| 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 |
| 41.1.131...641.1 |
$x^{41} - x - 1$ |
$41$ |
[1,20] |
$2251\cdot 272583857708203\cdot 761889448323748621067\cdot 2821028813073407561156582291$ |
$4$ |
$40.9908758335$ |
$1.1483851150361388e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
trivial |
$2$ |
$20$ |
$28450692757863310$ |
| 41.1.343...976.1 |
$x^{41} + 4 x - 4$ |
$41$ |
[1,20] |
$2^{40}\cdot 63506090654183\cdot 49\!\cdots\!47$ |
$3$ |
$69.5586596583$ |
$1.0997338366416402e+32$ |
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.141...416.1 |
$x^{41} - 4 x - 4$ |
$41$ |
[1,20] |
$2^{40}\cdot 2313020109848347\cdot 2947885124842583399107\cdot 188093758458159369641352727129$ |
$4$ |
$80.5526095167$ |
$2.2269987591329257e+33$ |
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.143...416.1 |
$x^{41} - 2 x - 2$ |
$41$ |
[1,20] |
$2^{40}\cdot 3\cdot 53\cdot 67\cdot 19183\cdot 332415773971\cdot 2121795341959\cdot 90\!\cdots\!31$ |
$8$ |
$80.5893122191$ |
$2.2478928141179964e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.146...416.1 |
$x^{41} - x - 2$ |
$41$ |
[1,20] |
$2^{40}\cdot 139\cdot 1289\cdot 74\!\cdots\!71$ |
$4$ |
$80.6253582462$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.146...416.1 |
$x^{41} - x - 4$ |
$41$ |
[1,20] |
$2^{40}\cdot 13\!\cdots\!41$ |
$2$ |
$80.6253582462$ |
|
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.148...416.1 |
$x^{41} + 2 x - 2$ |
$41$ |
[1,20] |
$2^{40}\cdot 29\cdot 5227\cdot 7297\cdot 6697657\cdot 53935240897410251303\cdot 33\!\cdots\!21$ |
$7$ |
$80.6607709621$ |
$2.2891088582526597e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.440...416.1 |
$x^{41} + 3 x - 2$ |
$41$ |
[1,20] |
$2^{40}\cdot 11\cdot 367\cdot 104399\cdot 13038909447397913\cdot 19797069953357319509\cdot 3686170645074380678869761671$ |
$7$ |
$109.674748522$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.157...441.1 |
$x^{41} - 3 x - 3$ |
$41$ |
[1,20] |
$3^{40}\cdot 7\cdot 32261\cdot 253464984011\cdot 1238514877771\cdot 76247312349973837\cdot 239507603770962778439$ |
$7$ |
$119.667259082$ |
$3.3231780104649844e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.161...441.1 |
$x^{41} - 2 x - 3$ |
$41$ |
[1,20] |
$19\cdot 23\cdot 31\cdot 23297\cdot 24551\cdot 61559\cdot 192233\cdot 17\!\cdots\!67$ |
$8$ |
$119.747928028$ |
$4.0224824391897956e+42$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.161...441.1 |
$x^{41} - x - 3$ |
$41$ |
[1,20] |
$307\cdot 5719838273\cdot 92\!\cdots\!31$ |
$3$ |
$119.747928032$ |
$4.022482442494292e+42$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.166...441.1 |
$x^{41} + 3 x - 3$ |
$41$ |
[1,20] |
$3^{40}\cdot 11\cdot 123191\cdot 11537809\cdot 901418971\cdot 13197674429\cdot 39039118092749\cdot 188276273322445488239$ |
$8$ |
$119.826480163$ |
$3.415006263366723e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.3.584...584.1 |
$x^{41} - 4 x - 2$ |
$41$ |
[3,19] |
$-\,2^{40}\cdot 859\cdot 228505873\cdot 27\!\cdots\!37$ |
$4$ |
$146.232986193$ |
$4.534376065245929e+38$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
|
| 41.1.402...704.1 |
$x^{41} - 2 x - 4$ |
$41$ |
[1,20] |
$2^{78}\cdot 3\cdot 2358722227395221\cdot 18\!\cdots\!07$ |
$4$ |
$153.276321083$ |
|
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.402...704.1 |
$x^{41} + 2 x - 4$ |
$41$ |
[1,20] |
$2^{78}\cdot 2339\cdot 1104312393641791\cdot 51\!\cdots\!09$ |
$4$ |
$153.276321083$ |
|
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.160...816.1 |
$x^{41} - 3 x - 4$ |
$41$ |
[1,20] |
$2^{80}\cdot 7\cdot 37\cdot 67\cdot 108499\cdot 543997\cdot 270310655161\cdot 312570029227603619\cdot 15379092216330540575461$ |
$9$ |
$158.547520704$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.160...816.1 |
$x^{41} + x - 4$ |
$41$ |
[1,20] |
$2^{80}\cdot 3\cdot 263\cdot 587\cdot 6397\cdot 336221\cdot 7665197\cdot 4370168129\cdot 621071121653\cdot 64218333671912404841959$ |
$10$ |
$158.547521764$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.137...104.1 |
$x^{41} + 5 x - 2$ |
$41$ |
[1,20] |
$2^{38}\cdot 163\cdot 743\cdot 10289\cdot 104597\cdot 31257021937\cdot 13675604446553671\cdot 95253739993542479\cdot 94216078858946850824041$ |
$9$ |
$176.714005801$ |
|
|
|
|
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.3.549...559.1 |
$x^{41} - 5 x - 3$ |
$41$ |
[3,19] |
$-\,13\cdot 3357247\cdot 6299663\cdot 93408687929\cdot 21\!\cdots\!47$ |
$5$ |
$182.79123261$ |
$2.344687181070505e+46$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
|
| 41.3.549...584.1 |
$x^{41} - 5 x - 2$ |
$41$ |
[3,19] |
$-\,2^{40}\cdot 3\cdot 13\cdot 27277\cdot 84809\cdot 128519\cdot 211271\cdot 11833317469\cdot 17\!\cdots\!57$ |
$9$ |
$182.791232741$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
|
| 41.3.549...359.1 |
$x^{41} - 5 x - 1$ |
$41$ |
[3,19] |
$-\,3\cdot 7\cdot 115979\cdot 1907696227638017\cdot 11\!\cdots\!53$ |
$5$ |
$182.791232741$ |
$2.3446872155748193e+46$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$21$ |
|
| 41.1.549...641.1 |
$x^{41} + 5 x - 1$ |
$41$ |
[1,20] |
$43\cdot 191\cdot 9901\cdot 55082201453159\cdot 467781923539898069\cdot 251911473477379412779567\cdot 10\!\cdots\!01$ |
$7$ |
$182.791232741$ |
$2.3446872155748193e+46$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.551...816.1 |
$x^{41} + 5 x - 4$ |
$41$ |
[1,20] |
$2^{80}\cdot 53\cdot 2252852353\cdot 11587626304193\cdot 32\!\cdots\!93$ |
$5$ |
$182.804262015$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.128...625.1 |
$x^{41} - 5 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 245129\cdot 204113313923\cdot 28\!\cdots\!47$ |
$4$ |
$186.611859549$ |
$1.8062435116388302e+33$ |
|
|
? |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} - 4 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 23\cdot 43\cdot 7678031\cdot 17\!\cdots\!43$ |
$5$ |
$197.108685196$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} - 3 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 13\!\cdots\!13$ |
$2$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} - 2 x - 5$ |
$41$ |
[1,20] |
$3\cdot 5^{40}\cdot 13\cdot 157\cdot 6298160107\cdot 50991976651363487\cdot 67\!\cdots\!27$ |
$7$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} - x - 5$ |
$41$ |
[1,20] |
$5^{41}\cdot 7033139213\cdot 64812836603\cdot 37176884662660649\cdot 15706697658577462999892991283$ |
$5$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} + x - 5$ |
$41$ |
[1,20] |
$3\cdot 5^{40}\cdot 7\cdot 11287\cdot 706035413231\cdot 1169722373977559\cdot 67\!\cdots\!99$ |
$7$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} + 2 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 29\cdot 131\cdot 163\cdot 2089\cdot 10\!\cdots\!01$ |
$6$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.121...625.1 |
$x^{41} + 3 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 11\cdot 89\cdot 3571\cdot 20521\cdot 218655088207\cdot 84\!\cdots\!03$ |
$7$ |
$197.108708415$ |
|
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
| 41.1.126...625.1 |
$x^{41} + 5 x - 5$ |
$41$ |
[1,20] |
$5^{40}\cdot 19\cdot 607\cdot 1420817\cdot 36720491\cdot 23\!\cdots\!91$ |
$6$ |
$197.322360921$ |
$5.670692287910047e+33$ |
|
|
✓ |
$S_{41}$ (as 41T10) |
not computed |
$2$ |
$20$ |
|
