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 |
11.5.132326332471.1 |
$x^{11} - 2 x^{10} + 2 x^{7} + x^{6} - 3 x^{5} + 2 x^{2} + x - 1$ |
$11$ |
[5,3] |
$-\,211441\cdot 625831$ |
$2$ |
$10.2579068817$ |
$363766.8655485268$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$15.3396861125$ |
11.5.145065457639.1 |
$x^{11} - x^{10} - 4 x^{9} + 7 x^{8} + 4 x^{7} - 9 x^{6} - 5 x^{5} + 2 x^{4} + 8 x^{3} + 2 x^{2} - 3 x - 1$ |
$11$ |
[5,3] |
$-\,2389\cdot 2617\cdot 23203$ |
$3$ |
$10.3439791741$ |
$380874.5956860342$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$16.2407020956$ |
11.5.157519649831.1 |
$x^{11} - x^{10} - x^{9} - x^{7} + x^{6} + 2 x^{4} + 3 x^{3} - 2 x - 1$ |
$11$ |
[5,3] |
$-\,19457\cdot 8095783$ |
$2$ |
$10.4217228987$ |
$396887.4523476397$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$17.2118083495$ |
11.5.167050542839.1 |
$x^{11} - 2 x^{10} + 2 x^{9} - 3 x^{7} + x^{6} - x^{5} + 2 x + 1$ |
$11$ |
[5,3] |
$-\,2089\cdot 79966751$ |
$2$ |
$10.4775296669$ |
$408718.1704292091$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$17.654115853304827$ |
11.5.167720394923.1 |
$x^{11} - 2 x^{10} - 3 x^{9} + 9 x^{8} - x^{7} - 13 x^{6} + 9 x^{5} + 7 x^{4} - 5 x^{3} - 1$ |
$11$ |
[5,3] |
$-\,167720394923$ |
$1$ |
$10.4813421415$ |
$409536.80533378193$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$17.7118832979$ |
11.5.200601609583.1 |
$x^{11} + x^{9} - 2 x^{7} - x^{6} - 3 x^{5} + x^{4} + x^{3} + x^{2} + x - 1$ |
$11$ |
[5,3] |
$-\,200601609583$ |
$1$ |
$10.6533193695$ |
$447885.7104027767$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$19.635566037183242$ |
11.5.234360387559.1 |
$x^{11} + x^{9} - 2 x^{8} - x^{7} - x^{5} - x^{3} + 2 x^{2} + x - 1$ |
$11$ |
[5,3] |
$-\,71\cdot 3300850529$ |
$2$ |
$10.8050265172$ |
$484107.8263765212$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$21.919668485422946$ |
11.5.236131740703.1 |
$x^{11} - x^{10} - 2 x^{9} + 2 x^{8} - x^{7} + 2 x^{5} - x^{4} + x^{3} + x^{2} - 1$ |
$11$ |
[5,3] |
$-\,372881\cdot 633263$ |
$2$ |
$10.8124254085$ |
$485933.8851150432$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$22.027596379016778$ |
11.5.248686333151.1 |
$x^{11} - 2 x^{9} - x^{7} - x^{6} + 2 x^{3} + x + 1$ |
$11$ |
[5,3] |
$-\,2381\cdot 104446171$ |
$2$ |
$10.863464669$ |
$498684.6028814204$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$22.52935578711483$ |
11.5.987614208000000000.1 |
$x^{11} - x^{10} + 9 x^{9} - 45 x^{8} - 180 x^{6} + 120 x^{5} + 720 x^{4} + 285 x^{3} + 455 x^{2} - 35 x - 105$ |
$11$ |
[5,3] |
$-\,2^{19}\cdot 3^{9}\cdot 5^{9}\cdot 7^{2}$ |
$4$ |
$43.2385951874$ |
$267.5908462678598$ |
|
|
|
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$1376067.70771$ |
11.5.195...000.1 |
$x^{11} - 5 x^{10} + 10 x^{9} + 8 x^{8} - 115 x^{7} + 47 x^{6} + 425 x^{5} + 65 x^{4} - 184 x^{3} - 1020 x^{2} - 960 x - 240$ |
$11$ |
[5,3] |
$-\,2^{15}\cdot 3^{13}\cdot 5^{6}\cdot 7^{4}$ |
$4$ |
$46.0183207242$ |
$288.40767800645347$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$1139358.89632$ |
11.5.520...000.1 |
$x^{11} - x^{10} - 18 x^{9} + 90 x^{7} - 114 x^{6} - 390 x^{5} + 678 x^{4} - 405 x^{3} - 1035 x^{2} + 1080 x + 270$ |
$11$ |
[5,3] |
$-\,2^{23}\cdot 3^{10}\cdot 5^{4}\cdot 7^{5}$ |
$4$ |
$50.2897333839$ |
$747.7885817500154$ |
|
|
|
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$5645514.82931$ |
11.5.637...000.1 |
$x^{11} - x^{10} - 20 x^{9} + 30 x^{8} + 90 x^{7} - 90 x^{6} - 30 x^{5} - 1110 x^{4} + 2280 x^{3} - 1000 x^{2} + 328 x - 568$ |
$11$ |
[5,3] |
$-\,2^{14}\cdot 3^{13}\cdot 5^{12}$ |
$3$ |
$51.2285886435$ |
$293.8430827385019$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$2859461.06402$ |
11.5.967...000.1 |
$x^{11} - 4 x^{10} + 6 x^{9} - 8 x^{8} - 31 x^{7} + 168 x^{6} + 106 x^{5} - 748 x^{4} - 396 x^{3} + 1008 x^{2} + 882 x + 168$ |
$11$ |
[5,3] |
$-\,2^{19}\cdot 3^{9}\cdot 5^{8}\cdot 7^{4}$ |
$4$ |
$53.2087475948$ |
$332.46081383675426$ |
|
|
|
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$8123279.63873$ |
11.5.847...000.1 |
$x^{11} - x^{10} + 10 x^{9} - 405 x^{3} + 405 x^{2} + 324 x - 324$ |
$11$ |
[5,3] |
$-\,2^{8}\cdot 3^{25}\cdot 5^{8}$ |
$3$ |
$64.8095812334$ |
$202.89500913181897$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$5378394.89404$ |
11.5.245...000.1 |
$x^{11} - 4 x^{10} - 2 x^{9} + 36 x^{8} - 30 x^{7} - 264 x^{6} - 16 x^{5} + 1078 x^{4} + 2261 x^{3} - 1220 x^{2} - 5185 x - 1382$ |
$11$ |
[5,3] |
$-\,2^{10}\cdot 3^{12}\cdot 5^{7}\cdot 7^{8}$ |
$4$ |
$71.3798114949$ |
$740.633570458652$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$10477083.7506$ |
11.5.287...000.1 |
$x^{11} - 2 x^{10} - 20 x^{9} + 105 x^{8} - 255 x^{7} - 444 x^{6} + 4878 x^{5} - 12735 x^{4} + 14040 x^{3} - 3040 x^{2} - 6016 x - 1048$ |
$11$ |
[5,3] |
$-\,2^{20}\cdot 3^{15}\cdot 5^{8}\cdot 7^{2}$ |
$4$ |
$72.4341166334$ |
$1261.9981524803231$ |
|
|
|
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$60162090.9342$ |
11.5.941...000.1 |
$x^{11} - 2 x^{10} - 14 x^{9} + 63 x^{8} + 108 x^{7} - 351 x^{6} - 1119 x^{5} - 957 x^{4} + 375 x^{3} + 812 x^{2} + 203 x - 91$ |
$11$ |
[5,3] |
$-\,2^{9}\cdot 3^{14}\cdot 5^{6}\cdot 7^{5}\cdot 11^{4}$ |
$5$ |
$99.4540768028$ |
$6154.131433480169$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$85295653.9896$ |
11.5.467...000.1 |
$x^{11} - 3 x^{10} - 50 x^{9} + 142 x^{8} + 299 x^{7} - 1207 x^{6} + 1430 x^{5} - 3722 x^{4} + 10566 x^{3} - 12480 x^{2} + 4650 x + 630$ |
$11$ |
[5,3] |
$-\,2^{13}\cdot 3^{7}\cdot 5^{8}\cdot 7^{3}\cdot 11^{7}$ |
$5$ |
$115.056955954$ |
$4670.1112810272725$ |
|
|
|
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$7$ |
$1057226413.01$ |