653.885124$
13.1.212...040.1	$x^{13} + 7 x - 4$	$13$	[1,6]	$2^{14}\cdot 5\cdot 180287\cdot 14364226951$	$4$	$36.6089634033$				?	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$312667.755821$
13.3.119...080.1	$x^{13} - 8 x - 4$	$13$	[3,5]	$-\,2^{12}\cdot 5\cdot 23\cdot 1993\cdot 1273413051689$	$5$	$41.8166077225$	$1024379927.742423$			?	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$834014.333738$
13.1.506...960.1	$x^{13} - 3 x - 4$	$13$	[1,6]	$2^{25}\cdot 5\cdot 18539\cdot 1629148379$	$4$	$46.7301795074$				✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$2995618.86239$
13.1.122...965.1	$x^{13} - 8 x - 9$	$13$	[1,6]	$3^{4}\cdot 5\cdot 4871\cdot 6230214637061743$	$4$	$50.0262750153$	$21335665737.373096$				$S_{13}$ (as 13T9)	$[2]$	$2$	$6$	$1140064.994$
13.1.732...240.1	$x^{13} + 2 x - 6$	$13$	[1,6]	$2^{12}\cdot 3^{11}\cdot 5\cdot 20191676009779$	$4$	$57.389646274$	$137086968.15353632$				$S_{13}$ (as 13T9)	trivial	$2$	$6$	$14178379.279$
13.1.164...080.1	$x^{13} - 3 x - 6$	$13$	[1,6]	$2^{10}\cdot 3^{12}\cdot 5\cdot 241979\cdot 250326331$	$5$	$61.0834821791$	$117456522.53457107$				$S_{13}$ (as 13T9)	trivial	$2$	$6$	$30342478.6125$
13.1.863...445.1	$x^{13} + 7 x - 1$	$13$	[1,6]	$5\cdot 172774429884761611118489$	$2$	$69.3849602895$	$929447227885.3749$			✓	$S_{13}$ (as 13T9)	$[2]$	$2$	$6$	$3954664.2587$
13.1.863...480.1	$x^{13} + 7 x - 2$	$13$	[1,6]	$2^{12}\cdot 5\cdot 59\cdot 18033839\cdot 39644226101$	$5$	$69.3849679524$	$36331445116.107185$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$36185343.0466$
13.1.864...765.1	$x^{13} + 7 x - 3$	$13$	[1,6]	$3^{12}\cdot 5\cdot 23330159\cdot 13937588087$	$4$	$69.3859546709$				✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$8943720.96915$
13.1.419...165.1	$x^{13} - 3 x - 7$	$13$	[1,6]	$5\cdot 288098916137\cdot 2910227624209$	$3$	$78.3490504662$	$2047478234617.6106$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$16819172.8048$
13.1.419...005.1	$x^{13} + 2 x - 7$	$13$	[1,6]	$5\cdot 2083\cdot 185661767\cdot 2167995188341$	$4$	$78.3490710075$	$2047481723829.924$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$17397718.2342$
13.3.424...320.1	$x^{13} - 8 x - 6$	$13$	[3,5]	$-\,2^{12}\cdot 3^{12}\cdot 5\cdot 11943947\cdot 32634517$	$5$	$78.4208496831$	$417620777.2365524$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$60261510.7411$
13.3.490...755.1	$x^{13} - 8 x - 3$	$13$	[3,5]	$-\,3^{12}\cdot 5\cdot 11\cdot 59\cdot 103\cdot 27594564189113$	$6$	$79.2968971654$	$15151249753.105644$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$64236665.3802$
13.3.490...040.1	$x^{13} - 8 x - 2$	$13$	[3,5]	$-\,2^{12}\cdot 5\cdot 239339688381919058023$	$3$	$79.2970959278$	$65594315580.91077$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$40345047.207$
13.1.505...045.1	$x^{13} + 7 x - 7$	$13$	[1,6]	$5\cdot 7^{12}\cdot 23\cdot 929\cdot 21557\cdot 158611$	$6$	$79.486468941$	$115188225.55455989$			✓	$S_{13}$ (as 13T9)	$[2]$	$2$	$6$	$9863204.921$
13.1.520...840.1	$x^{13} + 2 x - 8$	$13$	[1,6]	$2^{34}\cdot 5\cdot 47\cdot 337\cdot 3824422093$	$5$	$79.662250603$	$218430299.72573835$			?	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$59778926.8359$
13.1.950...445.1	$x^{13} - 3 x - 9$	$13$	[1,6]	$3^{22}\cdot 5\cdot 60575011252121$	$3$	$83.4409646523$	$213607668.56664515$			?	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$45322987.6702$
13.1.208...520.1	$x^{13} - 3 x - 8$	$13$	[1,6]	$2^{24}\cdot 5\cdot 4973\cdot 49892442763453$	$4$	$88.6267565724$	$4455245159.249056$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$268448687.385$
13.1.855...845.1	$x^{13} + 2 x - 9$	$13$	[1,6]	$3^{12}\cdot 5\cdot 3703769\cdot 8691700246961$	$4$	$98.8058347994$	$45708901301.3603$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$266108695.211$
13.1.864...885.1	$x^{13} + 7 x - 9$	$13$	[1,6]	$3^{12}\cdot 5\cdot 295553\cdot 110021402170249$	$4$	$98.8822358008$	$45939127201.713135$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$92346119.4592$
17.13.483...800.1	$x^{17} - 4 x^{16} - 6 x^{15} + 41 x^{14} - 5 x^{13} - 163 x^{12} + 112 x^{11} + 322 x^{10} - 315 x^{9} - 342 x^{8} + 381 x^{7} + 204 x^{6} - 216 x^{5} - 70 x^{4} + 55 x^{3} + 13 x^{2} - 5 x - 1$	$17$	[13,2]	$2^{6}\cdot 5^{2}\cdot 7529\cdot 4014102427748751372137$	$4$	$48.6766113617$	$22267608975849.832$			?	$S_{17}$ (as 17T10)	trivial	$2$	$14$	$682339734.776$
18.0.186...395.1	$x^{18} - 2 x^{17} + 2 x^{16} - 2 x^{15} + 3 x^{14} - 3 x^{13} + 2 x^{12} - 2 x^{11} + 2 x^{10} + x^{9} - 2 x^{8} + 3 x^{5} - 3 x^{4} - x^{3} + 5 x^{2} - 3 x + 1$	$18$	[0,9]	$-\,5\cdot 13\cdot 19\cdot 71^{2}\cdot 277\cdot 18191\cdot 594058899611$	$7$	$25.3459343592$	$512325034345.1479$			?	$S_{18}$ (as 18T983)	trivial	$2$	$8$	$333593.823441$
22.2.347...005.1	$x^{22} - x - 1$	$22$	[2,10]	$5\cdot 69454092876521107983605569601$	$2$	$22.0169739943$	$589296584397538.8$			✓	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$912353.207873$
22.2.245...305.1	$x^{22} - 4 x - 1$	$22$	[2,10]	$5\cdot 549569\cdot 7345029585473\cdot 1214169483036053$	$4$	$36.571974928$	$1.5654260155512237e+17$			?	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$364755463.699$
22.2.156...320.1	$x^{22} - 8 x - 4$	$22$	[2,10]	$2^{26}\cdot 5\cdot 1213\cdot 2791\cdot 144349\cdot 1885069\cdot 5073819587$	$7$	$44.1822238667$				?	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$5313442979.16$
22.2.183...805.1	$x^{22} - 3 x + 1$	$22$	[2,10]	$5\cdot 141073679\cdot 259930232844232011712508929559$	$3$	$54.8579623874$	$1.3540552837802164e+19$			✓	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$27087582193.6$
22.0.100...795.1	$x^{22} - 9 x + 9$	$22$	[0,11]	$-\,3^{20}\cdot 5\cdot 17\cdot 5791\cdot 24023\cdot 24426683885548437839$	$6$	$59.2744724236$	$1459078698808233.8$			?	$S_{22}$ (as 22T59)	trivial	$2$	$10$	$64985594632.5$
22.2.375...680.1	$x^{22} - 2 x - 4$	$22$	[2,10]	$2^{20}\cdot 5\cdot 261563\cdot 273749027024197539409418576947$	$4$	$77.5800304972$	$1.1578296934433628e+18$			?	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$4719003322200$
22.0.150...315.1	$x^{22} - x + 4$	$22$	[0,11]	$-\,5\cdot 356579\cdot 84\!\cdots\!97$	$3$	$82.6259201382$	$1.225404294441367e+21$			✓	$S_{22}$ (as 22T59)	$[2]$	$2$	$10$	$6589731323400$
22.0.781...915.1	$x^{22} - x + 9$	$22$	[0,11]	$-\,3^{7}\cdot 5\cdot 197609\cdot 33539836790136769\cdot 107772425603920829$	$5$	$89.0569698212$	$1.0351023414011252e+20$			?	$S_{22}$ (as 22T59)	trivial	$2$	$10$	$8965046463610$
22.2.191...880.1	$x^{22} - 6 x + 4$	$22$	[2,10]	$2^{20}\cdot 5\cdot 42163799\cdot 867988951454801464103727637199$	$4$	$103.006521261$	$2.6176236261157114e+19$			?	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$101271114237000$
22.2.769...840.1	$x^{22} - 6 x - 1$	$22$	[2,10]	$2^{23}\cdot 5\cdot 17\cdot 1063\cdot 5743\cdot 176665517968982637898053783407$	$6$	$109.715924784$				✓	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$256949862922000$
22.0.832...880.1	$x^{22} - 2 x + 6$	$22$	[0,11]	$-\,2^{22}\cdot 3^{19}\cdot 5\cdot 44687\cdot 80071\cdot 9542068409472622141$	$6$	$110.110506485$				?	$S_{22}$ (as 22T59)	trivial	$2$	$10$	$149993687037000$
22.2.832...560.1	$x^{22} - 4 x - 6$	$22$	[2,10]	$2^{43}\cdot 3^{21}\cdot 5\cdot 13\cdot 139\cdot 281\cdot 1663\cdot 3049\cdot 13187\cdot 53281$	$10$	$110.110575169$				?	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$250561588364000$
22.0.748...515.1	$x^{22} - 3 x + 6$	$22$	[0,11]	$-\,3^{21}\cdot 5\cdot 47\cdot 67\cdot 240033317\cdot 189458757487545844247197$	$6$	$121.675578385$	$2.414895616392203e+18$			✓	$S_{22}$ (as 22T59)	$[2]$	$2$	$10$	$518995826970000$
22.2.825...160.1	$x^{22} - 6 x - 6$	$22$	[2,10]	$2^{22}\cdot 3^{21}\cdot 5\cdot 61\cdot 967\cdot 1291\cdot 1471\cdot 336086143452512773$	$8$	$122.217338583$				✓	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$540346454822000$
22.2.228...045.1	$x^{22} - 7 x + 1$	$22$	[2,10]	$5\cdot 17\cdot 146164661\cdot 411260814053084977\cdot 4470781339127615341$	$5$	$128.001912248$	$1.511405627310658e+23$			✓	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$450538214345000$
22.2.228...365.1	$x^{22} - 7 x - 4$	$22$	[2,10]	$5\cdot 234811\cdot 47809051\cdot 40\!\cdots\!93$	$4$	$128.0022947$	$1.5114553026255217e+23$			✓	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$1587151285520000$
22.2.423...440.1	$x^{22} - 8 x + 6$	$22$	[2,10]	$2^{43}\cdot 3^{21}\cdot 5\cdot 67\cdot 43223\cdot 317963629399156207$	$6$	$146.171405779$				✓	$S_{22}$ (as 22T59)	$[2]$	$2$	$11$	$2419229210220000$
22.2.431...760.1	$x^{22} - 8 x + 1$	$22$	[2,10]	$2^{22}\cdot 5\cdot 131\cdot 39727\cdot 3378541027\cdot 5215350781\cdot 224173982411777$	$7$	$146.287899712$				✓	$S_{22}$ (as 22T59)	$[2]$	$2$	$11$	$1640113479820000$
22.2.415...605.1	$x^{22} - 3 x - 9$	$22$	[2,10]	$3^{40}\cdot 5\cdot 101\cdot 676094806665138999978013021$	$4$	$162.1495961$				?	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$10534457309700000$
22.2.575...165.1	$x^{22} - 9 x + 4$	$22$	[2,10]	$5\cdot 1049\cdot 109913\cdot 9221893\cdot 10\!\cdots\!13$	$5$	$164.573885224$	$2.3986680027812382e+24$			✓	$S_{22}$ (as 22T59)	$[2]$	$2$	$11$	$18584303063900000$
22.2.575...485.1	$x^{22} - 9 x - 1$	$22$	[2,10]	$5\cdot 9343\cdot 193345432279\cdot 68719382648701\cdot 9269810970758141501$	$5$	$164.573887176$	$2.3986683157915393e+24$			✓	$S_{22}$ (as 22T59)	$[2]$	$2$	$11$	$3853077040720000$
22.2.576...805.1	$x^{22} - 9 x - 6$	$22$	[2,10]	$3^{21}\cdot 5\cdot 13\cdot 84\!\cdots\!99$	$4$	$164.583619205$	$6.697511087695173e+19$			✓	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$52018958112500000$
22.0.373...920.1	$x^{22} - 4 x + 9$	$22$	[0,11]	$-\,2^{22}\cdot 3^{21}\cdot 5\cdot 457\cdot 3527\cdot 744601027\cdot 141895991315806619$	$7$	$179.180411931$				✓	$S_{22}$ (as 22T59)	$[2]$	$2$	$10$	$12757611973800000$