| 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 |
| 17.5.362...901.1 |
$x^{17} - 5 x^{15} - x^{14} + 5 x^{13} + 6 x^{12} + 9 x^{11} - 16 x^{10} - 21 x^{9} + 19 x^{8} + 13 x^{7} - 5 x^{6} - 4 x^{5} - 5 x^{4} + 3 x^{3} - x + 1$ |
$17$ |
[5,6] |
$55954279\cdot 64715583419$ |
$2$ |
$12.3508429254$ |
$1902922439.3743691$ |
|
|
? |
$S_{17}$ (as 17T10) |
trivial |
$2$ |
$10$ |
$284.067800863$ |
| 17.5.475...701.1 |
$x^{17} - 6 x^{15} - 2 x^{14} + 17 x^{13} + 13 x^{12} - 27 x^{11} - 34 x^{10} + 20 x^{9} + 47 x^{8} - 38 x^{6} - 13 x^{5} + 17 x^{4} + 12 x^{3} - 2 x^{2} - 3 x - 1$ |
$17$ |
[5,6] |
$97\cdot 2927\cdot 2315407\cdot 7234597$ |
$4$ |
$12.5504977321$ |
$2180811211.971046$ |
|
|
? |
$S_{17}$ (as 17T10) |
trivial |
$2$ |
$10$ |
$331.845168707$ |
| 17.5.145...793.1 |
$x^{17} - 2 x^{16} + 4 x^{15} - 2 x^{14} + 6 x^{12} - 5 x^{11} + x^{10} + 3 x^{9} - 6 x^{8} - 7 x^{7} - x^{6} - 5 x^{5} - 9 x^{4} - 3 x^{3} - 2 x^{2} - 3 x - 1$ |
$17$ |
[5,6] |
$10170343\cdot 1427427651151$ |
$2$ |
$13.4020113891$ |
$3810174381.821653$ |
|
|
? |
$S_{17}$ (as 17T10) |
trivial |
$2$ |
$10$ |
$621.862699097$ |
| 17.5.890...861.1 |
$x^{17} - 2 x^{16} - 5 x^{15} + 8 x^{14} + 14 x^{13} - 6 x^{12} - 34 x^{11} - 12 x^{10} + 42 x^{9} + 47 x^{8} - 33 x^{7} - 52 x^{6} + 13 x^{5} + 21 x^{4} + 3 x^{3} - 5 x^{2} - 2 x + 1$ |
$17$ |
[5,6] |
$946391\cdot 3063653\cdot 30715207$ |
$3$ |
$14.9110980105$ |
$9436953412.576094$ |
|
|
? |
$S_{17}$ (as 17T10) |
trivial |
$2$ |
$10$ |
$1603.54336024$ |
| 17.5.374...388.1 |
$x^{17} - x^{16} - 4 x^{15} + 4 x^{14} + 6 x^{13} - 6 x^{12} - 8 x^{11} + 8 x^{10} + 9 x^{9} - 7 x^{8} - 9 x^{7} + 3 x^{6} + 9 x^{5} - 2 x^{4} - 6 x^{3} + 4 x^{2} + 2 x - 1$ |
$17$ |
[5,6] |
$2^{2}\cdot 9368869340728638677625097$ |
$2$ |
$31.9402321982$ |
$4858813784474.296$ |
|
|
? |
$S_{17}$ (as 17T10) |
trivial |
$2$ |
$10$ |
$3367432.32884$ |
| 17.5.478...988.1 |
$x^{17} - 2 x^{16} - 2 x^{15} + 9 x^{14} - 8 x^{13} - 6 x^{12} + 22 x^{11} - 20 x^{10} - 4 x^{9} + 23 x^{8} - 20 x^{7} + 7 x^{6} + x^{5} - 11 x^{4} + 11 x^{3} - x^{2} - 3 x + 1$ |
$17$ |
[5,6] |
$2^{2}\cdot 71\cdot 113\cdot 398023\cdot 3743302227733793$ |
$5$ |
$32.4012931788$ |
$5488284177909.384$ |
|
|
? |
$S_{17}$ (as 17T10) |
trivial |
$2$ |
$10$ |
$4697339.96204$ |
| 17.5.878...000.1 |
$x^{17} - 8 x^{16} - 17 x^{15} + 376 x^{14} - 1517 x^{13} + 2374 x^{12} - 258 x^{11} - 2424 x^{10} - 507 x^{9} - 2266 x^{8} + 26723 x^{7} - 46312 x^{6} + 33731 x^{5} - 13660 x^{4} + 980 x^{3} + 10560 x^{2} - 10440 x + 2880$ |
$17$ |
[5,6] |
$2^{18}\cdot 3^{28}\cdot 5^{14}\cdot 7^{4}$ |
$4$ |
$75.6925905596$ |
$1452.1836922844575$ |
|
|
|
$A_{17}$ (as 17T9) |
trivial |
$2$ |
$10$ |
$270930416645$ |
| 17.5.353...000.1 |
$x^{17} - 6 x^{16} + 36 x^{15} + 16 x^{14} - 159 x^{13} + 1746 x^{12} - 1916 x^{11} + 3324 x^{10} + 11532 x^{9} - 36888 x^{8} + 40500 x^{7} - 24420 x^{6} - 123199 x^{5} + 197142 x^{4} - 110508 x^{3} + 40728 x^{2} - 3663 x + 1494$ |
$17$ |
[5,6] |
$2^{32}\cdot 3^{16}\cdot 5^{12}\cdot 23^{8}$ |
$4$ |
$141.22243220940072$ |
$264.2654436111253$ |
|
|
|
$\PSL(2,16):C_2$ (as 17T7) |
trivial |
$2$ |
$10$ |
$10386811718044.676$ |
