| 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 |
| 40.0.287...625.1 |
$x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} - x^{12} + x^{10} - x^{6} + x^{5} - x + 1$ |
$40$ |
[0,20] |
$5^{30}\cdot 11^{36}$ |
$2$ |
$28.9388267568$ |
$28.93882675684651$ |
✓ |
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
$[10]$ |
$110$ |
$19$ |
$30395381425048.965$ |
| 40.0.295...625.1 |
$x^{40} - x^{35} + x^{25} - x^{20} + x^{15} - x^{5} + 1$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{70}$ |
$2$ |
$28.9573046322$ |
$28.957304632206725$ |
✓ |
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
$[11]$ |
$150$ |
$19$ |
$32146857615014.19$ |
| 40.0.931...000.1 |
$x^{40} - x^{30} + x^{20} - x^{10} + 1$ |
$40$ |
[0,20] |
$2^{40}\cdot 5^{70}$ |
$2$ |
$33.4370152488$ |
$33.4370152488211$ |
✓ |
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
$[55]$ |
$100$ |
$19$ |
$144312257071955.8$ |
| 40.0.685...625.1 |
$x^{40} - x^{39} - 4 x^{38} + 7 x^{37} - x^{36} - x^{35} + 43 x^{34} - 99 x^{33} - 80 x^{32} + 377 x^{31} + 182 x^{30} - 676 x^{29} + 119 x^{28} - 544 x^{27} - 3261 x^{26} + 6247 x^{25} + 11925 x^{24} - 19250 x^{23} - 3176 x^{22} + 16639 x^{21} - 17018 x^{20} + 43346 x^{19} + 2424 x^{18} - 96822 x^{17} + 39515 x^{16} + 82301 x^{15} + 12498 x^{14} - 25677 x^{13} - 3560 x^{12} - 33345 x^{11} - 17836 x^{10} + 19768 x^{9} + 19004 x^{8} - 7029 x^{7} + 393 x^{6} + 406 x^{5} - 125 x^{4} + 46 x^{3} - 3 x^{2} - 3 x + 1$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{30}\cdot 11^{32}$ |
$3$ |
$39.4368554623$ |
$39.436855462307015$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[55]$ |
$30$ |
$19$ |
$636238292225226.0$ |
| 40.0.675...625.1 |
$x^{40} - 11 x^{35} + 89 x^{30} - 627 x^{25} + 4049 x^{20} - 20064 x^{15} + 91136 x^{10} - 360448 x^{5} + 1048576$ |
$40$ |
[0,20] |
$5^{70}\cdot 7^{20}$ |
$2$ |
$44.2330134663$ |
$44.23301346632757$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$50$ |
$19$ |
|
| 40.0.216...000.1 |
$x^{40} - 9 x^{38} + 53 x^{36} - 260 x^{34} + 1156 x^{32} - 3971 x^{30} + 11685 x^{28} - 30590 x^{26} + 70035 x^{24} - 124361 x^{22} + 193618 x^{20} - 264514 x^{18} + 292022 x^{16} - 203056 x^{14} + 128969 x^{12} - 72116 x^{10} + 29056 x^{8} - 2353 x^{6} + 190 x^{4} - 15 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{40}\cdot 5^{30}\cdot 11^{32}$ |
$3$ |
$45.5377582343$ |
$45.53775823431064$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[155]$ |
$20$ |
$19$ |
$2347083738648341.5$ |
| 40.0.976...000.1 |
$x^{40} - 32 x^{30} + 1024 x^{20} - 32768 x^{10} + 1048576$ |
$40$ |
[0,20] |
$2^{60}\cdot 5^{70}$ |
$2$ |
$47.2870804502$ |
$47.28708045015879$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$50$ |
$19$ |
|
| 40.0.976...000.2 |
$x^{40} + 32 x^{30} + 1024 x^{20} + 32768 x^{10} + 1048576$ |
$40$ |
[0,20] |
$2^{60}\cdot 5^{70}$ |
$2$ |
$47.2870804502$ |
$47.28708045015879$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$50$ |
$19$ |
|
| 40.0.100...625.1 |
$x^{40} - x^{39} + 11 x^{38} - 11 x^{37} + 77 x^{36} - 76 x^{35} + 439 x^{34} - 429 x^{33} + 2233 x^{32} - 2167 x^{31} + 9197 x^{30} - 8833 x^{29} + 32603 x^{28} - 30778 x^{27} + 102597 x^{26} - 95699 x^{25} + 285912 x^{24} - 263693 x^{23} + 659494 x^{22} - 595562 x^{21} + 1330759 x^{20} - 1163338 x^{19} + 2342802 x^{18} - 1938861 x^{17} + 3371093 x^{16} - 2519131 x^{15} + 3317622 x^{14} - 1836384 x^{13} + 2360500 x^{12} - 558855 x^{11} + 869342 x^{10} - 264572 x^{9} + 355025 x^{8} - 154704 x^{7} + 86679 x^{6} - 26432 x^{5} + 14707 x^{4} - 1397 x^{3} + 132 x^{2} - 12 x + 1$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{30}\cdot 11^{36}$ |
$3$ |
$50.1235182543$ |
$50.12351825429183$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[2, 4210]$ |
$10$ |
$19$ |
$276594299286030.2$ |
| 40.40.100...625.1 |
$x^{40} - x^{39} - 39 x^{38} + 39 x^{37} + 702 x^{36} - 701 x^{35} - 7736 x^{34} + 7701 x^{33} + 58378 x^{32} - 57817 x^{31} - 319703 x^{30} + 314247 x^{29} + 1313873 x^{28} - 1277913 x^{27} - 4133168 x^{26} + 3963256 x^{25} + 10063407 x^{24} - 9469608 x^{23} - 19054236 x^{22} + 17493203 x^{21} + 28043254 x^{20} - 24933608 x^{19} - 31915288 x^{18} + 27222459 x^{17} + 27803858 x^{16} - 22476466 x^{15} - 18249278 x^{14} + 13764066 x^{13} + 8815690 x^{12} - 6077890 x^{11} - 3029168 x^{10} + 1857788 x^{9} + 703905 x^{8} - 369684 x^{7} - 102396 x^{6} + 43393 x^{5} + 8232 x^{4} - 2512 x^{3} - 288 x^{2} + 48 x + 1$ |
$40$ |
[40,0] |
$3^{20}\cdot 5^{30}\cdot 11^{36}$ |
$3$ |
$50.1235182543$ |
$50.12351825429183$ |
|
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
trivial |
$2$ |
$39$ |
$1967499665744724500000$ |
| 40.0.100...625.2 |
$x^{40} - x^{39} + 5 x^{38} - 5 x^{37} + 20 x^{36} - 19 x^{35} + 74 x^{34} - 65 x^{33} + 265 x^{32} - 210 x^{31} + 936 x^{30} - 1475 x^{29} + 4114 x^{28} - 6060 x^{27} + 15680 x^{26} - 21989 x^{25} + 56355 x^{24} - 75531 x^{23} + 197315 x^{22} - 252030 x^{21} + 682811 x^{20} - 826140 x^{19} + 1114445 x^{18} - 1435731 x^{17} + 1906140 x^{16} - 2365144 x^{15} + 3132335 x^{14} - 3532620 x^{13} + 4695244 x^{12} - 3931240 x^{11} + 5449401 x^{10} + 1139235 x^{9} + 238165 x^{8} + 49790 x^{7} + 10409 x^{6} + 2176 x^{5} + 455 x^{4} + 95 x^{3} + 20 x^{2} + 4 x + 1$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{30}\cdot 11^{36}$ |
$3$ |
$50.1235182543$ |
$50.12351825429183$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$22$ |
$19$ |
|
| 40.0.100...625.3 |
$x^{40} - x^{39} + 21 x^{38} - 18 x^{37} + 249 x^{36} - 191 x^{35} + 2008 x^{34} - 1359 x^{33} + 12160 x^{32} - 7243 x^{31} + 57502 x^{30} - 29496 x^{29} + 218159 x^{28} - 94389 x^{27} + 671689 x^{26} - 234893 x^{25} + 1690845 x^{24} - 452550 x^{23} + 3479454 x^{22} - 637891 x^{21} + 5838877 x^{20} - 598784 x^{19} + 7925819 x^{18} - 188442 x^{17} + 8602640 x^{16} + 356201 x^{15} + 7327393 x^{14} + 688488 x^{13} + 4739830 x^{12} + 533615 x^{11} + 2212864 x^{10} + 232193 x^{9} + 670719 x^{8} + 9081 x^{7} + 109203 x^{6} - 5639 x^{5} + 12525 x^{4} - 994 x^{3} + 252 x^{2} + 12 x + 1$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{30}\cdot 11^{36}$ |
$3$ |
$50.1235182543$ |
$50.12351825429183$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[2, 9262]$ |
$6$ |
$19$ |
$60790762850097.93$ |
| 40.0.280...496.1 |
$x^{40} + 257 x^{32} + 14016 x^{24} + 105419 x^{16} + 23219 x^{8} + 1$ |
$40$ |
[0,20] |
$2^{120}\cdot 11^{32}$ |
$2$ |
$54.4758650202$ |
$54.47586502017841$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[2605]$ |
$16$ |
$19$ |
$4506035972876552.0$ |
| 40.0.569...625.1 |
$x^{40} - 31 x^{35} + 718 x^{30} - 14725 x^{25} + 282001 x^{20} - 3578175 x^{15} + 42397182 x^{10} - 444816117 x^{5} + 3486784401$ |
$40$ |
[0,20] |
$5^{70}\cdot 11^{20}$ |
$2$ |
$55.4490168449$ |
$55.449016844865795$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$50$ |
$19$ |
|
| 40.40.316...000.1 |
$x^{40} - 39 x^{38} + 702 x^{36} - 7735 x^{34} + 58344 x^{32} - 319177 x^{30} + 1308973 x^{28} - 4102514 x^{26} + 9927425 x^{24} - 18613969 x^{22} + 26988270 x^{20} - 30037766 x^{18} + 25334997 x^{16} - 15882694 x^{14} + 7199257 x^{12} - 2269345 x^{10} + 470613 x^{8} - 59241 x^{6} + 4018 x^{4} - 120 x^{2} + 1$ |
$40$ |
[40,0] |
$2^{40}\cdot 5^{30}\cdot 11^{36}$ |
$3$ |
$57.8776535137$ |
$57.87765351369302$ |
|
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
trivial |
$2$ |
$39$ |
$33894240488185236000000$ |
| 40.0.316...000.1 |
$x^{40} + 41 x^{38} + 778 x^{36} + 9065 x^{34} + 72556 x^{32} + 422839 x^{30} + 1855505 x^{28} + 6253910 x^{26} + 16367625 x^{24} + 33406879 x^{22} + 53106978 x^{20} + 65321146 x^{18} + 61394717 x^{16} + 43240794 x^{14} + 22168369 x^{12} + 7925719 x^{10} + 1852081 x^{8} + 255047 x^{6} + 17190 x^{4} + 360 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{40}\cdot 5^{30}\cdot 11^{36}$ |
$3$ |
$57.8776535137$ |
$57.87765351369302$ |
✓ |
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
$[2, 85622]$ |
$4$ |
$19$ |
$60790762850097.93$ |
| 40.0.316...000.2 |
$x^{40} + 11 x^{38} + 77 x^{36} + 440 x^{34} + 2244 x^{32} + 9273 x^{30} + 33033 x^{28} + 104786 x^{26} + 294635 x^{24} + 688611 x^{22} + 1416910 x^{20} + 2574154 x^{18} + 3942422 x^{16} + 4573316 x^{14} + 4694437 x^{12} + 4152720 x^{10} + 2752508 x^{8} + 863819 x^{6} + 263538 x^{4} + 73205 x^{2} + 14641$ |
$40$ |
[0,20] |
$2^{40}\cdot 5^{30}\cdot 11^{36}$ |
$3$ |
$57.8776535137$ |
$57.87765351369302$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$10$ |
$19$ |
|
| 40.0.316...000.3 |
$x^{40} + 5 x^{38} + 20 x^{36} + 75 x^{34} + 275 x^{32} + 1000 x^{30} + 3625 x^{28} + 13125 x^{26} + 47500 x^{24} + 171875 x^{22} + 621875 x^{20} + 859375 x^{18} + 1187500 x^{16} + 1640625 x^{14} + 2265625 x^{12} + 3125000 x^{10} + 4296875 x^{8} + 5859375 x^{6} + 7812500 x^{4} + 9765625 x^{2} + 9765625$ |
$40$ |
[0,20] |
$2^{40}\cdot 5^{30}\cdot 11^{36}$ |
$3$ |
$57.8776535137$ |
$57.87765351369302$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$22$ |
$19$ |
|
| 40.40.324...000.1 |
$x^{40} - 40 x^{38} + 740 x^{36} - 8400 x^{34} + 65450 x^{32} - 371007 x^{30} + 1582210 x^{28} - 5177835 x^{26} + 13144625 x^{24} - 25995750 x^{22} + 39996264 x^{20} - 47552155 x^{18} + 43139880 x^{16} - 29279950 x^{14} + 14438100 x^{12} - 4952883 x^{10} + 1106455 x^{8} - 144655 x^{6} + 9150 x^{4} - 200 x^{2} + 1$ |
$40$ |
[40,0] |
$2^{40}\cdot 3^{20}\cdot 5^{70}$ |
$3$ |
$57.9146092644$ |
$57.91460926441345$ |
|
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
trivial |
$2$ |
$39$ |
$31857175264724490000000$ |
| 40.0.324...000.1 |
$x^{40} + 40 x^{38} + 740 x^{36} + 8400 x^{34} + 65450 x^{32} + 371009 x^{30} + 1582270 x^{28} + 5178645 x^{26} + 13151125 x^{24} + 26030250 x^{22} + 40123776 x^{20} + 47888645 x^{18} + 43779420 x^{16} + 30152050 x^{14} + 15277900 x^{12} + 5507149 x^{10} + 1345115 x^{8} + 206465 x^{6} + 17450 x^{4} + 600 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{40}\cdot 3^{20}\cdot 5^{70}$ |
$3$ |
$57.9146092644$ |
$57.91460926441345$ |
✓ |
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
$[237710]$ |
$4$ |
$19$ |
$64293715230028.38$ |
| 40.0.324...000.2 |
$x^{40} + 20 x^{38} + 230 x^{36} + 1800 x^{34} + 10625 x^{32} + 49005 x^{30} + 181750 x^{28} + 546975 x^{26} + 1346750 x^{24} + 2703375 x^{22} + 4412520 x^{20} + 5771300 x^{18} + 5985150 x^{16} + 4782125 x^{14} + 2915250 x^{12} + 1285650 x^{10} + 409750 x^{8} + 82625 x^{6} + 11250 x^{4} + 625 x^{2} + 25$ |
$40$ |
[0,20] |
$2^{40}\cdot 3^{20}\cdot 5^{70}$ |
$3$ |
$57.9146092644$ |
$57.91460926441345$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$6$ |
$19$ |
|
| 40.0.324...000.3 |
$x^{40} + 243 x^{30} + 59049 x^{20} + 14348907 x^{10} + 3486784401$ |
$40$ |
[0,20] |
$2^{40}\cdot 3^{20}\cdot 5^{70}$ |
$3$ |
$57.9146092644$ |
$57.91460926441345$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$50$ |
$19$ |
|
| 40.0.401...664.1 |
$x^{40} - 4 x^{38} + 14 x^{36} - 48 x^{34} + 164 x^{32} - 560 x^{30} + 1912 x^{28} - 6528 x^{26} + 22288 x^{24} - 76096 x^{22} + 259808 x^{20} - 152192 x^{18} + 89152 x^{16} - 52224 x^{14} + 30592 x^{12} - 17920 x^{10} + 10496 x^{8} - 6144 x^{6} + 3584 x^{4} - 2048 x^{2} + 1024$ |
$40$ |
[0,20] |
$2^{110}\cdot 11^{36}$ |
$2$ |
$58.2218370878$ |
$58.22183708777889$ |
✓ |
✓ |
|
$C_2\times C_{20}$ (as 40T2) |
$[5731]$ |
$22$ |
$19$ |
$59973097516991576$ |
| 40.0.401...664.2 |
$x^{40} + 4 x^{38} + 14 x^{36} + 48 x^{34} + 164 x^{32} + 560 x^{30} + 1912 x^{28} + 6528 x^{26} + 22288 x^{24} + 76096 x^{22} + 259808 x^{20} + 152192 x^{18} + 89152 x^{16} + 52224 x^{14} + 30592 x^{12} + 17920 x^{10} + 10496 x^{8} + 6144 x^{6} + 3584 x^{4} + 2048 x^{2} + 1024$ |
$40$ |
[0,20] |
$2^{110}\cdot 11^{36}$ |
$2$ |
$58.2218370878$ |
$58.22183708777889$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$22$ |
$19$ |
|
| 40.0.673...721.1 |
$x^{40} - x^{39} + 20 x^{38} - 17 x^{37} + 226 x^{36} - 172 x^{35} + 1735 x^{34} - 1174 x^{33} + 9997 x^{32} - 6058 x^{31} + 44934 x^{30} - 24189 x^{29} + 161911 x^{28} - 77302 x^{27} + 472811 x^{26} - 197858 x^{25} + 1127150 x^{24} - 410723 x^{23} + 2190299 x^{22} - 682496 x^{21} + 3457565 x^{20} - 911552 x^{19} + 4383590 x^{18} - 948272 x^{17} + 4405640 x^{16} - 773063 x^{15} + 3426005 x^{14} - 457001 x^{13} + 2008708 x^{12} - 207142 x^{11} + 846197 x^{10} - 53834 x^{9} + 244002 x^{8} - 13431 x^{7} + 43098 x^{6} - 33 x^{5} + 4180 x^{4} - 220 x^{3} + 155 x^{2} + 10 x + 1$ |
$40$ |
[0,20] |
$3^{20}\cdot 41^{38}$ |
$2$ |
$58.9800710306$ |
$58.98007103060146$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[8, 8, 8, 136]$ |
$6$ |
$19$ |
$310417721980536.1$ |
| 40.0.809...689.1 |
$x^{40} - x^{39} - x^{38} + 7 x^{37} - 12 x^{36} - 3 x^{35} + 58 x^{34} - 121 x^{33} + 29 x^{32} + 454 x^{31} - 1170 x^{30} - 413 x^{29} + 4482 x^{28} - 9698 x^{27} + 2592 x^{26} + 35971 x^{25} - 93393 x^{24} + 60913 x^{23} + 261981 x^{22} - 865292 x^{21} + 865161 x^{20} + 1730608 x^{19} + 1651223 x^{18} + 944081 x^{17} + 80422 x^{16} - 555516 x^{15} - 782673 x^{14} - 616850 x^{13} - 281134 x^{12} + 50690 x^{11} + 392197 x^{10} + 232437 x^{9} + 29331 x^{8} - 123822 x^{7} - 181683 x^{6} - 150660 x^{5} - 69255 x^{4} + 15309 x^{3} + 65610 x^{2} + 78732 x + 59049$ |
$40$ |
[0,20] |
$11^{36}\cdot 13^{30}$ |
$2$ |
$59.2530801083$ |
$59.253080108324006$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[1525]$ |
$22$ |
$19$ |
$44099133482673080$ |
| 40.0.156...625.1 |
$x^{40} - x^{39} - 13 x^{38} + 20 x^{37} + 84 x^{36} - 41 x^{35} - 359 x^{34} - 768 x^{33} + 987 x^{32} + 9239 x^{31} - 11046 x^{30} - 44916 x^{29} + 133166 x^{28} - 66478 x^{27} - 944653 x^{26} + 1164448 x^{25} + 4678770 x^{24} - 4718023 x^{23} - 13472506 x^{22} - 1446413 x^{21} + 34263783 x^{20} + 108753318 x^{19} - 122648476 x^{18} - 339047952 x^{17} + 362849376 x^{16} + 551628320 x^{15} - 458037312 x^{14} - 301074432 x^{13} + 809304320 x^{12} - 994491904 x^{11} - 1301196800 x^{10} + 916971520 x^{9} + 1464213504 x^{8} - 551878656 x^{7} - 96944128 x^{6} + 86966272 x^{5} - 1048576 x^{4} + 17432576 x^{3} - 4718592 x^{2} - 1572864 x + 1048576$ |
$40$ |
[0,20] |
$5^{30}\cdot 7^{20}\cdot 11^{32}$ |
$3$ |
$60.2407917757$ |
$60.24079177568486$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$10$ |
$19$ |
|
| 40.0.160...625.1 |
$x^{40} - 61 x^{35} + 3964 x^{30} - 256627 x^{25} + 16617499 x^{20} + 62360361 x^{15} + 234070236 x^{10} + 875283327 x^{5} + 3486784401$ |
$40$ |
[0,20] |
$5^{70}\cdot 13^{20}$ |
$2$ |
$60.279436489$ |
$60.27943648904789$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$50$ |
$19$ |
|
| 40.0.226...000.1 |
$x^{40} - 18 x^{38} + 212 x^{36} - 2080 x^{34} + 18496 x^{32} - 127072 x^{30} + 747840 x^{28} - 3915520 x^{26} + 17928960 x^{24} - 63672832 x^{22} + 198264832 x^{20} - 541724672 x^{18} + 1196122112 x^{16} - 1663434752 x^{14} + 2113028096 x^{12} - 2363097088 x^{10} + 1904214016 x^{8} - 308412416 x^{6} + 49807360 x^{4} - 7864320 x^{2} + 1048576$ |
$40$ |
[0,20] |
$2^{60}\cdot 5^{30}\cdot 11^{32}$ |
$3$ |
$64.400115295$ |
$64.4001152950292$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$10$ |
$19$ |
|
| 40.0.226...000.2 |
$x^{40} + 18 x^{38} + 212 x^{36} + 2080 x^{34} + 18496 x^{32} + 127072 x^{30} + 747840 x^{28} + 3915520 x^{26} + 17928960 x^{24} + 63672832 x^{22} + 198264832 x^{20} + 541724672 x^{18} + 1196122112 x^{16} + 1663434752 x^{14} + 2113028096 x^{12} + 2363097088 x^{10} + 1904214016 x^{8} + 308412416 x^{6} + 49807360 x^{4} + 7864320 x^{2} + 1048576$ |
$40$ |
[0,20] |
$2^{60}\cdot 5^{30}\cdot 11^{32}$ |
$3$ |
$64.400115295$ |
$64.4001152950292$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$10$ |
$19$ |
|
| 40.40.102...000.1 |
$x^{40} - 40 x^{38} + 740 x^{36} - 8400 x^{34} + 65450 x^{32} - 371008 x^{30} + 1582240 x^{28} - 5178240 x^{26} + 13147875 x^{24} - 26013000 x^{22} + 40060019 x^{20} - 47720380 x^{18} + 43459480 x^{16} - 29715200 x^{14} + 14855725 x^{12} - 5226012 x^{10} + 1221495 x^{8} - 172920 x^{6} + 12475 x^{4} - 300 x^{2} + 1$ |
$40$ |
[40,0] |
$2^{80}\cdot 5^{70}$ |
$2$ |
$66.8740304976$ |
$66.8740304976422$ |
|
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
trivial |
$2$ |
$39$ |
$759341976624057400000000$ |
| 40.0.102...000.1 |
$x^{40} + 40 x^{38} + 740 x^{36} + 8400 x^{34} + 65450 x^{32} + 371008 x^{30} + 1582240 x^{28} + 5178240 x^{26} + 13147875 x^{24} + 26013000 x^{22} + 40060019 x^{20} + 47720380 x^{18} + 43459480 x^{16} + 29715200 x^{14} + 14855725 x^{12} + 5226012 x^{10} + 1221495 x^{8} + 172920 x^{6} + 12475 x^{4} + 300 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{80}\cdot 5^{70}$ |
$2$ |
$66.8740304976$ |
$66.8740304976422$ |
✓ |
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
$[542102]$ |
$2$ |
$19$ |
$144312257071955.8$ |
| 40.0.102...000.2 |
$x^{40} + 60 x^{36} + 1450 x^{32} + 18100 x^{28} + 124375 x^{24} + 462515 x^{20} + 846200 x^{16} + 609125 x^{12} + 139875 x^{8} + 6875 x^{4} + 25$ |
$40$ |
[0,20] |
$2^{80}\cdot 5^{70}$ |
$2$ |
$66.8740304976$ |
$66.8740304976422$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[66110]$ |
$4$ |
$19$ |
$4715770945035671.0$ |
| 40.0.212...096.1 |
$x^{40} + 39 x^{38} + 703 x^{36} + 7770 x^{34} + 58905 x^{32} + 324632 x^{30} + 1344904 x^{28} + 4272048 x^{26} + 10518300 x^{24} + 20160075 x^{22} + 30045015 x^{20} + 34597290 x^{18} + 30421755 x^{16} + 20058300 x^{14} + 9657700 x^{12} + 3268760 x^{10} + 735471 x^{8} + 100947 x^{6} + 7315 x^{4} + 210 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{40}\cdot 41^{38}$ |
$2$ |
$68.1043197727$ |
$68.104319772682$ |
✓ |
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$4$ |
$19$ |
|
| 40.0.344...625.1 |
$x^{40} - 101 x^{35} + 11225 x^{30} - 1237149 x^{25} + 136446449 x^{20} + 1266840576 x^{15} + 11770265600 x^{10} + 108447924224 x^{5} + 1099511627776$ |
$40$ |
[0,20] |
$5^{70}\cdot 17^{20}$ |
$2$ |
$68.9321728381$ |
$68.9321728381389$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$50$ |
$19$ |
|
| 40.0.410...936.1 |
$x^{40} + 40 x^{38} + 740 x^{36} + 8400 x^{34} + 65449 x^{32} + 370976 x^{30} + 1581776 x^{28} + 5174208 x^{26} + 13124476 x^{24} + 25917344 x^{22} + 39776912 x^{20} + 47106624 x^{18} + 42484835 x^{16} + 28593712 x^{14} + 13942072 x^{12} + 4719648 x^{10} + 1042879 x^{8} + 137208 x^{6} + 9260 x^{4} + 240 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{120}\cdot 11^{36}$ |
$2$ |
$69.2378229133$ |
$69.23782291331595$ |
✓ |
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
$[1068050]$ |
$2$ |
$19$ |
$172972974175441.34$ |
| 40.40.410...936.1 |
$x^{40} - 40 x^{38} + 740 x^{36} - 8400 x^{34} + 65449 x^{32} - 370976 x^{30} + 1581776 x^{28} - 5174208 x^{26} + 13124476 x^{24} - 25917344 x^{22} + 39776912 x^{20} - 47106624 x^{18} + 42484835 x^{16} - 28593712 x^{14} + 13942072 x^{12} - 4719648 x^{10} + 1042879 x^{8} - 137208 x^{6} + 9260 x^{4} - 240 x^{2} + 1$ |
$40$ |
[40,0] |
$2^{120}\cdot 11^{36}$ |
$2$ |
$69.2378229133$ |
$69.23782291331595$ |
|
✓ |
✓ |
$C_2\times C_{20}$ (as 40T2) |
trivial |
$2$ |
$39$ |
$1209836226640861800000000$ |
| 40.0.410...936.2 |
$x^{40} + 385 x^{32} + 38720 x^{24} + 842523 x^{16} + 1449459 x^{8} + 14641$ |
$40$ |
[0,20] |
$2^{120}\cdot 11^{36}$ |
$2$ |
$69.2378229133$ |
$69.23782291331595$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$8$ |
$19$ |
|
| 40.0.253...489.1 |
$x^{40} - x^{39} + 7 x^{38} - 12 x^{37} + 52 x^{36} - 116 x^{35} + 409 x^{34} - 1041 x^{33} + 3327 x^{32} - 9048 x^{31} + 27560 x^{30} + 44511 x^{29} + 108474 x^{28} + 195200 x^{27} + 472595 x^{26} + 762568 x^{25} + 2159728 x^{24} + 2693075 x^{23} + 10555266 x^{22} + 7000344 x^{21} + 56864599 x^{20} - 7000344 x^{19} + 10555266 x^{18} - 2693075 x^{17} + 2159728 x^{16} - 762568 x^{15} + 472595 x^{14} - 195200 x^{13} + 108474 x^{12} - 44511 x^{11} + 27560 x^{10} + 9048 x^{9} + 3327 x^{8} + 1041 x^{7} + 409 x^{6} + 116 x^{5} + 52 x^{4} + 12 x^{3} + 7 x^{2} + x + 1$ |
$40$ |
[0,20] |
$11^{36}\cdot 17^{30}$ |
$2$ |
$72.4586282071$ |
$72.45862820705953$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[167977]$ |
$22$ |
$19$ |
$65411797196858550$ |
| 40.0.318...625.1 |
$x^{40} - 101 x^{35} + 7076 x^{30} - 399051 x^{25} + 18191651 x^{20} - 1247034375 x^{15} + 69101562500 x^{10} - 3082275390625 x^{5} + 95367431640625$ |
$40$ |
[0,20] |
$5^{70}\cdot 19^{20}$ |
$2$ |
$72.8742852216$ |
$72.87428522161984$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$50$ |
$19$ |
|
| 40.0.455...625.1 |
$x^{40} - x^{39} - x^{38} + 19 x^{37} - 24 x^{36} + 53 x^{35} + 236 x^{34} - 529 x^{33} + 884 x^{32} + 3395 x^{31} - 2402 x^{30} + 4304 x^{29} + 47648 x^{28} - 36412 x^{27} - 24459 x^{26} + 155327 x^{25} - 180921 x^{24} - 713657 x^{23} + 926706 x^{22} - 293393 x^{21} - 1658812 x^{20} + 3360939 x^{19} + 3678122 x^{18} - 6001107 x^{17} + 7599798 x^{16} + 4424280 x^{15} - 12065200 x^{14} - 5513654 x^{13} + 11699025 x^{12} - 5547842 x^{11} - 5967172 x^{10} + 6548168 x^{9} + 2801471 x^{8} - 3833465 x^{7} - 78700 x^{6} + 576250 x^{5} + 228750 x^{4} + 1281250 x^{3} - 734375 x^{2} - 312500 x + 390625$ |
$40$ |
[0,20] |
$5^{30}\cdot 31^{36}$ |
$2$ |
$73.5280464922$ |
$73.52804649223957$ |
✓ |
✓ |
|
$C_2\times C_{20}$ (as 40T2) |
$[2, 4, 4, 20, 60]$ |
$10$ |
$19$ |
$969023078310684700$ |
| 40.40.184...625.1 |
$x^{40} - x^{39} - 58 x^{38} + 53 x^{37} + 1486 x^{36} - 1226 x^{35} - 22237 x^{34} + 16342 x^{33} + 216813 x^{32} - 139848 x^{31} - 1457140 x^{30} + 812165 x^{29} + 6977251 x^{28} - 3307776 x^{27} - 24306985 x^{26} + 9650330 x^{25} + 62453182 x^{24} - 20449687 x^{23} - 119327033 x^{22} + 31725068 x^{21} + 170133237 x^{20} - 36107412 x^{19} - 180748378 x^{18} + 30022768 x^{17} + 142090232 x^{16} - 18029877 x^{15} - 81534233 x^{14} + 7661653 x^{13} + 33400952 x^{12} - 2229292 x^{11} - 9440783 x^{10} + 421058 x^{9} + 1747746 x^{8} - 46431 x^{7} - 195228 x^{6} + 2013 x^{5} + 11440 x^{4} + 110 x^{3} - 265 x^{2} - 10 x + 1$ |
$40$ |
[40,0] |
$5^{20}\cdot 41^{38}$ |
$2$ |
$76.1429442865$ |
$76.14294428654999$ |
|
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
trivial |
$2$ |
$39$ |
$10069514429260745000000000$ |
| 40.0.229...625.1 |
$x^{40} - x^{39} + 22 x^{38} - 22 x^{37} + 308 x^{36} - 307 x^{35} + 3519 x^{34} - 3498 x^{33} + 35882 x^{32} - 35596 x^{31} + 296429 x^{30} - 293150 x^{29} + 2110547 x^{28} - 2075282 x^{27} + 13374064 x^{26} - 13145659 x^{25} + 75162890 x^{24} - 74206309 x^{23} + 351383846 x^{22} - 349430224 x^{21} + 1448005637 x^{20} - 1445089910 x^{19} + 5267002532 x^{18} - 5024257635 x^{17} + 15902796162 x^{16} - 13906613709 x^{15} + 35229430126 x^{14} - 25437652416 x^{13} + 65099228501 x^{12} - 34784643894 x^{11} + 95934413763 x^{10} - 61702659106 x^{9} + 117125088960 x^{8} - 82784517200 x^{7} + 52680368047 x^{6} - 26420704463 x^{5} + 15228656432 x^{4} - 3213685552 x^{3} + 662073632 x^{2} - 126019697 x + 20151121$ |
$40$ |
[0,20] |
$5^{30}\cdot 7^{20}\cdot 11^{36}$ |
$3$ |
$76.5649388326$ |
$76.5649388325977$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$10$ |
$19$ |
|
| 40.40.229...625.1 |
$x^{40} - x^{39} - 78 x^{38} + 78 x^{37} + 2808 x^{36} - 2797 x^{35} - 61891 x^{34} + 61132 x^{33} + 934252 x^{32} - 910316 x^{31} - 10236731 x^{30} + 9779770 x^{29} + 84201027 x^{28} - 78304622 x^{27} - 530401956 x^{26} + 476024791 x^{25} + 2587528870 x^{24} - 2217966289 x^{23} - 9822625214 x^{22} + 7941388686 x^{21} + 28998395977 x^{20} - 21780235070 x^{19} - 66197093248 x^{18} + 45356621385 x^{17} + 115530235482 x^{16} - 70671998879 x^{15} - 151353912514 x^{14} + 80642756914 x^{13} + 144757030391 x^{12} - 65437791794 x^{11} - 96911211847 x^{10} + 36333104654 x^{9} + 42561792020 x^{8} - 13143856660 x^{7} - 11039037933 x^{6} + 2893122177 x^{5} + 1401644442 x^{4} - 331925242 x^{3} - 55346148 x^{2} + 11969793 x - 440429$ |
$40$ |
[40,0] |
$5^{30}\cdot 7^{20}\cdot 11^{36}$ |
$3$ |
$76.5649388326$ |
$76.5649388325977$ |
|
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$2$ |
$39$ |
|
| 40.0.229...625.2 |
$x^{40} - x^{39} + 10 x^{38} - 10 x^{37} + 80 x^{36} - 69 x^{35} + 589 x^{34} - 380 x^{33} + 4180 x^{32} - 1540 x^{31} + 29261 x^{30} - 73920 x^{29} + 277429 x^{28} - 662420 x^{27} + 2172130 x^{26} - 4823929 x^{25} + 15359600 x^{24} - 31939171 x^{23} + 102866780 x^{22} - 199019700 x^{21} + 668412581 x^{20} - 1182457980 x^{19} + 2618352220 x^{18} - 5055544111 x^{17} + 10626053880 x^{16} - 19553743119 x^{15} + 40886456620 x^{14} - 65624674550 x^{13} + 140732503379 x^{12} - 148285290440 x^{11} + 374504727081 x^{10} + 279391609420 x^{9} + 208525783180 x^{8} + 155444907860 x^{7} + 116259627649 x^{6} + 86168888091 x^{5} + 65388316510 x^{4} + 46574338690 x^{3} + 38584598580 x^{2} + 21221529219 x + 25937424601$ |
$40$ |
[0,20] |
$5^{30}\cdot 7^{20}\cdot 11^{36}$ |
$3$ |
$76.5649388326$ |
$76.5649388325977$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$22$ |
$19$ |
|
| 40.0.229...625.3 |
$x^{40} - 18 x^{39} + 152 x^{38} - 800 x^{37} + 3064 x^{36} - 10008 x^{35} + 32049 x^{34} - 101440 x^{33} + 296109 x^{32} - 789250 x^{31} + 2021570 x^{30} - 5108510 x^{29} + 12425384 x^{28} - 28608228 x^{27} + 63471622 x^{26} - 137818978 x^{25} + 290635519 x^{24} - 589420568 x^{23} + 1156452894 x^{22} - 2209847288 x^{21} + 4106579731 x^{20} - 7379250472 x^{19} + 12845371352 x^{18} - 21684279952 x^{17} + 35554968308 x^{16} - 56311944536 x^{15} + 86289035972 x^{14} - 127319828864 x^{13} + 181966505414 x^{12} - 248991356996 x^{11} + 328793281400 x^{10} - 410912987056 x^{9} + 496328054189 x^{8} - 557798882542 x^{7} + 606994857502 x^{6} - 589952434929 x^{5} + 562299424896 x^{4} - 442214109777 x^{3} + 359771906472 x^{2} - 185412094428 x + 113102086801$ |
$40$ |
[0,20] |
$5^{30}\cdot 7^{20}\cdot 11^{36}$ |
$3$ |
$76.5649388326$ |
$76.5649388325977$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$2$ |
$19$ |
|
| 40.0.235...625.1 |
$x^{40} - 151 x^{35} + 25926 x^{30} - 4386701 x^{25} + 743410601 x^{20} + 13708440625 x^{15} + 253183593750 x^{10} + 4608154296875 x^{5} + 95367431640625$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{70}\cdot 7^{20}$ |
$3$ |
$76.6138266956$ |
$76.61382669555769$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$50$ |
$19$ |
|
| 40.40.235...625.1 |
$x^{40} - 80 x^{38} + 2960 x^{36} - 11 x^{35} - 67200 x^{34} + 770 x^{33} + 1047200 x^{32} - 24640 x^{31} - 11872224 x^{30} + 477400 x^{29} + 101261440 x^{28} - 6252400 x^{27} - 662762880 x^{26} + 58522739 x^{25} + 3365024000 x^{24} - 403616950 x^{23} - 13309824000 x^{22} + 2084212900 x^{21} + 40956171311 x^{20} - 8107946000 x^{19} - 97386692440 x^{18} + 23720246000 x^{17} + 176698891480 x^{16} - 51717568485 x^{15} - 239841990400 x^{14} + 82634574550 x^{13} + 236443720400 x^{12} - 94254254600 x^{11} - 161908455840 x^{10} + 73797867000 x^{9} + 71681548800 x^{8} - 37349092000 x^{7} - 17934217600 x^{6} + 11028952605 x^{5} + 1748896000 x^{4} - 1531206050 x^{3} + 60864000 x^{2} + 46652100 x - 3248255$ |
$40$ |
[40,0] |
$3^{20}\cdot 5^{70}\cdot 7^{20}$ |
$3$ |
$76.6138266956$ |
$76.61382669555769$ |
|
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$2$ |
$39$ |
|
| 40.0.235...625.2 |
$x^{40} + 40 x^{38} + 920 x^{36} - 11 x^{35} + 14400 x^{34} - 550 x^{33} + 170000 x^{32} - 12760 x^{31} + 1568160 x^{30} - 195800 x^{29} + 11635630 x^{28} - 2147200 x^{27} + 70128960 x^{26} - 17908429 x^{25} + 346655600 x^{24} - 115196290 x^{23} + 1404165600 x^{22} - 582311180 x^{21} + 4665057839 x^{20} - 2298348800 x^{19} + 12597743150 x^{18} - 7107601600 x^{17} + 27443275180 x^{16} - 16844703909 x^{15} + 47090141000 x^{14} - 30216401600 x^{13} + 62111345600 x^{12} - 38642127260 x^{11} + 58711819680 x^{10} - 33262310400 x^{9} + 36511599630 x^{8} - 14898545200 x^{7} + 9859544360 x^{6} - 1520467971 x^{5} + 964792600 x^{4} - 59831420 x^{3} + 79872000 x^{2} + 3440580 x + 160801$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{70}\cdot 7^{20}$ |
$3$ |
$76.6138266956$ |
$76.61382669555769$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$6$ |
$19$ |
|
| 40.0.235...625.3 |
$x^{40} + 60 x^{38} + 1770 x^{36} - 11 x^{35} + 33600 x^{34} - 595 x^{33} + 455875 x^{32} - 15470 x^{31} + 4661804 x^{30} - 253575 x^{29} + 37017890 x^{28} - 2905350 x^{27} + 232121040 x^{26} - 24470367 x^{25} + 1159115225 x^{24} - 155450395 x^{23} + 4619721900 x^{22} - 753390260 x^{21} + 14652746289 x^{20} - 2789292800 x^{19} + 36699315280 x^{18} - 7836540800 x^{17} + 71660476320 x^{16} - 16477469024 x^{15} + 107073932800 x^{14} - 25427153280 x^{13} + 119352953600 x^{12} - 28074777600 x^{11} + 95896866816 x^{10} - 21629696000 x^{9} + 53124833280 x^{8} - 11098112000 x^{7} + 18835046400 x^{6} - 3369566208 x^{5} + 3815833600 x^{4} - 429260800 x^{3} + 288358400 x^{2} + 10485760 x + 1048576$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{70}\cdot 7^{20}$ |
$3$ |
$76.6138266956$ |
$76.61382669555769$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
not computed |
$2$ |
$19$ |
|
