| 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 |
| 40.0.597...625.1 |
$x^{40} - 10 x^{35} + 139 x^{30} + 5380 x^{25} + 28941 x^{20} - 5380 x^{15} + 139 x^{10} + 10 x^{5} + 1$ |
$40$ |
[0,20] |
$5^{50}\cdot 11^{20}$ |
$2$ |
$24.797554190130167$ |
$55.449016844865795$ |
|
|
|
$D_5\times C_{20}$ (as 40T149) |
$[2]$ |
$10$ |
$19$ |
$1598432511220.758$ |
| 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) |
$[11]$ |
$150$ |
$19$ |
$32146857615014.19$ |
| 40.0.118...536.1 |
$x^{40} + x^{38} - x^{34} - x^{32} + x^{28} + x^{26} - x^{22} - x^{20} - x^{18} + x^{14} + x^{12} - x^{8} - x^{6} + x^{2} + 1$ |
$40$ |
[0,20] |
$2^{40}\cdot 3^{20}\cdot 11^{36}$ |
$3$ |
$29.9808567728$ |
$29.980856772829956$ |
✓ |
✓ |
✓ |
$C_2^2\times C_{10}$ (as 40T7) |
$[11]$ |
$132$ |
$19$ |
$45016485591237.79$ |
| 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) |
$[55]$ |
$100$ |
$19$ |
$144312257071955.8$ |
| 40.0.102...625.1 |
$x^{40} - x^{39} - x^{38} + 4 x^{37} - 4 x^{36} - 4 x^{35} + 17 x^{34} - 17 x^{33} - 17 x^{32} + 72 x^{31} - 72 x^{30} + 127 x^{29} + 106 x^{28} - 504 x^{27} + 491 x^{26} + 496 x^{25} - 2088 x^{24} + 2091 x^{23} + 2090 x^{22} - 8856 x^{21} + 8855 x^{20} + 8856 x^{19} + 2090 x^{18} - 2091 x^{17} - 2088 x^{16} - 496 x^{15} + 491 x^{14} + 504 x^{13} + 106 x^{12} - 127 x^{11} - 72 x^{10} - 72 x^{9} - 17 x^{8} + 17 x^{7} + 17 x^{6} + 4 x^{5} - 4 x^{4} - 4 x^{3} - x^{2} + x + 1$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{20}\cdot 11^{36}$ |
$3$ |
$33.5196168839$ |
$33.51961688386638$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
$[22]$ |
$66$ |
$19$ |
$138297149643015.1$ |
| 40.0.373...536.1 |
$x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1$ |
$40$ |
[0,20] |
$2^{80}\cdot 11^{36}$ |
$2$ |
$34.6189114567$ |
$34.618911456657976$ |
✓ |
✓ |
✓ |
$C_2^2\times C_{10}$ (as 40T7) |
$[55]$ |
$88$ |
$19$ |
$172972974175441.34$ |
| 40.0.791...161.1 |
$x^{40} - x^{39} + x^{38} - x^{37} + x^{36} - x^{35} + x^{34} - x^{33} + x^{32} - x^{31} + x^{30} - x^{29} + x^{28} - x^{27} + x^{26} - x^{25} + x^{24} - x^{23} + x^{22} - x^{21} + x^{20} - x^{19} + x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ |
$40$ |
[0,20] |
$41^{39}$ |
$1$ |
$37.3649375129$ |
$37.36493751286065$ |
✓ |
✓ |
✓ |
$C_{40}$ (as 40T1) |
$[11, 11]$ |
$82$ |
$19$ |
$310417721980536.1$ |
| 40.0.324...000.1 |
$x^{40} - 3 x^{38} + 8 x^{36} - 21 x^{34} + 55 x^{32} - 144 x^{30} + 377 x^{28} - 987 x^{26} + 2584 x^{24} - 6765 x^{22} + 17711 x^{20} - 6765 x^{18} + 2584 x^{16} - 987 x^{14} + 377 x^{12} - 144 x^{10} + 55 x^{8} - 21 x^{6} + 8 x^{4} - 3 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{40}\cdot 5^{20}\cdot 11^{36}$ |
$3$ |
$38.7051196621$ |
$38.70511966206675$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
$[62]$ |
$44$ |
$19$ |
$645826241875575.0$ |
| 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) |
$[55]$ |
$30$ |
$19$ |
$636238292225226.0$ |
| 40.0.860...761.1 |
$x^{40} - x^{39} + 2 x^{38} - 5 x^{37} + 5 x^{36} - 10 x^{35} + 17 x^{34} - 17 x^{33} + 34 x^{32} - 45 x^{31} + 45 x^{30} - 23 x^{29} + 22 x^{28} + 45 x^{27} - 157 x^{26} + 250 x^{25} - 585 x^{24} + 969 x^{23} - 1426 x^{22} + 2565 x^{21} - 3589 x^{20} + 5130 x^{19} - 5704 x^{18} + 7752 x^{17} - 9360 x^{16} + 8000 x^{15} - 10048 x^{14} + 5760 x^{13} + 5632 x^{12} - 11776 x^{11} + 46080 x^{10} - 92160 x^{9} + 139264 x^{8} - 139264 x^{7} + 278528 x^{6} - 327680 x^{5} + 327680 x^{4} - 655360 x^{3} + 524288 x^{2} - 524288 x + 1048576$ |
$40$ |
[0,20] |
$3^{20}\cdot 7^{20}\cdot 11^{36}$ |
$3$ |
$39.6609455568$ |
$39.66094555677728$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
not computed |
$66$ |
$19$ |
|
| 40.0.119...041.1 |
$x^{40} - x + 1$ |
$40$ |
[0,20] |
$89\cdot 2963\cdot 2969\cdot 36703533640127\cdot 206798756592464370511\cdot 2015339302026829599091$ |
$6$ |
$39.9906437988$ |
$1.0943794154078476e+32$ |
|
|
✓ |
$S_{40}$ (as 40T315842) |
trivial |
$2$ |
$19$ |
$9483736502678452.0$ |
| 40.2.122...959.1 |
$x^{40} - x - 1$ |
$40$ |
[2,19] |
$-\,25788481\cdot 47\!\cdots\!39$ |
$2$ |
$40.0092716221$ |
$1.1046199954558292e+32$ |
|
|
✓ |
$S_{40}$ (as 40T315842) |
trivial |
$2$ |
$20$ |
$8469994147830637.0$ |
| 40.0.124...736.1 |
$x^{40} - 2 x^{38} + 8 x^{34} - 16 x^{32} + 64 x^{28} - 128 x^{26} + 512 x^{22} - 1024 x^{20} + 2048 x^{18} - 8192 x^{14} + 16384 x^{12} - 65536 x^{8} + 131072 x^{6} - 524288 x^{2} + 1048576$ |
$40$ |
[0,20] |
$2^{60}\cdot 3^{20}\cdot 11^{36}$ |
$3$ |
$42.3993342597$ |
$42.399334259701384$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
not computed |
$66$ |
$19$ |
|
| 40.0.124...736.2 |
$x^{40} + 2 x^{38} - 8 x^{34} - 16 x^{32} + 64 x^{28} + 128 x^{26} - 512 x^{22} - 1024 x^{20} - 2048 x^{18} + 8192 x^{14} + 16384 x^{12} - 65536 x^{8} - 131072 x^{6} + 524288 x^{2} + 1048576$ |
$40$ |
[0,20] |
$2^{60}\cdot 3^{20}\cdot 11^{36}$ |
$3$ |
$42.3993342597$ |
$42.399334259701384$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
not computed |
$66$ |
$19$ |
|
| 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) |
$[155]$ |
$20$ |
$19$ |
$2347083738648341.5$ |
| 40.0.271...136.1 |
$x^{40} + 3 x^{38} + 5 x^{36} + 3 x^{34} - 11 x^{32} - 45 x^{30} - 91 x^{28} - 93 x^{26} + 85 x^{24} + 627 x^{22} + 1541 x^{20} + 2508 x^{18} + 1360 x^{16} - 5952 x^{14} - 23296 x^{12} - 46080 x^{10} - 45056 x^{8} + 49152 x^{6} + 327680 x^{4} + 786432 x^{2} + 1048576$ |
$40$ |
[0,20] |
$2^{40}\cdot 7^{20}\cdot 11^{36}$ |
$3$ |
$45.796515187$ |
$45.79651518704091$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
not computed |
$44$ |
$19$ |
|
| 40.0.890...496.1 |
$x^{40} - 25 x^{36} + 441 x^{32} - 3794 x^{28} + 23626 x^{24} - 66403 x^{20} + 133864 x^{16} - 62097 x^{12} + 23622 x^{8} - 155 x^{4} + 1$ |
$40$ |
[0,20] |
$2^{80}\cdot 3^{20}\cdot 11^{32}$ |
$3$ |
$47.1774830006$ |
$47.177483000606586$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
$[5, 5, 5]$ |
$24$ |
$19$ |
$7121371366090164.0$ |
| 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 |
$50$ |
$19$ |
|
| 40.40.100...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...625.1 |
$x^{40} - x^{39} + 11 x^{38} - 11 x^{37} + 77 x^{36} - 76 x^{35} + 439 x^{34} - 429 x^{33} + 2233 x^{32} - 2167 x^{31} + 9197 x^{30} - 8833 x^{29} + 32603 x^{28} - 30778 x^{27} + 102597 x^{26} - 95699 x^{25} + 285912 x^{24} - 263693 x^{23} + 659494 x^{22} - 595562 x^{21} + 1330759 x^{20} - 1163338 x^{19} + 2342802 x^{18} - 1938861 x^{17} + 3371093 x^{16} - 2519131 x^{15} + 3317622 x^{14} - 1836384 x^{13} + 2360500 x^{12} - 558855 x^{11} + 869342 x^{10} - 264572 x^{9} + 355025 x^{8} - 154704 x^{7} + 86679 x^{6} - 26432 x^{5} + 14707 x^{4} - 1397 x^{3} + 132 x^{2} - 12 x + 1$ |
$40$ |
[0,20] |
$3^{20}\cdot 5^{30}\cdot 11^{36}$ |
$3$ |
$50.1235182543$ |
$50.12351825429183$ |
✓ |
✓ |
? |
$C_2\times C_{20}$ (as 40T2) |
$[2, 4210]$ |
$10$ |
$19$ |
$276594299286030.2$ |
| 40.0.100...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) |
$[2, 9262]$ |
$6$ |
$19$ |
$60790762850097.93$ |
| 40.0.235...625.1 |
$x^{40} - x^{38} - 8 x^{36} + 17 x^{34} + 55 x^{32} - 208 x^{30} - 287 x^{28} + 2159 x^{26} + 424 x^{24} - 19855 x^{22} + 16039 x^{20} - 178695 x^{18} + 34344 x^{16} + 1573911 x^{14} - 1883007 x^{12} - 12282192 x^{10} + 29229255 x^{8} + 81310473 x^{6} - 344373768 x^{4} - 387420489 x^{2} + 3486784401$ |
$40$ |
[0,20] |
$5^{20}\cdot 7^{20}\cdot 11^{36}$ |
$3$ |
$51.2020605454$ |
$51.202060545412486$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
not computed |
$22$ |
$19$ |
|
| 40.0.771...000.1 |
$x^{40} - 27 x^{38} + 452 x^{36} - 4707 x^{34} + 35613 x^{32} - 189939 x^{30} + 758623 x^{28} - 2202717 x^{26} + 4873258 x^{24} - 8161689 x^{22} + 10602647 x^{20} - 10506063 x^{18} + 8018080 x^{16} - 4542648 x^{14} + 1926084 x^{12} - 569703 x^{10} + 122757 x^{8} - 16992 x^{6} + 1555 x^{4} - 45 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{40}\cdot 3^{20}\cdot 5^{20}\cdot 11^{32}$ |
$4$ |
$52.7460294983$ |
$52.74602949834854$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
$[341]$ |
$12$ |
$19$ |
$17492090815064632$ |
| 40.0.129...000.1 |
$x^{40} - 20 x^{38} + 230 x^{36} - 1800 x^{34} + 10625 x^{32} - 49003 x^{30} + 181750 x^{28} - 547185 x^{26} + 1349050 x^{24} - 2717025 x^{22} + 4465008 x^{20} - 5912800 x^{18} + 6247290 x^{16} - 5116175 x^{14} + 3173350 x^{12} - 1380878 x^{10} + 400970 x^{8} - 52915 x^{6} + 4850 x^{4} - 75 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{40}\cdot 3^{20}\cdot 5^{68}$ |
$3$ |
$53.4367000111$ |
$53.43670001107682$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
$[11, 55]$ |
$12$ |
$19$ |
$12293887094064384$ |
| 40.0.204...561.1 |
$x^{40} - x^{39} - 3 x^{38} + 10 x^{37} - 10 x^{36} - 30 x^{35} + 127 x^{34} - 127 x^{33} - 381 x^{32} + 1540 x^{31} - 1540 x^{30} + 5017 x^{29} + 9192 x^{28} - 47740 x^{27} + 39883 x^{26} + 133500 x^{25} - 518980 x^{24} + 534289 x^{23} + 1583184 x^{22} - 6478780 x^{21} + 6419731 x^{20} + 19436340 x^{19} + 14248656 x^{18} - 14425803 x^{17} - 42037380 x^{16} - 32440500 x^{15} + 29074707 x^{14} + 104407380 x^{13} + 60308712 x^{12} - 98749611 x^{11} - 90935460 x^{10} - 272806380 x^{9} - 202479021 x^{8} + 202479021 x^{7} + 607437063 x^{6} + 430467210 x^{5} - 430467210 x^{4} - 1291401630 x^{3} - 1162261467 x^{2} + 1162261467 x + 3486784401$ |
$40$ |
[0,20] |
$3^{20}\cdot 11^{36}\cdot 13^{20}$ |
$3$ |
$54.0487581884$ |
$54.04875818839011$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
not computed |
$66$ |
$19$ |
|
| 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) |
$[2605]$ |
$16$ |
$19$ |
$4506035972876552.0$ |
| 40.0.339...000.1 |
$x^{40} - 6 x^{38} + 32 x^{36} - 168 x^{34} + 880 x^{32} - 4608 x^{30} + 24128 x^{28} - 126336 x^{26} + 661504 x^{24} - 3463680 x^{22} + 18136064 x^{20} - 13854720 x^{18} + 10584064 x^{16} - 8085504 x^{14} + 6176768 x^{12} - 4718592 x^{10} + 3604480 x^{8} - 2752512 x^{6} + 2097152 x^{4} - 1572864 x^{2} + 1048576$ |
$40$ |
[0,20] |
$2^{60}\cdot 5^{20}\cdot 11^{36}$ |
$3$ |
$54.7373051594$ |
$54.73730515936835$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
not computed |
$22$ |
$19$ |
|
| 40.0.339...000.2 |
$x^{40} + 6 x^{38} + 32 x^{36} + 168 x^{34} + 880 x^{32} + 4608 x^{30} + 24128 x^{28} + 126336 x^{26} + 661504 x^{24} + 3463680 x^{22} + 18136064 x^{20} + 13854720 x^{18} + 10584064 x^{16} + 8085504 x^{14} + 6176768 x^{12} + 4718592 x^{10} + 3604480 x^{8} + 2752512 x^{6} + 2097152 x^{4} + 1572864 x^{2} + 1048576$ |
$40$ |
[0,20] |
$2^{60}\cdot 5^{20}\cdot 11^{36}$ |
$3$ |
$54.7373051594$ |
$54.73730515936835$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
not computed |
$22$ |
$19$ |
|
| 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 |
$22$ |
$19$ |
|
| 40.0.445...000.1 |
$x^{40} - 3 x^{20} + 3$ |
$40$ |
[0,20] |
$2^{80}\cdot 3^{39}\cdot 5^{40}$ |
$3$ |
$58.3745060922$ |
$114.60734901103238$ |
|
|
✓ |
$D_8:C_2\times F_5$ (as 40T523) |
not computed |
$6$ |
$19$ |
|
| 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) |
$[1525]$ |
$22$ |
$19$ |
$44099133482673080$ |
| 40.0.130...936.1 |
$x^{40} - 20 x^{38} + 231 x^{36} - 1812 x^{34} + 10709 x^{32} - 49280 x^{30} + 181674 x^{28} - 540148 x^{26} + 1304886 x^{24} - 2544812 x^{22} + 3994121 x^{20} - 4954644 x^{18} + 4817692 x^{16} - 3548680 x^{14} + 1959963 x^{12} - 753104 x^{10} + 202622 x^{8} - 30356 x^{6} + 3025 x^{4} - 60 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{80}\cdot 3^{20}\cdot 11^{36}$ |
$3$ |
$59.9617135457$ |
$59.96171354565991$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
$[22, 110]$ |
$6$ |
$19$ |
$25665787785126296$ |
| 40.40.130...936.1 |
$x^{40} - 40 x^{38} + 741 x^{36} - 8436 x^{34} + 66044 x^{32} - 376960 x^{30} + 1622694 x^{28} - 5375528 x^{26} + 13860054 x^{24} - 27947920 x^{22} + 44043506 x^{20} - 53927016 x^{18} + 50713585 x^{16} - 35964944 x^{14} + 18713229 x^{12} - 6857500 x^{10} + 1662386 x^{8} - 240976 x^{6} + 17560 x^{4} - 480 x^{2} + 1$ |
$40$ |
[40,0] |
$2^{80}\cdot 3^{20}\cdot 11^{36}$ |
$3$ |
$59.9617135457$ |
$59.96171354565991$ |
|
✓ |
✓ |
$C_2^2\times C_{10}$ (as 40T7) |
trivial |
$2$ |
$39$ |
$73555688392588420000000$ |
| 40.0.130...936.2 |
$x^{40} - 4 x^{38} + 15 x^{36} - 56 x^{34} + 209 x^{32} - 780 x^{30} + 2911 x^{28} - 10864 x^{26} + 40545 x^{24} - 151316 x^{22} + 564719 x^{20} - 151316 x^{18} + 40545 x^{16} - 10864 x^{14} + 2911 x^{12} - 780 x^{10} + 209 x^{8} - 56 x^{6} + 15 x^{4} - 4 x^{2} + 1$ |
$40$ |
[0,20] |
$2^{80}\cdot 3^{20}\cdot 11^{36}$ |
$3$ |
$59.9617135457$ |
$59.96171354565991$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
$[5, 10, 110]$ |
$22$ |
$19$ |
$24039412784024376$ |
| 40.0.130...936.3 |
$x^{40} + 57 x^{36} + 1280 x^{32} + 14374 x^{28} + 85046 x^{24} + 259698 x^{20} + 379157 x^{16} + 222625 x^{12} + 41990 x^{8} + 820 x^{4} + 1$ |
$40$ |
[0,20] |
$2^{80}\cdot 3^{20}\cdot 11^{36}$ |
$3$ |
$59.9617135457$ |
$59.96171354565991$ |
✓ |
✓ |
? |
$C_2^2\times C_{10}$ (as 40T7) |
$[110, 110]$ |
$4$ |
$19$ |
$1535102994471753.0$ |
