Number field search results

Results (1-50 of 100 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
34.0.116...023.1	x^34 - x + 1	$34$	[0,17]	$-\,83\cdot 1291\cdot 12973\cdot 4134484433\cdot 64200532307\cdot 31512487292285521887257$	$6$	$33.9889591634$			✓	$S_{34}$ (as 34T115)	trivial	$2$	$16$	$1946991838336.107$
34.2.118...049.1	x^34 - x - 1	$34$	[2,16]	$7\cdot 191\cdot 607\cdot 14\!\cdots\!11$	$4$	$34.0109237751$			✓	$S_{34}$ (as 34T115)	trivial	$2$	$17$	$2995765078540.3994$
34.0.770...296.1	x^34 - 2x^17 + 2	$34$	[0,17]	$-\,2^{50}\cdot 17^{34}$	$2$	$47.1129275253$			✓	$C_{17}:(C_2\times C_{16})$ (as 34T9)	trivial	$4$	$16$	$2332460652781060.5$
34.0.380...067.1	x^34 - 3x^17 + 3	$34$	[0,17]	$-\,3^{33}\cdot 17^{34}$	$2$	$49.3784209847$			✓	$C_{17}:(C_2\times C_{16})$ (as 34T9)	trivial	$6$	$16$	$6031882093114950.0$
34.2.221...721.1	x^34 - 4x - 1	$34$	[2,16]	$151163\cdot 3136253\cdot 9671606647\cdot 432210572699\cdot 6906809950567\cdot 162051016270589$	$6$	$59.5499993173$			not computed	$S_{34}$ (as 34T115)	trivial	$2$	$17$	$45896286039491820$
34.2.221...928.1	x^34 - 2x - 1	$34$	[2,16]	$2^{35}\cdot 307\cdot 135071166289\cdot 15\!\cdots\!27$	$4$	$59.5499993265$			✓	$S_{34}$ (as 34T115)	trivial	$2$	$17$	$65073117810876920$
34.0.482...264.1	x^34 - 4x + 4	$34$	[0,17]	$-\,2^{34}\cdot 41\cdot 131\cdot 149\cdot 2536801\cdot 13\!\cdots\!49$	$6$	$65.1969780561$			not computed	$S_{34}$ (as 34T115)	trivial	$2$	$16$	$380534576916766400$
34.2.527...048.1	x^34 - 4x - 4	$34$	[2,16]	$2^{34}\cdot 1459\cdot 2074583276749091\cdot 12353611446652867\cdot 82056584977043939$	$5$	$65.3657718729$			not computed	$S_{34}$ (as 34T115)	trivial	$2$	$17$	$398929487841893600$
34.0.987...920.1	x^34 - 2x + 2	$34$	[0,17]	$-\,2^{34}\cdot 5\cdot 4463\cdot 4597\cdot 1786284823\cdot 13682879113045277\cdot 2293023653476192171$	$7$	$66.5842345064$			✓	$S_{34}$ (as 34T115)	trivial	$2$	$16$	$659225846999345700$
34.0.100...799.1	x^34 - x + 2	$34$	[0,17]	$-\,13\cdot 1061\cdot 192313073533859878065118129\cdot 38\!\cdots\!67$	$4$	$66.6277410694$			✓	$S_{34}$ (as 34T115)	trivial	$2$	$16$	$606779702973969700$
34.0.100...312.1	x^34 + 2	$34$	[0,17]	$-\,2^{67}\cdot 17^{34}$	$2$	$66.6277410694$			✓	$C_{17}:(C_2\times C_{16})$ (as 34T9)	trivial	$2$	$16$	$585226461963806300$
34.2.100...312.1	x^34 - 2	$34$	[2,16]	$2^{67}\cdot 17^{34}$	$2$	$66.6277410694$			✓	$C_{17}:(C_2\times C_{16})$ (as 34T9)	trivial	$2$	$17$	$504347647410496830$
34.2.103...704.1	x^34 - 2x - 2	$34$	[2,16]	$2^{34}\cdot 371237\cdot 768749632105135909\cdot 21050019716166134869652117257$	$4$	$66.6703298768$			✓	$S_{34}$ (as 34T115)	trivial	$2$	$17$	$612915422175067900$
34.2.796...125.1	x^34 - 5	$34$	[2,16]	$5^{33}\cdot 17^{34}$	$2$	$81.0701514633$			not computed	$C_{17}:(C_2\times C_{16})$ (as 34T9)	trivial	$2$	$17$	$10116155297585506000$
34.2.215...361.1	x^34 - 3x + 1	$34$	[2,16]	$197\cdot 10\!\cdots\!13$	$2$	$89.3249989759$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.215...433.1	x^34 - 3x - 1	$34$	[2,16]	$244429\cdot 1673257207\cdot 38358820791399678810111461\cdot 137246726042042407050370751$	$4$	$89.3249989759$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.215...209.1	x^34 - 3x - 2	$34$	[2,16]	$313\cdot 4493\cdot 100109\cdot 401951069061523\cdot 38\!\cdots\!43$	$5$	$89.325122194$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.0.265...823.1	x^34 - x^33 + 2x^32 + 64x^31 - 57x^30 + 107x^29 + 1603x^28 - 1261x^27 + 2206x^26 + 20286x^25 - 13891x^24 + 22349x^23 + 140429x^22 - 82189x^21 + 120996x^20 + 538574x^19 - 264119x^18 + 327327x^17 + 1143572x^16 - 499882x^15 + 128724x^14 + 1425880x^13 - 737516x^12 - 1133952x^11 + 1294431x^10 - 1061173x^9 - 1305757x^8 + 907693x^7 - 16051x^6 - 713165x^5 + 590348x^4 + 474529x^3 + 129602x^2 - 93135x + 56857	$34$	[0,17]	$-\,103^{33}$	$1$	$89.8744260341$	✓	✓	not computed	$C_{34}$ (as 34T1)	$[5105]$	$2$	$16$	$2016418740785133.8$
34.2.270...689.1	x^34 - 3x - 3	$34$	[2,16]	$3^{33}\cdot 37\cdot 59\cdot 1637\cdot 14076649\cdot 88307993\cdot 109350036125618252414991335369$	$7$	$89.9218750763$			not computed	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.0.632...431.1	x^34 - 3x + 3	$34$	[0,17]	$-\,3^{33}\cdot 271\cdot 41\!\cdots\!07$	$3$	$98.6595836685$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$16$	$$
34.0.653...936.1	x^34 - 2x + 3	$34$	[0,17]	$-\,2^{35}\cdot 3^{33}\cdot 269\cdot 2747421509655671\cdot 462973083335522483486401$	$5$	$98.7568418708$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$16$	$$
34.0.653...815.1	x^34 - x + 3	$34$	[0,17]	$-\,3^{33}\cdot 5\cdot 7\cdot 89\cdot 97\cdot 397\cdot 98\!\cdots\!83$	$7$	$98.7568419694$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$16$	$$
34.2.653...328.1	x^34 - 3	$34$	[2,16]	$2^{34}\cdot 3^{33}\cdot 17^{34}$	$3$	$98.7568419694$			✓	$C_{17}:(C_2\times C_{16})$ (as 34T9)	trivial	$2$	$17$	$520979448668698900000$
34.2.653...841.1	x^34 - x - 3	$34$	[2,16]	$3^{34}\cdot 1607\cdot 11167313250696079\cdot 21\!\cdots\!13$	$4$	$98.7568419694$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.34.324...297.1	x^34 - x^33 - 66x^32 + 61x^31 + 1891x^30 - 1607x^29 - 31023x^28 + 24095x^27 + 323844x^26 - 228291x^25 - 2262360x^24 + 1435905x^23 + 10839684x^22 - 6136823x^21 - 35945371x^20 + 17958849x^19 + 82324817x^18 - 35828109x^17 - 128721615x^16 + 47931532x^15 + 134553261x^14 - 41728477x^13 - 91025976x^12 + 22664245x^11 + 37938129x^10 - 7334043x^9 - 9042178x^8 + 1347387x^7 + 1118049x^6 - 116296x^5 - 61867x^4 + 1806x^3 + 1328x^2 + 77x + 1	$34$	[34,0]	$137^{33}$	$1$	$118.542981096$		✓	not computed	$C_{34}$ (as 34T1)	trivial	$2$	$33$	$5641198150779374000000000$
34.2.381...816.1	x^34 - 4x + 2	$34$	[2,16]	$2^{67}\cdot 19\cdot 211\cdot 63823\cdot 963227\cdot 10\!\cdots\!73$	$6$	$119.099998625$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.381...592.1	x^34 - 4x + 1	$34$	[2,16]	$2^{34}\cdot 40031\cdot 890177\cdot 992441\cdot 3833841872344077247\cdot 16359429946447811440468087$	$6$	$119.099998635$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.381...440.1	x^34 - 4x - 2	$34$	[2,16]	$2^{67}\cdot 5\cdot 109\cdot 10313\cdot 16961790757\cdot 27\!\cdots\!59$	$6$	$119.099998644$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.381...456.1	x^34 - 4x - 3	$34$	[2,16]	$2^{34}\cdot 3^{34}\cdot 47\cdot 181\cdot 6659\cdot 23\!\cdots\!47$	$6$	$119.106001471$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.0.216...328.1	x^34 - 2x + 4	$34$	[0,17]	$-\,2^{32}\cdot 50\!\cdots\!43$	$2$	$125.349791168$			not computed	$S_{34}$ (as 34T115)	not computed	$2$	$16$	$$
34.2.216...024.1	x^34 - 2x - 4	$34$	[2,16]	$2^{32}\cdot 29\cdot 719\cdot 9021071\cdot 501803421221301371189\cdot 534963847310065662766809302401$	$6$	$125.349791168$			not computed	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.0.867...191.1	x^34 - x + 4	$34$	[0,17]	$-\,463\cdot 14791637311627073\cdot 19252730983707458016119\cdot 65\!\cdots\!11$	$4$	$130.566349412$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$16$	$$
34.2.867...217.1	x^34 - x - 4	$34$	[2,16]	$7\cdot 59\cdot 71\cdot 29\!\cdots\!79$	$4$	$130.566349412$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.0.332...283.1	x^34 - x^33 + 49x^32 - 162x^31 + 1646x^30 - 6093x^29 + 37764x^28 - 140505x^27 + 642029x^26 - 2158868x^25 + 7867204x^24 - 23451724x^23 + 70989641x^22 - 182710441x^21 + 459461291x^20 - 1006591547x^19 + 2135502310x^18 - 4017190895x^17 + 7274499825x^16 - 11714663796x^15 + 18043531688x^14 - 24702818067x^13 + 32221074210x^12 - 36915149197x^11 + 39648896356x^10 - 36487346558x^9 + 31372407145x^8 - 23064375767x^7 + 16052201854x^6 - 9172737675x^5 + 4518648355x^4 - 1618857168x^3 + 448908855x^2 - 73089631x + 8048569	$34$	[0,17]	$-\,3^{17}\cdot 103^{32}$	$2$	$135.829988016$	✓	✓	not computed	$C_{34}$ (as 34T1)	not computed	$6$	$16$	$$
34.2.835...033.1	x^34 - 5x + 3	$34$	[2,16]	$3^{31}\cdot 2879\cdot 451547\cdot 77705103841531489\cdot 13\!\cdots\!27$	$5$	$139.558342322$			not computed	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.751...313.1	x^34 - 5x + 2	$34$	[2,16]	$540448112458718370989\cdot 1120554565382189936398951\cdot 124094676051448783765146935867$	$3$	$148.874998293$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.751...161.1	x^34 - 5x - 1	$34$	[2,16]	$37\cdot 31751\cdot 416341358907437\cdot 15\!\cdots\!19$	$4$	$148.874998293$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.751...937.1	x^34 - 5x - 2	$34$	[2,16]	$13\cdot 53\cdot 5007441207247\cdot 21\!\cdots\!39$	$4$	$148.874998293$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.751...953.1	x^34 - 5x - 3	$34$	[2,16]	$3^{34}\cdot 71\cdot 6977\cdot 16831387\cdot 233804957\cdot 551519538743363\cdot 4191372752126305286083$	$7$	$148.875002101$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.760...329.1	x^34 - 5x - 4	$34$	[2,16]	$41\cdot 35376678400421\cdot 24812344311226982363792027279\cdot 21\!\cdots\!91$	$4$	$148.925260818$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.34.342...149.1	x^34 - x^33 - 101x^32 - 39x^31 + 4475x^30 + 7317x^29 - 107886x^28 - 308922x^27 + 1428035x^26 + 6473545x^25 - 8038724x^24 - 76649821x^23 - 34999669x^22 + 511384499x^21 + 872682200x^20 - 1610027003x^19 - 5837837426x^18 - 597495179x^17 + 18112177824x^16 + 20594193249x^15 - 20555590855x^14 - 57678181587x^13 - 18084925848x^12 + 57474448334x^11 + 58215655753x^10 - 9898232087x^9 - 42024711035x^8 - 14514531077x^7 + 10323419848x^6 + 7567081746x^5 - 122533277x^4 - 1123034742x^3 - 160716846x^2 + 51273995x + 10497967	$34$	[34,0]	$3^{17}\cdot 103^{33}$	$2$	$155.667072192$		✓	not computed	$C_{34}$ (as 34T1)	not computed	$2$	$33$	$$
34.0.442...344.1	x^34 + 97x^32 + 4040x^30 + 96737x^28 + 1499007x^26 + 15996211x^24 + 121823703x^22 + 675554879x^20 + 2752450407x^18 + 8237696660x^16 + 17941689717x^14 + 27884282812x^12 + 29930432911x^10 + 21101216892x^8 + 9069664015x^6 + 2134903778x^4 + 234085541x^2 + 8048569	$34$	[0,17]	$-\,2^{34}\cdot 103^{32}$	$2$	$156.842960291$	✓	✓	not computed	$C_{34}$ (as 34T1)	not computed	$4$	$16$	$$
34.0.129...375.1	x^34 - 5x + 5	$34$	[0,17]	$-\,5^{33}\cdot 619\cdot 38671351\cdot 12202943359261453\cdot 38037505283446249225037203$	$5$	$161.871209035$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$16$	$$
34.0.136...872.1	x^34 - 4x + 5	$34$	[0,17]	$-\,2^{34}\cdot 547\cdot 14\!\cdots\!39$	$3$	$162.140170149$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$16$	$$
34.0.136...103.1	x^34 - 3x + 5	$34$	[0,17]	$-\,373\cdot 36\!\cdots\!11$	$2$	$162.140302919$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$16$	$$
34.0.136...000.1	x^34 + 5	$34$	[0,17]	$-\,2^{34}\cdot 5^{33}\cdot 17^{34}$	$3$	$162.140302927$			✓	$C_{17}:(C_2\times C_{16})$ (as 34T9)	not computed	$2$	$16$	$$
34.2.136...513.1	x^34 - x - 5	$34$	[2,16]	$176357\cdot 77\!\cdots\!09$	$2$	$162.140302927$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.136...392.1	x^34 - 2x - 5	$34$	[2,16]	$2^{35}\cdot 149309\cdot 2514616468092439\cdot 10\!\cdots\!69$	$4$	$162.140302927$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.136...897.1	x^34 - 3x - 5	$34$	[2,16]	$79\cdot 49002700382722932199\cdot 35\!\cdots\!57$	$3$	$162.140302934$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$
34.2.144...625.1	x^34 - 5x - 5	$34$	[2,16]	$5^{33}\cdot 13\cdot 2464393\cdot 725338571\cdot 53\!\cdots\!59$	$5$	$162.395420901$			✓	$S_{34}$ (as 34T115)	not computed	$2$	$17$	$$