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 |
23.3.121...973.1 |
$x^{23} - 3 x^{21} - 6 x^{20} + x^{19} + 17 x^{18} + 18 x^{17} - 10 x^{16} - 43 x^{15} - 25 x^{14} + 33 x^{13} + 60 x^{12} + 11 x^{11} - 54 x^{10} - 47 x^{9} + 12 x^{8} + 44 x^{7} + 15 x^{6} - 17 x^{5} - 16 x^{4} + 6 x^{2} + x - 1$ |
$23$ |
[3,10] |
$7\cdot 41\cdot 599\cdot 7069315563547560848845133621$ |
$4$ |
$27.445087043$ |
$3.4861257098334132e+16$ |
|
|
? |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$53774282.4892$ |
23.3.961...453.1 |
$x^{23} - x^{22} - x^{21} - x^{20} + x^{19} + 8 x^{18} - 3 x^{17} - 9 x^{16} - 6 x^{15} + 5 x^{14} + 23 x^{13} - x^{12} - 23 x^{11} - 13 x^{10} + 12 x^{9} + 27 x^{8} - 3 x^{7} - 20 x^{6} - 6 x^{5} + 9 x^{4} + 7 x^{3} - 4 x^{2} - 2 x + 1$ |
$23$ |
[3,10] |
$19\cdot 28201\cdot 55057\cdot 3258654194756619414566191$ |
$4$ |
$33.1890102516$ |
$3.1005194813504915e+17$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$177401273.772$ |
23.3.321...401.1 |
$x^{23} - 3 x - 1$ |
$23$ |
[3,10] |
$259028266789\cdot 124091112112198565028075828709$ |
$2$ |
$57.7002549387$ |
$1.7928498457579284e+20$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$208932361073$ |
23.3.240...408.1 |
$x^{23} - 4 x - 2$ |
$23$ |
[3,10] |
$2^{22}\cdot 877\cdot 19001\cdot 19571\cdot 263933\cdot 66547926528717936307$ |
$6$ |
$76.9336610607$ |
$4.644622058793635e+18$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$7510521361460$ |
23.3.240...209.1 |
$x^{23} - 4 x - 1$ |
$23$ |
[3,10] |
$79\cdot 30\!\cdots\!71$ |
$2$ |
$76.9336732537$ |
$4.901617177763348e+21$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$9167004154390$ |
23.3.480...184.1 |
$x^{23} - 8 x - 4$ |
$23$ |
[3,10] |
$2^{22}\cdot 3\cdot 2377\cdot 111863\cdot 115741\cdot 198173\cdot 4489367\cdot 139474352947$ |
$8$ |
$79.2874946137$ |
$6.568493493524864e+18$ |
|
|
? |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$13271946732000$ |
23.3.721...841.1 |
$x^{23} - 9 x - 4$ |
$23$ |
[3,10] |
$29357399\cdot 2802945917\cdot 8767675026551455678892251027$ |
$3$ |
$89.198438038$ |
$2.6860145997483168e+22$ |
|
|
? |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$52936041498100$ |
23.3.406...697.1 |
$x^{23} - 5 x - 3$ |
$23$ |
[3,10] |
$210197102102168605537\cdot 19360315520206385014193681$ |
$2$ |
$96.1664183877$ |
$6.379249343089687e+22$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$136459367279000$ |
23.3.407...632.1 |
$x^{23} - 5 x - 2$ |
$23$ |
[3,10] |
$2^{23}\cdot 3\cdot 16747\cdot 96\!\cdots\!19$ |
$4$ |
$96.1670914772$ |
|
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$251262638330000$ |
23.3.407...433.1 |
$x^{23} - 5 x - 1$ |
$23$ |
[3,10] |
$3\cdot 251\cdot 37061\cdot 1703206550657\cdot 85630730582884052082230293$ |
$5$ |
$96.1670915672$ |
$6.3797629026022336e+22$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$93975082330300$ |
23.3.673...168.1 |
$x^{23} - 6 x - 4$ |
$23$ |
[3,10] |
$2^{42}\cdot 1213\cdot 25031\cdot 80799553\cdot 6239042049682651613$ |
$5$ |
$108.643929432$ |
|
|
|
? |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$1711119252340000$ |
23.3.269...241.1 |
$x^{23} - 6 x - 3$ |
$23$ |
[3,10] |
$3^{22}\cdot 29\cdot 491\cdot 19934477530995439\cdot 30270857948592169$ |
$5$ |
$115.400497688$ |
$8.38361625769388e+18$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$1015112848700000$ |
23.3.269...176.1 |
$x^{23} - 6 x - 2$ |
$23$ |
[3,10] |
$2^{22}\cdot 19\cdot 37\cdot 344047944109\cdot 265793000653027391320291747$ |
$5$ |
$115.400509879$ |
$4.920402733142511e+20$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$1019289158970000$ |
23.3.269...977.1 |
$x^{23} - 6 x - 1$ |
$23$ |
[3,10] |
$3449\cdot 9967345151\cdot 1056281512820207\cdot 7425494255063859089$ |
$4$ |
$115.400509881$ |
$5.1926478192494746e+23$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$1574174564310000$ |
23.3.233...736.1 |
$x^{23} - 7 x - 2$ |
$23$ |
[3,10] |
$2^{23}\cdot 541\cdot 51\!\cdots\!37$ |
$3$ |
$126.758764041$ |
|
|
|
? |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$4288457073080000$ |
23.3.929...937.1 |
$x^{23} - 7 x - 5$ |
$23$ |
[3,10] |
$229\cdot 27997\cdot 6781098636069157\cdot 213789785909465552840708957$ |
$4$ |
$134.602662929$ |
$3.048716188057928e+24$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$4914010135120000$ |
23.3.934...440.1 |
$x^{23} - 7 x - 4$ |
$23$ |
[3,10] |
$2^{22}\cdot 5\cdot 797\cdot 1117\cdot 1733\cdot 107123\cdot 138709907659\cdot 19435989258965663$ |
$8$ |
$134.633698081$ |
|
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$11515537754600000$ |
23.3.934...009.1 |
$x^{23} - 7 x - 3$ |
$23$ |
[3,10] |
$181\cdot 51\!\cdots\!89$ |
$2$ |
$134.633927784$ |
$3.0568697478286915e+24$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$8930791100670000$ |
23.3.934...745.1 |
$x^{23} - 7 x - 1$ |
$23$ |
[3,10] |
$5\cdot 19\cdot 211\cdot 330347\cdot 1280131\cdot 11\!\cdots\!73$ |
$6$ |
$134.633928194$ |
$3.056869855005518e+24$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$5047506980130000$ |
23.3.223...160.1 |
$x^{23} - 8 x - 2$ |
$23$ |
[3,10] |
$2^{22}\cdot 5\cdot 7\cdot 211\cdot 72\!\cdots\!29$ |
$5$ |
$139.848450734$ |
$4.4840956446034876e+21$ |
|
|
? |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$12968384279300000$ |
23.3.198...696.1 |
$x^{23} - 8 x - 6$ |
$23$ |
[3,10] |
$2^{22}\cdot 17862914155103\cdot 26\!\cdots\!83$ |
$3$ |
$153.77552041$ |
$1.3360251860138083e+22$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$23188187581900000$ |
23.3.201...433.1 |
$x^{23} - 8 x - 5$ |
$23$ |
[3,10] |
$3\cdot 7\cdot 41\cdot 170908943\cdot 4352121637\cdot 314624419069868068094497723583$ |
$6$ |
$153.865693855$ |
$1.4194846340579026e+25$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$36238915593800000$ |
23.3.201...505.1 |
$x^{23} - 8 x - 3$ |
$23$ |
[3,10] |
$5\cdot 40\!\cdots\!01$ |
$2$ |
$153.867346486$ |
$1.4196599765173122e+25$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$53438746912400000$ |
23.3.201...241.1 |
$x^{23} - 8 x - 1$ |
$23$ |
[3,10] |
$3\cdot 103\cdot 24767\cdot 26\!\cdots\!47$ |
$4$ |
$153.867346507$ |
$1.4196599788250875e+25$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$25580963014300000$ |
23.3.294...753.1 |
$x^{23} - 9 x - 7$ |
$23$ |
[3,10] |
$191\cdot 42953\cdot 180300563316486553\cdot 1990559237888165571886856887$ |
$4$ |
$172.895053277$ |
$5.426246636592656e+25$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$107684244107000000$ |
23.3.302...424.1 |
$x^{23} - 9 x - 6$ |
$23$ |
[3,10] |
$2^{23}\cdot 3^{22}\cdot 7\cdot 2699647\cdot 324329267\cdot 1873843928641659619$ |
$6$ |
$173.093926478$ |
|
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$265930664144000000$ |
23.3.302...161.1 |
$x^{23} - 9 x - 5$ |
$23$ |
[3,10] |
$19\cdot 1571\cdot 28663\cdot 446863\cdot 546386660312214989\cdot 14485838402884945429$ |
$6$ |
$173.100641004$ |
$5.500912984667423e+25$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$120789378212000000$ |
23.3.302...233.1 |
$x^{23} - 9 x - 3$ |
$23$ |
[3,10] |
$3^{22}\cdot 563\cdot 1663\cdot 14870740319\cdot 6925894270378748955660067$ |
$5$ |
$173.100764819$ |
$8.881399340302265e+20$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$75511406524500000$ |
23.3.302...168.1 |
$x^{23} - 9 x - 2$ |
$23$ |
[3,10] |
$2^{23}\cdot 13\cdot 83\cdot 1093\cdot 64706587659437\cdot 4727120690565738876772139$ |
$6$ |
$173.100764821$ |
|
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$190921630547000000$ |
23.3.302...969.1 |
$x^{23} - 9 x - 1$ |
$23$ |
[3,10] |
$7\cdot 468913\cdot 16626889561\cdot 55\!\cdots\!19$ |
$4$ |
$173.100764821$ |
$5.500958234165554e+25$ |
|
|
✓ |
$S_{23}$ (as 23T7) |
trivial |
$2$ |
$12$ |
$70045166746400000$ |
23.3.823...336.1 |
$x^{23} - 13248 x - 12672$ |
$23$ |
[3,10] |
$2^{26}\cdot 3^{22}\cdot 11^{22}\cdot 23^{24}$ |
$4$ |
$1635.76068738$ |
|
|
|
? |
$A_{23}$ (as 23T6) |
trivial |
$2$ |
$12$ |
$72619230064900000000000000000$ |
23.3.131...376.1 |
$x^{23} - 89424 x - 85536$ |
$23$ |
[3,10] |
$2^{30}\cdot 3^{22}\cdot 11^{22}\cdot 23^{24}$ |
$4$ |
$1845.32476081$ |
|
|
|
? |
$A_{23}$ (as 23T6) |
trivial |
$2$ |
$12$ |
$199639980384000000000000000000$ |