| 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 |
| 25.1.874...849.1 |
$x^{25} - x - 1$ |
$25$ |
[1,12] |
$10667\cdot 282401201\cdot 925997749\cdot 31362479733103$ |
$4$ |
$24.9848741581$ |
$2.9577712249794144e+17$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$13759573.23594141$ |
| 25.1.901...401.1 |
$x^{25} + x - 1$ |
$25$ |
[1,12] |
$13\cdot 2957\cdot 8969\cdot 6212881\cdot 42086382270382828249$ |
$5$ |
$25.0149093419$ |
$3.002525232980779e+17$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$36955124.38960424$ |
| 25.1.123...944.1 |
$x^{25} - x - 2$ |
$25$ |
[1,12] |
$2^{24}\cdot 739\cdot 12239\cdot 2507149\cdot 272308609\cdot 118872926969$ |
$6$ |
$40.143699191$ |
|
|
|
? |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$29964620111.03697$ |
| 25.1.447...857.1 |
$x^{25} + 2 x - 1$ |
$25$ |
[1,12] |
$2377\cdot 5147\cdot 460493604849521\cdot 7943531120919741043$ |
$4$ |
$42.2700559021$ |
$2.1154865929173837e+20$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$34275814896.984695$ |
| 25.1.140...536.1 |
$x^{25} - 4 x - 4$ |
$25$ |
[1,12] |
$2^{24}\cdot 7\cdot 19\cdot 2579\cdot 1081796927611\cdot 224982529004839973$ |
$6$ |
$48.5123928684$ |
$5.620663122436464e+17$ |
|
|
? |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$208280915557.53195$ |
| 25.1.144...768.1 |
$x^{25} - 2 x - 2$ |
$25$ |
[1,12] |
$2^{24}\cdot 86\!\cdots\!73$ |
$2$ |
$48.5734646332$ |
$5.7097536444436717e+17$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$353974245955.4027$ |
| 25.1.149...464.1 |
$x^{25} - x - 4$ |
$25$ |
[1,12] |
$2^{24}\cdot 389\cdot 766126533933601\cdot 298023226053735461$ |
$4$ |
$48.6327473706$ |
|
|
|
? |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$173113750880.608$ |
| 25.1.153...232.1 |
$x^{25} + 2 x - 2$ |
$25$ |
[1,12] |
$2^{24}\cdot 11\cdot 83\cdot 139\cdot 177347\cdot 386150417\cdot 10526535234089689$ |
$7$ |
$48.6903449189$ |
$5.883889204334063e+17$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$198284213067.61386$ |
| 25.1.157...464.1 |
$x^{25} + 4 x - 4$ |
$25$ |
[1,12] |
$2^{24}\cdot 8054869\cdot 11688928159776857914348061941$ |
$3$ |
$48.7463522756$ |
$5.969052262562249e+17$ |
|
|
? |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$248830673715.64108$ |
| 25.3.113...143.1 |
$x^{25} - 3 x - 1$ |
$25$ |
[3,11] |
$-\,131\cdot 13259\cdot 3933670000864773133\cdot 165394543991056112099$ |
$4$ |
$63.4050788196$ |
$3.3616352146582453e+22$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$13$ |
$6280286129297.773$ |
| 25.1.113...393.1 |
$x^{25} + 3 x - 1$ |
$25$ |
[1,12] |
$7\cdot 14691751\cdot 10\!\cdots\!49$ |
$3$ |
$63.40507882$ |
$3.3616352149224554e+22$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$4423868533942.698$ |
| 25.1.113...768.1 |
$x^{25} + 3 x - 2$ |
$25$ |
[1,12] |
$2^{24}\cdot 7\cdot 1777\cdot 19854823\cdot 273087660366642710101853209$ |
$5$ |
$63.4084209876$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$22439086804455.46$ |
| 25.1.239...857.1 |
$x^{25} - 3 x - 3$ |
$25$ |
[1,12] |
$3^{24}\cdot 102715785599666749\cdot 825740991458053453$ |
$3$ |
$71.6433105717$ |
$8.36136000596636e+17$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$22229647392442.062$ |
| 25.1.250...393.1 |
$x^{25} - 2 x - 3$ |
$25$ |
[1,12] |
$3^{24}\cdot 4213063\cdot 105716820911311\cdot 199414803057521$ |
$4$ |
$71.7755257265$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$41251640648720.61$ |
| 25.1.250...849.1 |
$x^{25} - x - 3$ |
$25$ |
[1,12] |
$3^{25}\cdot 2351\cdot 126764421589739\cdot 99341097532143287$ |
$4$ |
$71.7755308486$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$50040091077622.54$ |
| 25.1.250...401.1 |
$x^{25} + x - 3$ |
$25$ |
[1,12] |
$3^{24}\cdot 13\cdot 2298962364929\cdot 2971837118443792802173$ |
$4$ |
$71.7755308486$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$16459696694938.55$ |
| 25.1.262...393.1 |
$x^{25} + 3 x - 3$ |
$25$ |
[1,12] |
$3^{24}\cdot 7\cdot 67\cdot 19\!\cdots\!37$ |
$4$ |
$71.9021520568$ |
$8.746916133008315e+17$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$18121347166420.11$ |
| 25.3.150...224.1 |
$x^{25} - 4 x - 2$ |
$25$ |
[3,11] |
$-\,2^{24}\cdot 7\cdot 11\cdot 173\cdot 431\cdot 2029499\cdot 218979707\cdot 3166728751\cdot 11077240423$ |
$9$ |
$84.5401017374$ |
$5.8198718858028633e+20$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$13$ |
$338438355338568.8$ |
| 25.3.150...599.1 |
$x^{25} - 4 x - 1$ |
$25$ |
[3,11] |
$-\,7\cdot 53\cdot 3847\cdot 1012717\cdot 140141898521\cdot 847814229733\cdot 8744131694867$ |
$7$ |
$84.540105093$ |
$1.2254195146594985e+24$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$13$ |
$323817690787630.7$ |
| 25.1.150...849.1 |
$x^{25} + 4 x - 1$ |
$25$ |
[1,12] |
$38117394317861\cdot 39\!\cdots\!09$ |
$2$ |
$84.540105093$ |
$1.225419514659571e+24$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
$[2]$ |
$2$ |
$12$ |
$101792268413442.38$ |
| 25.1.150...224.1 |
$x^{25} + 4 x - 2$ |
$25$ |
[1,12] |
$2^{24}\cdot 29\cdot 11136449\cdot 3349154609\cdot 82750417248561907056701$ |
$5$ |
$84.5401084487$ |
$5.819877660964827e+20$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$281396393824665.03$ |
| 25.1.152...849.1 |
$x^{25} + 4 x - 3$ |
$25$ |
[1,12] |
$3^{24}\cdot 54\!\cdots\!29$ |
$2$ |
$84.5961459834$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$310216853513864.2$ |
| 25.1.624...192.1 |
$x^{25} - 2 x - 4$ |
$25$ |
[1,12] |
$2^{46}\cdot 13751\cdot 431377\cdot 76457289497\cdot 195834881900887$ |
$5$ |
$89.5025070864$ |
|
|
|
? |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$1436614179210074.2$ |
| 25.1.625...808.1 |
$x^{25} + 2 x - 4$ |
$25$ |
[1,12] |
$2^{46}\cdot 88\!\cdots\!97$ |
$2$ |
$89.5025070992$ |
|
|
|
? |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$647777435547311.2$ |
| 25.3.158...375.1 |
$x^{25} - 5 x - 3$ |
$25$ |
[3,11] |
$-\,3^{24}\cdot 5^{23}\cdot 409\cdot 11545399656835619219$ |
$4$ |
$92.9082114519$ |
|
|
|
? |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$13$ |
$1137438749492350.0$ |
| 25.1.249...232.1 |
$x^{25} - 3 x - 4$ |
$25$ |
[1,12] |
$2^{48}\cdot 4813\cdot 18\!\cdots\!69$ |
$3$ |
$94.6055936127$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$3640732777248095.0$ |
| 25.1.250...776.1 |
$x^{25} + x - 4$ |
$25$ |
[1,12] |
$2^{48}\cdot 13\cdot 5969653\cdot 175300357\cdot 544585241\cdot 11988341597$ |
$6$ |
$94.6057646726$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$2845294424971493.0$ |
| 25.1.441...625.1 |
$x^{25} + 5 x - 3$ |
$25$ |
[1,12] |
$3^{23}\cdot 5^{25}\cdot 39301\cdot 40055507545130507$ |
$4$ |
$96.7841393096$ |
|
|
|
|
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$3887794187130357.5$ |
| 25.1.993...000.1 |
$x^{25} + 5 x - 2$ |
$25$ |
[1,12] |
$2^{22}\cdot 5^{25}\cdot 79496847501414068010394661$ |
$3$ |
$99.9747661128$ |
|
|
|
|
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$8545612733538318.0$ |
| 25.1.108...049.1 |
$x^{25} - 4 x - 5$ |
$25$ |
[1,12] |
$1663\cdot 6971\cdot 492251\cdot 268235921\cdot 264590126291\cdot 266683732590664933$ |
$6$ |
$100.308662897$ |
$1.0392750875600515e+25$ |
|
|
? |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$1770854208067528.0$ |
| 25.3.397...000.1 |
$x^{25} - 5 x - 2$ |
$25$ |
[3,11] |
$-\,2^{24}\cdot 5^{25}\cdot 11\cdot 7226986082306147296044401$ |
$4$ |
$105.67513135$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$13$ |
$24297329895974496$ |
| 25.3.397...375.1 |
$x^{25} - 5 x - 1$ |
$25$ |
[3,11] |
$-\,5^{25}\cdot 131\cdot 311\cdot 542960645459\cdot 60293398488673829$ |
$5$ |
$105.675131366$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$13$ |
$3544806216556346.0$ |
| 25.1.397...625.1 |
$x^{25} + 5 x - 1$ |
$25$ |
[1,12] |
$5^{25}\cdot 2389\cdot 83136689749\cdot 6715230479961176141$ |
$4$ |
$105.675131366$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
$[2]$ |
$2$ |
$12$ |
$780644257929814.2$ |
| 25.1.422...000.1 |
$x^{25} + 5 x - 4$ |
$25$ |
[1,12] |
$2^{48}\cdot 5^{25}\cdot 23\cdot 29\cdot 35541523\cdot 212450981$ |
$6$ |
$105.933280209$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$8383885813460554.0$ |
| 25.1.489...625.1 |
$x^{25} - 5 x - 5$ |
$25$ |
[1,12] |
$5^{25}\cdot 269\cdot 61\!\cdots\!21$ |
$3$ |
$116.841017382$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$7307953282555373.0$ |
| 25.1.529...857.1 |
$x^{25} - 3 x - 5$ |
$25$ |
[1,12] |
$35846147\cdot 76867751\cdot 19\!\cdots\!81$ |
$3$ |
$117.206368249$ |
$7.2759568376126625e+25$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$10786828262013908$ |
| 25.1.529...393.1 |
$x^{25} - 2 x - 5$ |
$25$ |
[1,12] |
$48407\cdot 10\!\cdots\!99$ |
$2$ |
$117.20636925$ |
$7.275957614152672e+25$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$17416422916825532$ |
| 25.1.529...849.1 |
$x^{25} - x - 5$ |
$25$ |
[1,12] |
$47\cdot 8641\cdot 6952808251\cdot 10464775307854799\cdot 179154737750394843163$ |
$5$ |
$117.20636925$ |
$7.2759576141834256e+25$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$16941382677340960$ |
| 25.1.529...401.1 |
$x^{25} + x - 5$ |
$25$ |
[1,12] |
$13\cdot 89\cdot 557\cdot 1597\cdot 2058253\cdot 8953100495557\cdot 279135218041860532289677$ |
$7$ |
$117.20636925$ |
$7.2759576141834256e+25$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$11239501839285880$ |
| 25.1.529...857.1 |
$x^{25} + 2 x - 5$ |
$25$ |
[1,12] |
$137\cdot 3187\cdot 319234466347\cdot 37\!\cdots\!49$ |
$4$ |
$117.20636925$ |
$7.27595761421418e+25$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$12233819879819124$ |
| 25.1.529...393.1 |
$x^{25} + 3 x - 5$ |
$25$ |
[1,12] |
$7\cdot 79\cdot 367\cdot 26\!\cdots\!43$ |
$4$ |
$117.206370251$ |
$7.275958390754107e+25$ |
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$11130177971379280$ |
| 25.1.569...625.1 |
$x^{25} + 5 x - 5$ |
$25$ |
[1,12] |
$5^{25}\cdot 127\cdot 390538849\cdot 963885163\cdot 399465067602449$ |
$5$ |
$117.546279306$ |
|
|
|
✓ |
$S_{25}$ (as 25T211) |
trivial |
$2$ |
$12$ |
$7950768287499577.0$ |
