| 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 |
| 34.0.116...023.1 |
$x^{34} - x + 1$ |
$34$ |
[0,17] |
$-\,83\cdot 1291\cdot 12973\cdot 4134484433\cdot 64200532307\cdot 31512487292285521887257$ |
$6$ |
$33.9889591634$ |
$1.0783101995845562e+26$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
trivial |
$2$ |
$16$ |
$1946991838336.107$ |
| 34.2.118...049.1 |
$x^{34} - x - 1$ |
$34$ |
[2,16] |
$7\cdot 191\cdot 607\cdot 14\!\cdots\!11$ |
$4$ |
$34.0109237751$ |
$1.0902178197707272e+26$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
trivial |
$2$ |
$17$ |
$2995765078540.3994$ |
| 34.0.770...296.1 |
$x^{34} - 2 x^{17} + 2$ |
$34$ |
[0,17] |
$-\,2^{50}\cdot 17^{34}$ |
$2$ |
$47.1129275253$ |
$55.08022815278142$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$4$ |
$16$ |
$2332460652781060.5$ |
| 34.0.380...067.1 |
$x^{34} - 3 x^{17} + 3$ |
$34$ |
[0,17] |
$-\,3^{33}\cdot 17^{34}$ |
$2$ |
$49.3784209847$ |
$57.728840819705006$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$6$ |
$16$ |
$6031882093114950.0$ |
| 34.2.221...721.1 |
$x^{34} - 4 x - 1$ |
$34$ |
[2,16] |
$151163\cdot 3136253\cdot 9671606647\cdot 432210572699\cdot 6906809950567\cdot 162051016270589$ |
$6$ |
$59.5499993173$ |
$1.4893265589012807e+30$ |
|
|
? |
$S_{34}$ (as 34T115) |
trivial |
$2$ |
$17$ |
$45896286039491820$ |
| 34.2.221...928.1 |
$x^{34} - 2 x - 1$ |
$34$ |
[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 |
$x^{34} - 4 x + 4$ |
$34$ |
[0,17] |
$-\,2^{34}\cdot 41\cdot 131\cdot 149\cdot 2536801\cdot 13\!\cdots\!49$ |
$6$ |
$65.1969780561$ |
|
|
|
? |
$S_{34}$ (as 34T115) |
trivial |
$2$ |
$16$ |
$380534576916766400$ |
| 34.2.527...048.1 |
$x^{34} - 4 x - 4$ |
$34$ |
[2,16] |
$2^{34}\cdot 1459\cdot 2074583276749091\cdot 12353611446652867\cdot 82056584977043939$ |
$5$ |
$65.3657718729$ |
|
|
|
? |
$S_{34}$ (as 34T115) |
trivial |
$2$ |
$17$ |
$398929487841893600$ |
| 34.0.987...920.1 |
$x^{34} - 2 x + 2$ |
$34$ |
[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] |
$-\,13\cdot 1061\cdot 192313073533859878065118129\cdot 38\!\cdots\!67$ |
$4$ |
$66.6277410694$ |
$1.0049316355790068e+31$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
trivial |
$2$ |
$16$ |
$606779702973969700$ |
| 34.0.100...312.1 |
$x^{34} + 2$ |
$34$ |
[0,17] |
$-\,2^{67}\cdot 17^{34}$ |
$2$ |
$66.6277410694$ |
$77.89520567226786$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$2$ |
$16$ |
$585226461963806300$ |
| 34.2.100...312.1 |
$x^{34} - 2$ |
$34$ |
[2,16] |
$2^{67}\cdot 17^{34}$ |
$2$ |
$66.6277410694$ |
$77.89520567226786$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$2$ |
$17$ |
$504347647410496830$ |
| 34.2.103...704.1 |
$x^{34} - 2 x - 2$ |
$34$ |
[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] |
$5^{33}\cdot 17^{34}$ |
$2$ |
$81.0701514633$ |
$94.77998234304803$ |
|
|
? |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$2$ |
$17$ |
$10116155297585506000$ |
| 34.2.215...361.1 |
$x^{34} - 3 x + 1$ |
$34$ |
[2,16] |
$197\cdot 10\!\cdots\!13$ |
$2$ |
$89.3249989759$ |
$1.467375752080841e+33$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.2.215...433.1 |
$x^{34} - 3 x - 1$ |
$34$ |
[2,16] |
$244429\cdot 1673257207\cdot 38358820791399678810111461\cdot 137246726042042407050370751$ |
$4$ |
$89.3249989759$ |
$1.467375752080849e+33$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.2.215...209.1 |
$x^{34} - 3 x - 2$ |
$34$ |
[2,16] |
$313\cdot 4493\cdot 100109\cdot 401951069061523\cdot 38\!\cdots\!43$ |
$5$ |
$89.325122194$ |
$1.4674101630266993e+33$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.0.265...823.1 |
$x^{34} - x^{33} + 2 x^{32} + 64 x^{31} - 57 x^{30} + 107 x^{29} + 1603 x^{28} - 1261 x^{27} + 2206 x^{26} + 20286 x^{25} - 13891 x^{24} + 22349 x^{23} + 140429 x^{22} - 82189 x^{21} + 120996 x^{20} + 538574 x^{19} - 264119 x^{18} + 327327 x^{17} + 1143572 x^{16} - 499882 x^{15} + 128724 x^{14} + 1425880 x^{13} - 737516 x^{12} - 1133952 x^{11} + 1294431 x^{10} - 1061173 x^{9} - 1305757 x^{8} + 907693 x^{7} - 16051 x^{6} - 713165 x^{5} + 590348 x^{4} + 474529 x^{3} + 129602 x^{2} - 93135 x + 56857$ |
$34$ |
[0,17] |
$-\,103^{33}$ |
$1$ |
$89.8744260341$ |
$89.87442603411633$ |
✓ |
✓ |
? |
$C_{34}$ (as 34T1) |
$[5105]$ |
$2$ |
$16$ |
$2016418740785133.8$ |
| 34.2.270...689.1 |
$x^{34} - 3 x - 3$ |
$34$ |
[2,16] |
$3^{33}\cdot 37\cdot 59\cdot 1637\cdot 14076649\cdot 88307993\cdot 109350036125618252414991335369$ |
$7$ |
$89.9218750763$ |
$6.401748342812544e+25$ |
|
|
? |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.0.632...431.1 |
$x^{34} - 3 x + 3$ |
$34$ |
[0,17] |
$-\,3^{33}\cdot 271\cdot 41\!\cdots\!07$ |
$3$ |
$98.6595836685$ |
$3.097100566074529e+26$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$16$ |
|
| 34.0.653...936.1 |
$x^{34} - 2 x + 3$ |
$34$ |
[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] |
$2^{34}\cdot 3^{33}\cdot 17^{34}$ |
$3$ |
$98.7568419694$ |
$115.45768163941001$ |
|
|
✓ |
$C_2\times F_{17}$ (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 |
$x^{34} - x^{33} - 66 x^{32} + 61 x^{31} + 1891 x^{30} - 1607 x^{29} - 31023 x^{28} + 24095 x^{27} + 323844 x^{26} - 228291 x^{25} - 2262360 x^{24} + 1435905 x^{23} + 10839684 x^{22} - 6136823 x^{21} - 35945371 x^{20} + 17958849 x^{19} + 82324817 x^{18} - 35828109 x^{17} - 128721615 x^{16} + 47931532 x^{15} + 134553261 x^{14} - 41728477 x^{13} - 91025976 x^{12} + 22664245 x^{11} + 37938129 x^{10} - 7334043 x^{9} - 9042178 x^{8} + 1347387 x^{7} + 1118049 x^{6} - 116296 x^{5} - 61867 x^{4} + 1806 x^{3} + 1328 x^{2} + 77 x + 1$ |
$34$ |
[34,0] |
$137^{33}$ |
$1$ |
$118.542981096$ |
$118.54298109569393$ |
|
✓ |
? |
$C_{34}$ (as 34T1) |
trivial |
$2$ |
$33$ |
$5641198150779374000000000$ |
| 34.2.381...816.1 |
$x^{34} - 4 x + 2$ |
$34$ |
[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 |
$x^{34} - 4 x + 1$ |
$34$ |
[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 |
$x^{34} - 4 x - 2$ |
$34$ |
[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 |
$x^{34} - 4 x - 3$ |
$34$ |
[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 |
$x^{34} - 2 x + 4$ |
$34$ |
[0,17] |
$-\,2^{32}\cdot 50\!\cdots\!43$ |
$2$ |
$125.349791168$ |
$1.391647984398307e+31$ |
|
|
? |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$16$ |
|
| 34.2.216...024.1 |
$x^{34} - 2 x - 4$ |
$34$ |
[2,16] |
$2^{32}\cdot 29\cdot 719\cdot 9021071\cdot 501803421221301371189\cdot 534963847310065662766809302401$ |
$6$ |
$125.349791168$ |
$1.3916479844018652e+31$ |
|
|
? |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.0.867...191.1 |
$x^{34} - x + 4$ |
$34$ |
[0,17] |
$-\,463\cdot 14791637311627073\cdot 19252730983707458016119\cdot 65\!\cdots\!11$ |
$4$ |
$130.566349412$ |
$9.313897337942945e+35$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$16$ |
|
| 34.2.867...217.1 |
$x^{34} - x - 4$ |
$34$ |
[2,16] |
$7\cdot 59\cdot 71\cdot 29\!\cdots\!79$ |
$4$ |
$130.566349412$ |
$9.313897337942945e+35$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.0.332...283.1 |
$x^{34} - x^{33} + 49 x^{32} - 162 x^{31} + 1646 x^{30} - 6093 x^{29} + 37764 x^{28} - 140505 x^{27} + 642029 x^{26} - 2158868 x^{25} + 7867204 x^{24} - 23451724 x^{23} + 70989641 x^{22} - 182710441 x^{21} + 459461291 x^{20} - 1006591547 x^{19} + 2135502310 x^{18} - 4017190895 x^{17} + 7274499825 x^{16} - 11714663796 x^{15} + 18043531688 x^{14} - 24702818067 x^{13} + 32221074210 x^{12} - 36915149197 x^{11} + 39648896356 x^{10} - 36487346558 x^{9} + 31372407145 x^{8} - 23064375767 x^{7} + 16052201854 x^{6} - 9172737675 x^{5} + 4518648355 x^{4} - 1618857168 x^{3} + 448908855 x^{2} - 73089631 x + 8048569$ |
$34$ |
[0,17] |
$-\,3^{17}\cdot 103^{32}$ |
$2$ |
$135.829988016$ |
$135.82998801634537$ |
✓ |
✓ |
? |
$C_{34}$ (as 34T1) |
not computed |
$6$ |
$16$ |
|
| 34.2.835...033.1 |
$x^{34} - 5 x + 3$ |
$34$ |
[2,16] |
$3^{31}\cdot 2879\cdot 451547\cdot 77705103841531489\cdot 13\!\cdots\!27$ |
$5$ |
$139.558342322$ |
$5.9601979834645525e+29$ |
|
|
? |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.2.751...313.1 |
$x^{34} - 5 x + 2$ |
$34$ |
[2,16] |
$540448112458718370989\cdot 1120554565382189936398951\cdot 124094676051448783765146935867$ |
$3$ |
$148.874998293$ |
$8.669021532988875e+36$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.2.751...161.1 |
$x^{34} - 5 x - 1$ |
$34$ |
[2,16] |
$37\cdot 31751\cdot 416341358907437\cdot 15\!\cdots\!19$ |
$4$ |
$148.874998293$ |
$8.669021532994699e+36$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.2.751...937.1 |
$x^{34} - 5 x - 2$ |
$34$ |
[2,16] |
$13\cdot 53\cdot 5007441207247\cdot 21\!\cdots\!39$ |
$4$ |
$148.874998293$ |
$8.669021533000524e+36$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.2.751...953.1 |
$x^{34} - 5 x - 3$ |
$34$ |
[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 |
$x^{34} - 5 x - 4$ |
$34$ |
[2,16] |
$41\cdot 35376678400421\cdot 24812344311226982363792027279\cdot 21\!\cdots\!91$ |
$4$ |
$148.925260818$ |
$8.718911696751103e+36$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.34.342...149.1 |
$x^{34} - x^{33} - 101 x^{32} - 39 x^{31} + 4475 x^{30} + 7317 x^{29} - 107886 x^{28} - 308922 x^{27} + 1428035 x^{26} + 6473545 x^{25} - 8038724 x^{24} - 76649821 x^{23} - 34999669 x^{22} + 511384499 x^{21} + 872682200 x^{20} - 1610027003 x^{19} - 5837837426 x^{18} - 597495179 x^{17} + 18112177824 x^{16} + 20594193249 x^{15} - 20555590855 x^{14} - 57678181587 x^{13} - 18084925848 x^{12} + 57474448334 x^{11} + 58215655753 x^{10} - 9898232087 x^{9} - 42024711035 x^{8} - 14514531077 x^{7} + 10323419848 x^{6} + 7567081746 x^{5} - 122533277 x^{4} - 1123034742 x^{3} - 160716846 x^{2} + 51273995 x + 10497967$ |
$34$ |
[34,0] |
$3^{17}\cdot 103^{33}$ |
$2$ |
$155.667072192$ |
$155.6670721921805$ |
|
✓ |
? |
$C_{34}$ (as 34T1) |
not computed |
$2$ |
$33$ |
|
| 34.0.442...344.1 |
$x^{34} + 97 x^{32} + 4040 x^{30} + 96737 x^{28} + 1499007 x^{26} + 15996211 x^{24} + 121823703 x^{22} + 675554879 x^{20} + 2752450407 x^{18} + 8237696660 x^{16} + 17941689717 x^{14} + 27884282812 x^{12} + 29930432911 x^{10} + 21101216892 x^{8} + 9069664015 x^{6} + 2134903778 x^{4} + 234085541 x^{2} + 8048569$ |
$34$ |
[0,17] |
$-\,2^{34}\cdot 103^{32}$ |
$2$ |
$156.842960291$ |
$156.8429602905213$ |
✓ |
✓ |
? |
$C_{34}$ (as 34T1) |
not computed |
$4$ |
$16$ |
|
| 34.0.129...375.1 |
$x^{34} - 5 x + 5$ |
$34$ |
[0,17] |
$-\,5^{33}\cdot 619\cdot 38671351\cdot 12202943359261453\cdot 38037505283446249225037203$ |
$5$ |
$161.871209035$ |
$5.026785693927254e+26$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$16$ |
|
| 34.0.136...872.1 |
$x^{34} - 4 x + 5$ |
$34$ |
[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 |
$x^{34} - 3 x + 5$ |
$34$ |
[0,17] |
$-\,373\cdot 36\!\cdots\!11$ |
$2$ |
$162.140302919$ |
$3.6995309156950676e+37$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$16$ |
|
| 34.0.136...000.1 |
$x^{34} + 5$ |
$34$ |
[0,17] |
$-\,2^{34}\cdot 5^{33}\cdot 17^{34}$ |
$3$ |
$162.140302927$ |
$189.55996468609607$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
not computed |
$2$ |
$16$ |
|
| 34.2.136...513.1 |
$x^{34} - x - 5$ |
$34$ |
[2,16] |
$176357\cdot 77\!\cdots\!09$ |
$2$ |
$162.140302927$ |
$3.6995309186051546e+37$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.2.136...392.1 |
$x^{34} - 2 x - 5$ |
$34$ |
[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 |
$x^{34} - 3 x - 5$ |
$34$ |
[2,16] |
$79\cdot 49002700382722932199\cdot 35\!\cdots\!57$ |
$3$ |
$162.140302934$ |
$3.699530921515242e+37$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
| 34.2.144...625.1 |
$x^{34} - 5 x - 5$ |
$34$ |
[2,16] |
$5^{33}\cdot 13\cdot 2464393\cdot 725338571\cdot 53\!\cdots\!59$ |
$5$ |
$162.395420901$ |
$5.310815787005474e+26$ |
|
|
✓ |
$S_{34}$ (as 34T115) |
not computed |
$2$ |
$17$ |
|
