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 |
42.0.148...423.1 |
$x^{42} - x + 1$ |
$42$ |
[0,21] |
$-\,250460976091\cdot 2191665374655671317777039\cdot 27\!\cdots\!27$ |
$3$ |
$41.9910966386$ |
$1.219836300143031e+34$ |
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$20$ |
|
42.2.151...705.1 |
$x^{42} - x - 1$ |
$42$ |
[2,20] |
$5\cdot 3355730803775717\cdot 90\!\cdots\!73$ |
$3$ |
$42.0088266452$ |
$1.2306982374893096e+34$ |
|
|
✓ |
$S_{42}$ (as 42T9491) |
trivial |
$2$ |
$21$ |
$239179039607002720$ |
42.2.585...728.1 |
$x^{42} - 2 x - 1$ |
$42$ |
[2,20] |
$2^{43}\cdot 151\cdot 4132611804876851\cdot 111869437509421489132043\cdot 9532243245509920520310487$ |
$5$ |
$75.060981117$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.0.636...560.1 |
$x^{42} - 4 x + 4$ |
$42$ |
[0,21] |
$-\,2^{42}\cdot 5\cdot 14815048403\cdot 223886382998191\cdot 87\!\cdots\!11$ |
$5$ |
$75.2119624159$ |
|
|
|
? |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$20$ |
|
42.2.170...328.1 |
$x^{42} - 4 x - 4$ |
$42$ |
[2,20] |
$2^{42}\cdot 37\cdot 479\cdot 22037\cdot 3375017\cdot 4905809483\cdot 799858695525167\cdot 7513694603813636232170428411$ |
$8$ |
$81.3401245086$ |
|
|
|
? |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.0.324...664.1 |
$x^{42} - 2 x + 2$ |
$42$ |
[0,21] |
$-\,2^{42}\cdot 19\cdot 11483\cdot 457151\cdot 73\!\cdots\!33$ |
$5$ |
$82.5898982026$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$20$ |
|
42.2.335...992.1 |
$x^{42} - 2 x - 2$ |
$42$ |
[2,20] |
$2^{42}\cdot 13\cdot 43\cdot 7237697\cdot 7281116753\cdot 16009936396480001782447\cdot 161984247228508288433890361$ |
$7$ |
$82.6596626942$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.2.145...905.1 |
$x^{42} - 3 x + 1$ |
$42$ |
[2,20] |
$3^{42}\cdot 5\cdot 277\cdot 9883\cdot 24851\cdot 5267491\cdot 28880594132963764921\cdot 25718507492700353234963282659$ |
$8$ |
$112.591471675$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.0.533...823.1 |
$x^{42} - 3 x + 3$ |
$42$ |
[0,21] |
$-\,3^{42}\cdot 17\cdot 28\!\cdots\!91$ |
$3$ |
$122.668144982$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$20$ |
|
42.2.562...761.1 |
$x^{42} - 3 x - 3$ |
$42$ |
[2,20] |
$3^{42}\cdot 733\cdot 68553343\cdot 351501200862401\cdot 10459852944644953\cdot 278075548230630365691581947$ |
$6$ |
$122.823626651$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.2.257...728.1 |
$x^{42} - 4 x + 2$ |
$42$ |
[2,20] |
$2^{83}\cdot 13\cdot 12436342330109\cdot 16\!\cdots\!73$ |
$4$ |
$150.121962234$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.2.257...992.1 |
$x^{42} - 4 x + 1$ |
$42$ |
[2,20] |
$2^{42}\cdot 349\cdot 16\!\cdots\!27$ |
$3$ |
$150.121962234$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.0.725...415.1 |
$x^{42} - x + 4$ |
$42$ |
[0,21] |
$-\,5\cdot 14\!\cdots\!83$ |
$2$ |
$162.545338792$ |
$2.6944176864135995e+46$ |
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$20$ |
|
42.2.302...297.1 |
$x^{42} - 5 x + 2$ |
$42$ |
[2,20] |
$19\cdot 103\cdot 12613\cdot 12\!\cdots\!17$ |
$4$ |
$187.652452792$ |
$5.500968446029659e+47$ |
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.2.302...689.1 |
$x^{42} - 5 x - 1$ |
$42$ |
[2,20] |
$14087\cdot 14537\cdot 2332805104561\cdot 63\!\cdots\!71$ |
$4$ |
$187.652452792$ |
$5.5009684460296616e+47$ |
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.0.170...584.1 |
$x^{42} - 2 x + 5$ |
$42$ |
[0,21] |
$-\,2^{42}\cdot 47\cdot 29989\cdot 133117577\cdot 20\!\cdots\!31$ |
$5$ |
$195.543052354$ |
|
|
|
? |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$20$ |
|
42.0.652...375.1 |
$x^{42} - 5 x + 5$ |
$42$ |
[0,21] |
$-\,5^{41}\cdot 14\!\cdots\!59$ |
$2$ |
$201.887002322$ |
$5.763925025224943e+34$ |
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$20$ |
|
42.0.682...944.1 |
$x^{42} - 4 x + 5$ |
$42$ |
[0,21] |
$-\,2^{42}\cdot 257\cdot 3481561\cdot 654827729\cdot 761992291147\cdot 1236911477052699683\cdot 28\!\cdots\!17$ |
$7$ |
$202.105025528$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$20$ |
|
42.0.682...359.1 |
$x^{42} - x + 5$ |
$42$ |
[0,21] |
$-\,2897\cdot 16037383\cdot 15911394874499255951\cdot 92\!\cdots\!59$ |
$4$ |
$202.105043673$ |
$2.612884347513774e+48$ |
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$20$ |
|
42.2.682...664.1 |
$x^{42} - 2 x - 5$ |
$42$ |
[2,20] |
$2^{43}\cdot 753458691670301\cdot 3525521090014396699\cdot 29\!\cdots\!17$ |
$4$ |
$202.105043673$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.2.682...969.1 |
$x^{42} - 3 x - 5$ |
$42$ |
[2,20] |
$3^{42}\cdot 10431018730019\cdot 17617983839831\cdot 33\!\cdots\!69$ |
$4$ |
$202.105043673$ |
|
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|
42.2.712...625.1 |
$x^{42} - 5 x - 5$ |
$42$ |
[2,20] |
$5^{41}\cdot 11\cdot 88163104517\cdot 308782183121\cdot 54247978409543239\cdot 9651394343916620260340096573$ |
$6$ |
$202.313847473$ |
$6.025326253439044e+34$ |
|
|
✓ |
$S_{42}$ (as 42T9491) |
not computed |
$2$ |
$21$ |
|