Number field search results

Results (1-50 of 218 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
17.1.133094720815439153.1	x^17 - 2x^16 + 7x^15 - 12x^14 + 22x^13 - 34x^12 + 46x^11 - 61x^10 + 65x^9 - 65x^8 + 53x^7 - 36x^6 + 20x^5 - 5x^4 - x^3 + 4x^2 - 2x + 1	$17$	[1,8]	$316968877\cdot 419898389$	$2$	$10.1695931395$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$23.323533439$
17.1.231494845017984433.1	x^17 - x^16 + 2x^13 + x^12 - 5x^11 + x^10 + 3x^9 + 3x^8 - x^7 - 7x^6 + 2x^5 + 6x^4 + x^3 - 3x^2 - 3x - 1	$17$	[1,8]	$59^{2}\cdot 1217\cdot 1579\cdot 34607051$	$4$	$10.5061502476$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$32.0498639783$
17.3.158...023.1	x^17 - x^15 - x^14 - 5x^13 + 4x^12 + x^11 + 15x^9 - 13x^8 - 2x^7 + 7x^6 - 18x^5 + 20x^4 - 10x^3 + 6x^2 - 4x + 1	$17$	[3,7]	$-\,2131\cdot 546781\cdot 1361451193$	$3$	$11.7655356049$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$130.579387289$
17.3.191...491.1	x^17 - 3x^16 + 4x^15 - 3x^14 + x^13 + 4x^12 - 8x^11 + 9x^10 - 2x^9 - 9x^8 + 12x^7 - x^6 - 4x^5 + 2x^4 - 3x^3 + x^2 - x - 1	$17$	[3,7]	$-\,227\cdot 2411\cdot 3533\cdot 988994191$	$4$	$11.895587848$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$144.902374432$
17.3.215...383.1	x^17 - 2x^15 - 4x^14 + 4x^13 + 7x^12 - 3x^11 - 3x^10 - 3x^9 + 5x^8 - 5x^7 - 4x^6 + 14x^5 - 2x^4 - 7x^3 + 2x + 1	$17$	[3,7]	$-\,37^{5}\cdot 433\cdot 5531\cdot 12953$	$4$	$11.978222741$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$154.682742806$
17.3.231...203.1	x^17 - x^16 + x^15 - 3x^14 + 4x^13 - 4x^12 - x^11 + 4x^10 - 5x^9 + 17x^8 - 42x^7 + 59x^6 - 45x^5 + 9x^4 + 15x^3 - 15x^2 + 6x - 1	$17$	[3,7]	$-\,16843\cdot 137239279050521$	$2$	$12.0289934072$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$161.12597366$
17.3.275...423.1	x^17 - 3x^16 + 7x^15 - 10x^14 + 12x^13 - 11x^12 + 10x^11 - 7x^10 + 2x^9 + 5x^8 - 13x^7 + 11x^6 - 5x^5 - 6x^4 + 11x^3 - 9x^2 + 5x - 1	$17$	[3,7]	$-\,75653\cdot 3119681\cdot 11682611$	$3$	$12.1544104314$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$178.334436956$
17.5.362...901.1	x^17 - 5x^15 - x^14 + 5x^13 + 6x^12 + 9x^11 - 16x^10 - 21x^9 + 19x^8 + 13x^7 - 5x^6 - 4x^5 - 5x^4 + 3x^3 - x + 1	$17$	[5,6]	$55954279\cdot 64715583419$	$2$	$12.3508429254$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$10$	$284.067800863$
17.3.377...359.1	x^17 - 4x^16 + 12x^15 - 26x^14 + 48x^13 - 75x^12 + 105x^11 - 126x^10 + 136x^9 - 129x^8 + 107x^7 - 80x^6 + 47x^5 - 23x^4 + 11x^3 - 2x^2 - 2x + 1	$17$	[3,7]	$-\,137\cdot 1926157\cdot 14323744651$	$3$	$12.3820423069$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$206.585713852$
17.5.475...701.1	x^17 - 6x^15 - 2x^14 + 17x^13 + 13x^12 - 27x^11 - 34x^10 + 20x^9 + 47x^8 - 38x^6 - 13x^5 + 17x^4 + 12x^3 - 2x^2 - 3x - 1	$17$	[5,6]	$97\cdot 2927\cdot 2315407\cdot 7234597$	$4$	$12.5504977321$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$10$	$331.845168707$
17.5.145...793.1	x^17 - 2x^16 + 4x^15 - 2x^14 + 6x^12 - 5x^11 + x^10 + 3x^9 - 6x^8 - 7x^7 - x^6 - 5x^5 - 9x^4 - 3x^3 - 2x^2 - 3x - 1	$17$	[5,6]	$10170343\cdot 1427427651151$	$2$	$13.4020113891$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$10$	$621.862699097$
17.5.890...861.1	x^17 - 2x^16 - 5x^15 + 8x^14 + 14x^13 - 6x^12 - 34x^11 - 12x^10 + 42x^9 + 47x^8 - 33x^7 - 52x^6 + 13x^5 + 21x^4 + 3x^3 - 5x^2 - 2x + 1	$17$	[5,6]	$946391\cdot 3063653\cdot 30715207$	$3$	$14.9110980105$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$10$	$1603.54336024$
17.1.142...644.1	x^17 - 2x^16 - x^15 + 5x^14 - x^13 - 8x^12 + 6x^11 + 8x^10 - 11x^9 - 3x^8 + 13x^7 - 3x^6 - 8x^5 + 5x^4 + 3x^3 - 3x^2 + 1	$17$	[1,8]	$2^{2}\cdot 1697\cdot 20928611178427313$	$3$	$15.3263991543$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$1990.43257715$
17.1.463...841.1	x^17 - x^16 - x^15 - x^14 + x^12 + 13x^11 + 7x^10 + 11x^9 + 4x^8 + x^7 + 7x^6 + 23x^5 + 31x^4 + 42x^3 + 24x^2 + 6x - 1	$17$	[1,8]	$383^{8}$	$1$	$16.4294472544$			not computed	$D_{17}$ (as 17T2)	trivial	$2$	$8$	$2610.31631075$
17.1.808...561.1	x^17 - x - 1	$17$	[1,8]	$808793517812627212561$	$1$	$16.9774634294$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$3677.70492523$
17.1.103...032.1	x^17 - 2x^16 - x^15 + 5x^14 - x^13 - 8x^12 + 6x^11 + 8x^10 - 11x^9 - 3x^8 + 12x^7 - 3x^6 - 7x^5 + 5x^4 + 3x^3 - 3x^2 + 1	$17$	[1,8]	$2^{3}\cdot 3^{2}\cdot 373\cdot 38369969405192597$	$4$	$17.2210945759$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$7633.46863529$
17.3.207...144.1	x^17 - 2x^16 + x^15 + 2x^14 - 3x^13 + 3x^11 - 3x^10 - x^9 + 6x^8 - 5x^7 - 4x^6 + 8x^5 - 3x^4 - 4x^3 + 3x^2 - 1	$17$	[3,7]	$-\,2^{3}\cdot 17\cdot 20759\cdot 9318913\cdot 78851137$	$5$	$17.9447075771$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$12720.6080668$
17.3.855...476.1	x^17 - 3x^16 + 4x^15 + x^14 - 13x^13 + 26x^12 - 25x^11 + 2x^10 + 35x^9 - 62x^8 + 59x^7 - 25x^6 - 13x^5 + 33x^4 - 30x^3 + 17x^2 - 6x + 1	$17$	[3,7]	$-\,2^{2}\cdot 11\cdot 53\cdot 34759\cdot 105529138935877$	$5$	$19.5041730705$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$30334.8896134$
17.1.175...952.1	x^17 - 4x - 4	$17$	[1,8]	$2^{16}\cdot 63535033\cdot 4221738529$	$3$	$20.348317308$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$38635.7554956$
17.1.124...441.1	x^17 - 4x^16 + 6x^15 - 5x^14 + 7x^13 - 17x^12 + 24x^11 - 16x^10 + 42x^9 - 83x^8 + 82x^7 - 72x^6 + 37x^5 + 24x^4 - 10x^3 + 14x^2 - 2x + 1	$17$	[1,8]	$11^{8}\cdot 17^{12}$	$2$	$22.8359627415$			not computed	$C_{17}:C_{4}$ (as 17T3)	trivial	$2$	$8$	$83428.2679357$
17.1.239...153.1	x^17 - 34x^12 + 17x^11 + 85x^10 + 102x^9 - 170x^8 - 272x^7 - 68x^6 + 255x^5 + 255x^4 + 68x^3 + 17x^2 + 17x + 4	$17$	[1,8]	$17^{19}$	$1$	$23.7250763118$			not computed	$F_{17}$ (as 17T5)	trivial	$2$	$8$	$195995.113671$
17.1.604...088.1	x^17 - 2x^16 + 8x^13 + 16x^12 - 16x^11 + 64x^9 - 32x^8 - 80x^7 + 32x^6 + 40x^5 + 80x^4 + 16x^3 - 128x^2 - 2x + 68	$17$	[1,8]	$2^{79}$	$1$	$25.0555590588$			not computed	$F_{17}$ (as 17T5)	trivial	$2$	$8$	$600164.932841$
17.1.930...721.1	x^17 - x^16 + 4x^15 - 18x^14 + 11x^13 + 14x^12 + 21x^11 - 62x^10 + 14x^9 + 50x^8 + 54x^7 - 121x^6 - 7x^5 + 36x^4 + 64x^3 - 23x^2 + 43x + 1	$17$	[1,8]	$991^{8}$	$1$	$25.6990467175$				$D_{17}$ (as 17T2)	trivial	$2$	$8$	$323467.453718$
17.1.183...561.1	x^17 - x^16 + 5x^15 - 19x^14 + 26x^13 - 30x^12 + 44x^11 - 48x^10 + 39x^9 - 62x^8 + 30x^7 + 112x^6 - 4x^5 + 16x^4 - 62x^3 + 180x^2 + 35x + 49	$17$	[1,8]	$13^{8}\cdot 83^{8}$	$2$	$26.7487941926$			not computed	$D_{17}$ (as 17T2)	trivial	$2$	$8$	$257874.899874$
17.1.200...521.1	x^17 - 2x^16 + 4x^15 - 18x^14 + 10x^13 - 16x^12 + 44x^11 + 10x^10 + 72x^9 + 18x^8 + 134x^7 + 88x^6 + 275x^5 + 200x^4 + 220x^3 + 240x^2 + 80x + 64	$17$	[1,8]	$1091^{8}$	$1$	$26.8883769874$				$D_{17}$ (as 17T2)	trivial	$2$	$8$	$1757145.67579$
17.1.241...529.1	x^17 + 2x - 1	$17$	[1,8]	$71437\cdot 234281\cdot 144516666425357$	$3$	$27.1849244342$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$452764.206499$
17.1.656...064.1	x^17 + 4x - 4	$17$	[1,8]	$2^{16}\cdot 3\cdot 33371379191895369283$	$3$	$28.8285021943$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$745858.628066$
17.1.105...401.1	x^17 - 3x^16 - 2x^15 + 24x^14 - 20x^13 - 80x^12 + 115x^11 + 27x^10 + 132x^9 - 302x^8 - 219x^7 - 172x^6 + 41x^5 - 25x^4 + 44x^3 + 39x^2 - 2x - 23	$17$	[1,8]	$17^{8}\cdot 79^{8}$	$2$	$29.6507559794$			not computed	$D_{17}$ (as 17T2)	trivial	$2$	$8$	$663161.006215$
17.1.160...625.1	x^17 - 4x^16 + x^15 + 16x^14 - 30x^13 - 2x^12 + 88x^11 + 143x^10 + 133x^9 - 515x^8 - 803x^7 - 68x^6 + 1252x^5 + 2972x^4 + 2855x^3 + 1505x^2 + 550x + 125	$17$	[1,8]	$5^{8}\cdot 283^{8}$	$2$	$30.3884754664$				$D_{17}$ (as 17T2)	trivial	$2$	$8$	$2534195.05633$
17.1.348...321.1	x^17 - 2x^16 - 3x^14 + 24x^13 + 18x^12 - 138x^10 - 203x^9 - 75x^8 + 352x^7 + 588x^6 + 384x^5 + 132x^4 + 493x^3 + 1015x^2 + 874x + 337	$17$	[1,8]	$1559^{8}$	$1$	$31.8064953944$			not computed	$D_{17}$ (as 17T2)	trivial	$2$	$8$	$432952.23952$
17.1.371...761.1	x^17 - x^16 + 5x^15 + 9x^14 - 13x^13 + 17x^12 + 56x^11 - 62x^10 + 55x^9 - 535x^8 + 181x^7 - 1027x^6 + 661x^5 - 1041x^4 + 166x^3 - 416x^2 - 88x - 16	$17$	[1,8]	$1571^{8}$	$1$	$31.921472057$				$D_{17}$ (as 17T2)	trivial	$2$	$8$	$8867681.2165$
17.5.374...388.1	x^17 - x^16 - 4x^15 + 4x^14 + 6x^13 - 6x^12 - 8x^11 + 8x^10 + 9x^9 - 7x^8 - 9x^7 + 3x^6 + 9x^5 - 2x^4 - 6x^3 + 4x^2 + 2x - 1	$17$	[5,6]	$2^{2}\cdot 9368869340728638677625097$	$2$	$31.9402321982$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$10$	$3367432.32884$
17.1.445...464.1	x^17 - 4x^9 - 18x^6 - 12x^3 + 4x - 2	$17$	[1,8]	$2^{16}\cdot 3\cdot 271\cdot 835997920414096373$	$4$	$32.2664740609$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$1877308.99113$
17.5.478...988.1	x^17 - 2x^16 - 2x^15 + 9x^14 - 8x^13 - 6x^12 + 22x^11 - 20x^10 - 4x^9 + 23x^8 - 20x^7 + 7x^6 + x^5 - 11x^4 + 11x^3 - x^2 - 3x + 1	$17$	[5,6]	$2^{2}\cdot 71\cdot 113\cdot 398023\cdot 3743302227733793$	$5$	$32.4012931788$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$10$	$4697339.96204$
17.1.517...520.1	x^17 - 2x - 2	$17$	[1,8]	$2^{16}\cdot 3\cdot 5\cdot 379\cdot 139023179197698797$	$5$	$32.5541036629$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$2311817.81868$
17.1.542...256.1	x^17 - x - 2	$17$	[1,8]	$2^{16}\cdot 2387563\cdot 346478807223667$	$3$	$32.6415866997$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$3196176.23159$
17.1.542...216.1	x^17 - x - 4	$17$	[1,8]	$2^{16}\cdot 67\cdot 12346869580328982043$	$3$	$32.6415873531$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$1828919.01859$
17.1.542...872.1	x^17 - 2	$17$	[1,8]	$2^{16}\cdot 17^{17}$	$2$	$32.6415873531$			✓	$F_{17}$ (as 17T5)	trivial	$2$	$8$	$2966240.41128$
17.1.566...224.1	x^17 + 2x - 2	$17$	[1,8]	$2^{16}\cdot 23\cdot 37\cdot 67\cdot 15155721101316377$	$5$	$32.7254732116$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$1744681.36197$
17.1.584...121.1	x^17 - 2x^16 + 9x^15 - 23x^14 + 59x^13 - 112x^12 + 156x^11 - 49x^10 + 221x^9 - 25x^8 - 162x^7 - 4x^6 + 553x^5 + 1435x^4 + 1716x^3 + 1462x^2 + 615x + 225	$17$	[1,8]	$1663^{8}$	$1$	$32.7879300307$				$D_{17}$ (as 17T2)	trivial	$2$	$8$	$3798575.81941$
17.1.638...280.1	x^17 + 4x^9 - 18x^6 + 12x^3 + 4x - 2	$17$	[1,8]	$2^{16}\cdot 5\cdot 7\cdot 27851834699314662203$	$4$	$32.9583006276$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$2034427.1525$
17.1.922...049.1	x^17 - 34x^14 - 68x^13 + 17x^12 + 323x^11 + 884x^10 + 1241x^9 + 1394x^8 + 1003x^7 + 935x^6 + 663x^5 + 901x^4 + 578x^3 + 493x^2 + 136x + 57	$17$	[1,8]	$3^{8}\cdot 17^{18}$	$2$	$33.6787464993$				$C_{17}:C_{8}$ (as 17T4)	trivial	$2$	$8$	$4992205.48619$
17.1.102...241.1	x^17 - 7x^16 + 30x^15 - 61x^14 + 115x^13 - 158x^12 + 94x^11 - 111x^10 + 268x^9 - 411x^8 + 465x^7 - 473x^6 + 314x^5 - 109x^4 + 446x^3 - 498x^2 + 175x + 1	$17$	[1,8]	$1783^{8}$	$1$	$33.8807935119$				$D_{17}$ (as 17T2)	trivial	$2$	$8$	$4818947.77807$
17.1.133...504.1	x^17 - 3x^16 - 4x^14 + 12x^13 + 24x^12 + 12x^11 - 28x^10 - 90x^9 - 74x^8 + 116x^6 + 132x^5 + 72x^4 + 28x^3 + 12x^2 + 5x + 1	$17$	[1,8]	$2^{30}\cdot 137^{8}$	$2$	$34.4147774247$			not computed	$\PSL(2,16)$ (as 17T6)	$[15]$	$2$	$8$	$810656.541895$
17.1.323...625.1	x^17 + 17x^15 + 119x^13 + 442x^11 + 935x^9 + 1122x^7 + 714x^5 + 204x^3 + 17x - 1	$17$	[1,8]	$5^{8}\cdot 17^{17}$	$2$	$36.2556739236$			✓	$F_{17}$ (as 17T5)	trivial	$2$	$8$	$7413165.64743$
17.1.861...144.1	x^17 - x^16 - 4x^15 + 2x^14 + 54x^13 - 6x^12 - 36x^11 + 16x^10 + 714x^9 + 1238x^8 + 484x^7 - 764x^6 - 1084x^5 + 520x^4 + 668x^3 - 776x^2 + 382x - 74	$17$	[1,8]	$2^{30}\cdot 173^{8}$	$2$	$38.408519781$			not computed	$\PSL(2,16)$ (as 17T6)	$[15]$	$2$	$8$	$781146.759847$
17.1.151...681.1	x^17 + 3x - 3	$17$	[1,8]	$3^{16}\cdot 35388253\cdot 997597133837$	$3$	$39.712454379$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$10106858.0011$
17.13.223...557.1	x^17 - x^16 - 17x^15 + 17x^14 + 112x^13 - 115x^12 - 356x^11 + 389x^10 + 547x^9 - 675x^8 - 342x^7 + 560x^6 + 27x^5 - 205x^4 + 42x^3 + 24x^2 - 10x + 1	$17$	[13,2]	$3^{3}\cdot 205542871\cdot 402308340646912121$	$3$	$40.6213567441$			not computed	$S_{17}$ (as 17T10)	trivial	$2$	$14$	$129255854.893$
17.3.238...231.1	x^17 - 3x - 1	$17$	[3,7]	$-\,17987\cdot 132440913396223585034213$	$2$	$40.7765652895$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$21794558.2023$
17.1.238...585.1	x^17 + 3x - 1	$17$	[1,8]	$5\cdot 90341351171\cdot 5273811677288927$	$3$	$40.7765669554$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$8$	$12577950.5849$