| 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 |
| 32.0.247...625.1 |
$x^{32} - 2 x^{31} + x^{29} + 14 x^{28} - 23 x^{27} - 25 x^{26} + 77 x^{25} + 32 x^{24} - 233 x^{23} + 130 x^{22} + 275 x^{21} - 204 x^{20} - 500 x^{19} + 369 x^{18} + 976 x^{17} - 775 x^{16} - 1988 x^{15} + 2706 x^{14} + 1255 x^{13} - 4074 x^{12} + 870 x^{11} + 3435 x^{10} - 2784 x^{9} - 528 x^{8} + 1624 x^{7} - 465 x^{6} - 564 x^{5} + 639 x^{4} - 293 x^{3} + 55 x^{2} - x + 1$ |
$32$ |
[0,16] |
$5^{28}\cdot 13^{16}$ |
$2$ |
$14.7424760172$ |
$22.606204673819228$ |
|
|
? |
$C_8.A_4$ (as 32T402) |
trivial |
$10$ |
$15$ |
$1271231.1521675275$ |
| 32.0.473...000.1 |
$x^{32} + x^{28} - x^{20} - x^{16} - x^{12} + x^{4} + 1$ |
$32$ |
[0,16] |
$2^{64}\cdot 3^{16}\cdot 5^{24}$ |
$3$ |
$23.1658437058$ |
$23.165843705765383$ |
✓ |
✓ |
✓ |
$C_2^3\times C_4$ (as 32T34) |
$[4]$ |
$120$ |
$15$ |
$5926511257.21094$ |
| 32.0.352...129.1 |
$x^{32} - x^{31} + x^{29} - x^{28} + x^{26} - x^{25} + x^{23} - x^{22} + x^{20} - x^{19} + x^{17} - x^{16} + x^{15} - x^{13} + x^{12} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1$ |
$32$ |
[0,16] |
$3^{16}\cdot 17^{30}$ |
$2$ |
$24.666440964$ |
$24.666440964016477$ |
✓ |
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[5]$ |
$102$ |
$15$ |
$9977645145.96466$ |
| 32.0.515...121.1 |
$x^{32} - 5 x^{31} + 22 x^{30} - 73 x^{29} + 220 x^{28} - 519 x^{27} + 1255 x^{26} - 2247 x^{25} + 4413 x^{24} - 6238 x^{23} + 9744 x^{22} - 10830 x^{21} + 13240 x^{20} - 10628 x^{19} + 12053 x^{18} - 5501 x^{17} + 12591 x^{16} - 3062 x^{15} + 17256 x^{14} + 194 x^{13} + 18165 x^{12} + 5659 x^{11} + 13232 x^{10} - 2318 x^{9} - 319 x^{8} - 13445 x^{7} - 6940 x^{6} - 4990 x^{5} + 1466 x^{4} + 2074 x^{3} + 1626 x^{2} + 264 x + 79$ |
$32$ |
[0,16] |
$7^{16}\cdot 13^{28}$ |
$2$ |
$24.960280023$ |
$34.52225265079909$ |
|
|
|
$C_8.A_4$ (as 32T402) |
trivial |
$2$ |
$15$ |
$1483068056.9314811$ |
| 32.0.472...000.1 |
$x^{32} - x^{24} + x^{16} - x^{8} + 1$ |
$32$ |
[0,16] |
$2^{96}\cdot 5^{24}$ |
$2$ |
$26.7496121991$ |
$26.74961219905688$ |
✓ |
✓ |
✓ |
$C_2\times C_4^2$ (as 32T36) |
$[5]$ |
$80$ |
$15$ |
$24306760628.406784$ |
| 32.0.551...000.1 |
$x^{32} + x^{30} - 14 x^{28} - 103 x^{26} + 62 x^{24} + 736 x^{22} + 1892 x^{20} + 4382 x^{18} + 7111 x^{16} + 4382 x^{14} + 1892 x^{12} + 736 x^{10} + 62 x^{8} - 103 x^{6} - 14 x^{4} + x^{2} + 1$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{24}\cdot 29^{8}$ |
$4$ |
$26.8792796542$ |
$62.37594312593305$ |
✓ |
|
|
$C_2^4:C_4$ (as 32T262) |
$[2, 4]$ |
$60$ |
$15$ |
$22391784240.2237$ |
| 32.0.766...000.1 |
$x^{32} - 4 x^{31} + 10 x^{30} - 20 x^{29} + 34 x^{28} - 32 x^{27} - 8 x^{26} + 112 x^{25} - 308 x^{24} + 608 x^{23} - 880 x^{22} + 944 x^{21} - 536 x^{20} - 672 x^{19} + 2960 x^{18} - 6176 x^{17} + 9744 x^{16} - 12352 x^{15} + 11840 x^{14} - 5376 x^{13} - 8576 x^{12} + 30208 x^{11} - 56320 x^{10} + 77824 x^{9} - 78848 x^{8} + 57344 x^{7} - 8192 x^{6} - 65536 x^{5} + 139264 x^{4} - 163840 x^{3} + 163840 x^{2} - 131072 x + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{24}\cdot 17^{8}$ |
$3$ |
$27.1581213743$ |
$55.14573827051111$ |
✓ |
|
? |
$C_4^2:C_2^2$ (as 32T204) |
$[5]$ |
$40$ |
$15$ |
$23735246685.523792$ |
| 32.0.146...776.1 |
$x^{32} - x^{16} + 1$ |
$32$ |
[0,16] |
$2^{128}\cdot 3^{16}$ |
$2$ |
$27.7128129211$ |
$27.712812921102035$ |
✓ |
✓ |
✓ |
$C_2^2\times C_8$ (as 32T37) |
$[3, 3]$ |
$96$ |
$15$ |
$47233168152.25636$ |
| 32.0.146...416.1 |
$x^{32} - 4 x^{30} + 10 x^{28} - 32 x^{26} + 83 x^{24} - 208 x^{22} + 458 x^{20} - 956 x^{18} + 2113 x^{16} - 3824 x^{14} + 7328 x^{12} - 13312 x^{10} + 21248 x^{8} - 32768 x^{6} + 40960 x^{4} - 65536 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{72}\cdot 3^{16}\cdot 13^{8}\cdot 97^{4}$ |
$4$ |
$27.7147153518$ |
$292.57395390451063$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[4]$ |
$24$ |
$15$ |
$32664023933.600838$ |
| 32.0.237...896.1 |
$x^{32} - 8 x^{30} + 32 x^{28} - 80 x^{26} + 127 x^{24} - 80 x^{22} - 224 x^{20} + 936 x^{18} - 2175 x^{16} + 3744 x^{14} - 3584 x^{12} - 5120 x^{10} + 32512 x^{8} - 81920 x^{6} + 131072 x^{4} - 131072 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{96}\cdot 3^{16}\cdot 17^{8}$ |
$3$ |
$28.1360317052$ |
$57.1314274283428$ |
✓ |
|
|
$C_2^4:C_4$ (as 32T262) |
$[12]$ |
$48$ |
$15$ |
$37735500852.51004$ |
| 32.0.351...304.1 |
$x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$ |
$32$ |
[0,16] |
$2^{32}\cdot 17^{30}$ |
$2$ |
$28.482352661$ |
$28.48235266104985$ |
✓ |
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[8]$ |
$68$ |
$15$ |
$36938367173.77557$ |
| 32.0.879...000.1 |
$x^{32} - 5 x^{30} + 19 x^{28} - 70 x^{26} + 215 x^{24} - 590 x^{22} + 1466 x^{20} - 3340 x^{18} + 7009 x^{16} - 13360 x^{14} + 23456 x^{12} - 37760 x^{10} + 55040 x^{8} - 71680 x^{6} + 77824 x^{4} - 81920 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{24}\cdot 41^{8}$ |
$4$ |
$29.3098833808$ |
$74.16688765648375$ |
✓ |
|
|
$C_2^4:C_4$ (as 32T262) |
$[4, 4]$ |
$60$ |
$15$ |
$43671525522.024$ |
| 32.0.366...000.1 |
$x^{32} - 3 x^{30} + 4 x^{28} - 9 x^{26} + 27 x^{24} - 93 x^{22} + 188 x^{20} - 279 x^{18} + 581 x^{16} - 1116 x^{14} + 3008 x^{12} - 5952 x^{10} + 6912 x^{8} - 9216 x^{6} + 16384 x^{4} - 49152 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 5^{24}\cdot 7^{16}$ |
$4$ |
$30.6455306782$ |
$30.645530678223075$ |
✓ |
✓ |
|
$C_2^3\times C_4$ (as 32T34) |
not computed |
$60$ |
$15$ |
|
| 32.0.520...000.1 |
$x^{32} - 47 x^{24} + 2208 x^{16} - 47 x^{8} + 1$ |
$32$ |
[0,16] |
$2^{96}\cdot 3^{16}\cdot 5^{16}$ |
$3$ |
$30.9838667697$ |
$30.983866769659336$ |
✓ |
✓ |
|
$C_2^3\times C_4$ (as 32T34) |
$[20]$ |
$48$ |
$15$ |
$82239790500.5115$ |
| 32.0.550...000.1 |
$x^{32} + 6 x^{28} + 315 x^{24} - 2036 x^{20} + 5109 x^{16} - 2036 x^{12} + 315 x^{8} + 6 x^{4} + 1$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{24}\cdot 29^{8}$ |
$3$ |
$31.0375186879$ |
$72.02553510942846$ |
✓ |
|
? |
$C_2^4:C_4$ (as 32T262) |
$[3, 6]$ |
$40$ |
$15$ |
$76396638760.7958$ |
| 32.0.845...000.1 |
$x^{32} - 6 x^{30} - 64 x^{29} + 18 x^{28} + 120 x^{27} + 884 x^{26} + 1360 x^{25} + 2453 x^{24} - 592 x^{23} + 11300 x^{22} + 12152 x^{21} - 15370 x^{20} + 39248 x^{19} + 6590 x^{18} - 25344 x^{17} + 75876 x^{16} - 25344 x^{15} + 6590 x^{14} + 39248 x^{13} - 15370 x^{12} + 12152 x^{11} + 11300 x^{10} - 592 x^{9} + 2453 x^{8} + 1360 x^{7} + 884 x^{6} + 120 x^{5} + 18 x^{4} - 64 x^{3} - 6 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{64}\cdot 3^{16}\cdot 5^{16}\cdot 17^{8}$ |
$4$ |
$31.457039755$ |
$63.874877690685246$ |
✓ |
|
|
$D_4\times C_2^3$ (as 32T273) |
$[4, 4]$ |
$24$ |
$15$ |
$124577213214.25456$ |
| 32.0.103...616.1 |
$x^{32} - 4 x^{31} + 8 x^{30} - 16 x^{29} + 25 x^{28} - 24 x^{27} + 24 x^{26} - 20 x^{25} - 36 x^{23} + 152 x^{22} - 256 x^{21} + 425 x^{20} - 584 x^{19} + 296 x^{18} + 4 x^{17} + 113 x^{16} + 8 x^{15} + 1184 x^{14} - 4672 x^{13} + 6800 x^{12} - 8192 x^{11} + 9728 x^{10} - 4608 x^{9} - 10240 x^{7} + 24576 x^{6} - 49152 x^{5} + 102400 x^{4} - 131072 x^{3} + 131072 x^{2} - 131072 x + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 3^{16}\cdot 41^{8}\cdot 113^{4}$ |
$4$ |
$31.6556611366$ |
$471.5760808183553$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[3, 6]$ |
$24$ |
$15$ |
$137041291644.51082$ |
| 32.0.115...176.1 |
$x^{32} + 10 x^{30} - 28 x^{29} + 56 x^{28} - 208 x^{27} + 604 x^{26} - 876 x^{25} + 2547 x^{24} - 5760 x^{23} + 7684 x^{22} - 11384 x^{21} + 37676 x^{20} - 21776 x^{19} + 12262 x^{18} - 135456 x^{17} + 96553 x^{16} + 443172 x^{15} + 1107228 x^{14} + 758160 x^{13} - 662400 x^{12} - 2309040 x^{11} - 1681344 x^{10} + 1407456 x^{9} + 4596912 x^{8} + 3872448 x^{7} - 62208 x^{6} - 4385664 x^{5} - 3545856 x^{4} + 3919104 x^{2} + 3359232 x + 1679616$ |
$32$ |
[0,16] |
$2^{72}\cdot 3^{16}\cdot 13^{8}\cdot 17^{8}$ |
$4$ |
$31.7669987565$ |
$122.48255985916441$ |
✓ |
|
|
$C_2\times D_4^2$ (as 32T1016) |
$[2, 6]$ |
$24$ |
$15$ |
$97772762708.42017$ |
| 32.0.125...625.1 |
$x^{32} - x^{31} + 2 x^{30} - 3 x^{29} + 5 x^{28} - 8 x^{27} + 13 x^{26} - 21 x^{25} + 34 x^{24} - 55 x^{23} + 89 x^{22} - 144 x^{21} + 233 x^{20} - 377 x^{19} + 610 x^{18} - 987 x^{17} + 1597 x^{16} + 987 x^{15} + 610 x^{14} + 377 x^{13} + 233 x^{12} + 144 x^{11} + 89 x^{10} + 55 x^{9} + 34 x^{8} + 21 x^{7} + 13 x^{6} + 8 x^{5} + 5 x^{4} + 3 x^{3} + 2 x^{2} + x + 1$ |
$32$ |
[0,16] |
$5^{16}\cdot 17^{30}$ |
$2$ |
$31.8442383546$ |
$31.844238354614745$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[17]$ |
$34$ |
$15$ |
$42597284566.379654$ |
| 32.0.146...976.1 |
$x^{32} + 1$ |
$32$ |
[0,16] |
$2^{160}$ |
$1$ |
$32.0$ |
$32.0$ |
✓ |
✓ |
✓ |
$C_2\times C_{16}$ (as 32T32) |
$[17]$ |
$64$ |
$15$ |
$211230625393.46567$ |
| 32.2.147...407.1 |
$x^{32} - x - 1$ |
$32$ |
[2,15] |
$-\,191\cdot 19329543076986451\cdot 400485847292917407445603765627$ |
$3$ |
$32.0116136343$ |
$1.2159649713135762e+24$ |
|
|
✓ |
$S_{32}$ (as 32T2801324) |
trivial |
$2$ |
$16$ |
$189619653779.73328$ |
| 32.0.229...625.1 |
$x^{32} - 11 x^{31} + 68 x^{30} - 336 x^{29} + 1315 x^{28} - 4335 x^{27} + 12498 x^{26} - 30713 x^{25} + 67152 x^{24} - 127199 x^{23} + 211471 x^{22} - 307078 x^{21} + 387026 x^{20} - 419617 x^{19} + 359728 x^{18} - 149755 x^{17} - 229142 x^{16} + 581095 x^{15} - 441722 x^{14} - 315448 x^{13} + 1021466 x^{12} - 946897 x^{11} + 366311 x^{10} - 50246 x^{9} + 132237 x^{8} - 215882 x^{7} + 157773 x^{6} - 97500 x^{5} + 79930 x^{4} - 54894 x^{3} + 25063 x^{2} - 7709 x + 3131$ |
$32$ |
[0,16] |
$3^{32}\cdot 5^{28}\cdot 7^{16}$ |
$3$ |
$32.4540595356$ |
$64.7379764195286$ |
|
|
? |
$C_8.A_4$ (as 32T402) |
trivial |
$10$ |
$15$ |
$584489557946.5273$ |
| 32.0.503...000.1 |
$x^{32} - 2 x^{31} + 3 x^{30} - 2 x^{29} - 12 x^{27} + 17 x^{26} - 24 x^{25} + 3 x^{24} + 8 x^{23} + 101 x^{22} - 128 x^{21} + 208 x^{20} - 34 x^{19} + 39 x^{18} - 726 x^{17} + 877 x^{16} - 1452 x^{15} + 156 x^{14} - 272 x^{13} + 3328 x^{12} - 4096 x^{11} + 6464 x^{10} + 1024 x^{9} + 768 x^{8} - 12288 x^{7} + 17408 x^{6} - 24576 x^{5} - 16384 x^{3} + 49152 x^{2} - 65536 x + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{24}\cdot 17^{8}$ |
$4$ |
$33.2617698699$ |
$67.53946012591136$ |
✓ |
|
|
$C_4^2:C_2^2$ (as 32T204) |
$[4, 4]$ |
$30$ |
$15$ |
$190465720691.2432$ |
| 32.0.614...625.1 |
$x^{32} - 4 x^{31} + 38 x^{30} - 130 x^{29} + 699 x^{28} - 2191 x^{27} + 8745 x^{26} - 25571 x^{25} + 83386 x^{24} - 222738 x^{23} + 612551 x^{22} - 1445800 x^{21} + 3366820 x^{20} - 6839883 x^{19} + 13440516 x^{18} - 23161945 x^{17} + 38310126 x^{16} - 55684805 x^{15} + 77474162 x^{14} - 94829103 x^{13} + 110710129 x^{12} - 113727761 x^{11} + 110357640 x^{10} - 94103904 x^{9} + 74479117 x^{8} - 51698016 x^{7} + 32429638 x^{6} - 17496051 x^{5} + 7973462 x^{4} - 3036857 x^{3} + 868340 x^{2} - 166271 x + 16531$ |
$32$ |
[0,16] |
$5^{28}\cdot 67^{16}$ |
$2$ |
$33.4684928079$ |
$67.45000024642073$ |
|
|
? |
$C_8.A_4$ (as 32T402) |
trivial |
$10$ |
$15$ |
$879491729100.8733$ |
| 32.0.664...000.1 |
$x^{32} - 8 x^{31} + 22 x^{30} - 40 x^{29} + 178 x^{28} - 712 x^{27} + 1264 x^{26} + 844 x^{25} - 9359 x^{24} + 23304 x^{23} - 31738 x^{22} + 20712 x^{21} + 4242 x^{20} - 53384 x^{19} + 309318 x^{18} - 1090772 x^{17} + 2225756 x^{16} - 2949980 x^{15} + 2866688 x^{14} - 2095500 x^{13} + 1173576 x^{12} - 535544 x^{11} + 258862 x^{10} - 119572 x^{9} + 42617 x^{8} - 13676 x^{7} + 3860 x^{6} - 916 x^{5} + 264 x^{4} - 80 x^{3} + 20 x^{2} - 4 x + 1$ |
$32$ |
[0,16] |
$2^{72}\cdot 3^{16}\cdot 5^{16}\cdot 11^{8}$ |
$4$ |
$33.5514497803$ |
$61.10256790565329$ |
✓ |
|
|
$D_4\times C_2^3$ (as 32T273) |
$[2, 12]$ |
$24$ |
$15$ |
$184122377962.3511$ |
| 32.0.779...216.1 |
$x^{32} - 16 x^{31} + 156 x^{30} - 1096 x^{29} + 6134 x^{28} - 28580 x^{27} + 114266 x^{26} - 399684 x^{25} + 1239490 x^{24} - 3440780 x^{23} + 8605010 x^{22} - 19473044 x^{21} + 39982438 x^{20} - 74587072 x^{19} + 126485556 x^{18} - 194983784 x^{17} + 273242634 x^{16} - 348358772 x^{15} + 405080242 x^{14} - 431986068 x^{13} + 426399702 x^{12} - 394223580 x^{11} + 344722538 x^{10} - 285681476 x^{9} + 222647745 x^{8} - 160135088 x^{7} + 103163456 x^{6} - 57484000 x^{5} + 26721528 x^{4} - 9914240 x^{3} + 2744800 x^{2} - 506176 x + 48016$ |
$32$ |
[0,16] |
$2^{64}\cdot 3^{24}\cdot 11^{8}\cdot 17^{8}$ |
$4$ |
$33.7179633297$ |
$124.68716072129577$ |
✓ |
|
|
$C_2\times D_4^2$ (as 32T1016) |
$[2, 12]$ |
$24$ |
$15$ |
$233422630699.0076$ |
| 32.0.877...000.1 |
$x^{32} + 13 x^{28} + 78 x^{24} + 356 x^{20} + 1505 x^{16} + 5696 x^{12} + 19968 x^{8} + 53248 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{24}\cdot 41^{8}$ |
$3$ |
$33.8441381197$ |
$85.64054510685526$ |
✓ |
|
? |
$C_2^4:C_4$ (as 32T262) |
$[2, 2, 8]$ |
$40$ |
$15$ |
$150821321458.18454$ |
| 32.0.365...000.1 |
$x^{32} - x^{28} - 15 x^{24} + 31 x^{20} + 209 x^{16} + 496 x^{12} - 3840 x^{8} - 4096 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 5^{24}\cdot 7^{16}$ |
$3$ |
$35.3864107731$ |
$35.38641077306205$ |
✓ |
✓ |
? |
$C_2^3\times C_4$ (as 32T34) |
not computed |
$40$ |
$15$ |
|
| 32.0.426...625.1 |
$x^{32} - 2 x^{31} - 14 x^{30} + 32 x^{29} + 110 x^{28} - 256 x^{27} - 822 x^{26} + 1761 x^{25} + 5076 x^{24} - 6234 x^{23} - 33617 x^{22} + 7049 x^{21} + 145847 x^{20} + 80587 x^{19} - 200297 x^{18} - 1040496 x^{17} + 909785 x^{16} - 126545 x^{15} + 4807173 x^{14} - 6468687 x^{13} + 4092091 x^{12} - 12326083 x^{11} + 15573178 x^{10} - 9966741 x^{9} + 15430857 x^{8} - 15762104 x^{7} + 7858456 x^{6} - 7358464 x^{5} + 5444944 x^{4} - 823424 x^{3} + 88384 x^{2} - 5760 x + 256$ |
$32$ |
[0,16] |
$3^{16}\cdot 5^{24}\cdot 7^{16}\cdot 29^{8}$ |
$4$ |
$35.5579446928$ |
$82.51561665216384$ |
✓ |
|
|
$C_2^4:C_4$ (as 32T262) |
not computed |
$30$ |
$15$ |
|
| 32.0.445...336.1 |
$x^{32} + 2 x^{30} + 9 x^{28} + 4 x^{26} + 26 x^{24} - 45 x^{22} + 10 x^{20} - 403 x^{18} - 171 x^{16} - 1612 x^{14} + 160 x^{12} - 2880 x^{10} + 6656 x^{8} + 4096 x^{6} + 36864 x^{4} + 32768 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{24}\cdot 61^{16}$ |
$3$ |
$35.6070385056$ |
$70.6465286301374$ |
✓ |
|
|
$C_2^2\times \SL(2,3)$ (as 32T405) |
$[2, 10]$ |
$12$ |
$15$ |
$333896890255.2903$ |
| 32.0.519...000.1 |
$x^{32} + 2207 x^{16} + 1$ |
$32$ |
[0,16] |
$2^{128}\cdot 5^{16}$ |
$2$ |
$35.77708764$ |
$35.77708763999664$ |
✓ |
✓ |
? |
$C_2^2\times C_8$ (as 32T37) |
$[17]$ |
$32$ |
$15$ |
$323273529801.8212$ |
| 32.0.596...336.1 |
$x^{32} - x^{30} + x^{28} - 8 x^{26} + 20 x^{24} - 16 x^{22} + 32 x^{20} - 128 x^{18} + 64 x^{16} - 512 x^{14} + 512 x^{12} - 1024 x^{10} + 5120 x^{8} - 8192 x^{6} + 4096 x^{4} - 16384 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{44}\cdot 3^{16}\cdot 4093^{8}$ |
$3$ |
$35.9324895179$ |
$332.05676010213426$ |
✓ |
|
|
$C_2^5:S_4$ (as 32T34907) |
$[2, 8]$ |
$12$ |
$15$ |
$658375568497.8936$ |
| 32.0.902...576.1 |
$x^{32} - 4 x^{28} + 22 x^{24} - 36 x^{20} + 209 x^{16} - 576 x^{12} + 5632 x^{8} - 16384 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{76}\cdot 89^{4}\cdot 257^{8}$ |
$3$ |
$36.4001582176$ |
$784.5268373963652$ |
✓ |
|
? |
$C_2^6:S_4$ (as 32T96908) |
$[24]$ |
$8$ |
$15$ |
$588107386863.9401$ |
| 32.0.974...336.1 |
$x^{32} - 10 x^{28} + 27 x^{24} + 150 x^{20} - 1215 x^{16} + 2400 x^{12} + 6912 x^{8} - 40960 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{72}\cdot 223^{8}\cdot 241^{4}$ |
$3$ |
$36.4876452071$ |
$1102.753495447589$ |
✓ |
|
|
$C_2^6:S_4$ (as 32T96908) |
$[2, 8]$ |
$8$ |
$15$ |
$423122700646.94574$ |
| 32.0.111...336.1 |
$x^{32} + 7 x^{30} + 23 x^{28} + 38 x^{26} + 11 x^{24} - 94 x^{22} - 186 x^{20} - 24 x^{18} + 385 x^{16} - 96 x^{14} - 2976 x^{12} - 6016 x^{10} + 2816 x^{8} + 38912 x^{6} + 94208 x^{4} + 114688 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 89^{4}\cdot 1327^{8}$ |
$4$ |
$36.6422475624$ |
$1190.4772152376543$ |
✓ |
|
|
$C_2^6:S_4$ (as 32T96908) |
$[3, 6]$ |
$12$ |
$15$ |
$382220804260.19714$ |
| 32.0.113...856.1 |
$x^{32} + 31 x^{24} + 705 x^{16} + 7936 x^{8} + 65536$ |
$32$ |
[0,16] |
$2^{96}\cdot 3^{16}\cdot 7^{16}$ |
$3$ |
$36.6606055596$ |
$36.66060555964672$ |
✓ |
✓ |
|
$C_2^3\times C_4$ (as 32T34) |
$[4, 4, 4]$ |
$48$ |
$15$ |
$374180447387.275$ |
| 32.0.126...296.1 |
$x^{32} + 2 x^{30} + x^{28} - 6 x^{26} - 28 x^{24} - 58 x^{22} + 9 x^{20} + 230 x^{18} + 593 x^{16} + 920 x^{14} + 144 x^{12} - 3712 x^{10} - 7168 x^{8} - 6144 x^{6} + 4096 x^{4} + 32768 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{32}\cdot 3^{16}\cdot 137^{4}\cdot 1087^{8}$ |
$4$ |
$36.7907024487$ |
$1336.7976660661852$ |
✓ |
|
|
$C_2^6:S_4$ (as 32T96908) |
$[12]$ |
$12$ |
$15$ |
$495183335125.27386$ |
| 32.0.133...000.1 |
$x^{32} - 2 x^{31} - 16 x^{30} + 24 x^{29} + 141 x^{28} - 120 x^{27} - 852 x^{26} - 70 x^{25} + 4216 x^{24} + 4978 x^{23} - 15640 x^{22} - 47344 x^{21} + 45797 x^{20} + 270436 x^{19} - 110380 x^{18} - 986938 x^{17} + 284105 x^{16} + 1973876 x^{15} - 441520 x^{14} - 2163488 x^{13} + 732752 x^{12} + 1515008 x^{11} - 1000960 x^{10} - 637184 x^{9} + 1079296 x^{8} + 35840 x^{7} - 872448 x^{6} + 245760 x^{5} + 577536 x^{4} - 196608 x^{3} - 262144 x^{2} + 65536 x + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{16}\cdot 13^{8}\cdot 97^{4}$ |
$5$ |
$36.8487642351$ |
$388.99871465083277$ |
✓ |
|
|
$D_4^2:C_2^3$ (as 32T12882) |
$[20]$ |
$12$ |
$15$ |
$564327334704.2394$ |
| 32.0.170...000.1 |
$x^{32} - 24 x^{30} + 407 x^{28} - 3048 x^{26} + 15745 x^{24} - 51120 x^{22} + 120578 x^{20} - 196608 x^{18} + 236974 x^{16} - 196608 x^{14} + 120578 x^{12} - 51120 x^{10} + 15745 x^{8} - 3048 x^{6} + 407 x^{4} - 24 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{64}\cdot 3^{24}\cdot 5^{16}\cdot 11^{8}$ |
$4$ |
$37.1307828516$ |
$67.62110714844763$ |
✓ |
|
|
$D_4\times C_2^3$ (as 32T273) |
$[2, 4, 8]$ |
$24$ |
$15$ |
$547885182394.1923$ |
| 32.0.184...576.1 |
$x^{32} - 28 x^{30} + 502 x^{28} - 5304 x^{26} + 40319 x^{24} - 205348 x^{22} + 769870 x^{20} - 2005384 x^{18} + 3886261 x^{16} - 5310988 x^{14} + 5324752 x^{12} - 3494768 x^{10} + 1644300 x^{8} - 452512 x^{6} + 81152 x^{4} - 1184 x^{2} + 16$ |
$32$ |
[0,16] |
$2^{64}\cdot 3^{16}\cdot 7^{16}\cdot 17^{8}$ |
$4$ |
$37.2204713862$ |
$75.57777451076474$ |
✓ |
|
|
$D_4\times C_2^3$ (as 32T273) |
not computed |
$24$ |
$15$ |
|
| 32.0.272...249.1 |
$x^{32} - x^{31} - x^{30} + 3 x^{29} - x^{28} - 5 x^{27} + 7 x^{26} + 3 x^{25} - 17 x^{24} + 11 x^{23} + 23 x^{22} - 45 x^{21} - x^{20} + 91 x^{19} - 89 x^{18} - 93 x^{17} + 271 x^{16} - 186 x^{15} - 356 x^{14} + 728 x^{13} - 16 x^{12} - 1440 x^{11} + 1472 x^{10} + 1408 x^{9} - 4352 x^{8} + 1536 x^{7} + 7168 x^{6} - 10240 x^{5} - 4096 x^{4} + 24576 x^{3} - 16384 x^{2} - 32768 x + 65536$ |
$32$ |
[0,16] |
$7^{16}\cdot 17^{30}$ |
$2$ |
$37.6786109476$ |
$37.67861094758833$ |
✓ |
✓ |
? |
$C_2\times C_{16}$ (as 32T32) |
$[3, 15]$ |
$34$ |
$15$ |
$308154877506.37555$ |
| 32.0.301...000.1 |
$x^{32} + 46 x^{30} + 899 x^{28} + 9779 x^{26} + 65207 x^{24} + 277346 x^{22} + 763587 x^{20} + 1370784 x^{18} + 1627006 x^{16} + 1296861 x^{14} + 701262 x^{12} + 257219 x^{10} + 63092 x^{8} + 10001 x^{6} + 959 x^{4} + 49 x^{2} + 1$ |
$32$ |
[0,16] |
$2^{12}\cdot 3^{24}\cdot 5^{16}\cdot 41^{4}\cdot 167^{8}$ |
$5$ |
$37.7997816771$ |
$1192.946866180926$ |
✓ |
|
|
$C_2^6:S_4$ (as 32T96908) |
$[18]$ |
$6$ |
$15$ |
$617565056600.4795$ |
| 32.0.334...416.1 |
$x^{32} - x^{30} - 3 x^{28} + 20 x^{26} - 12 x^{24} - 64 x^{22} + 160 x^{20} + 64 x^{18} - 704 x^{16} + 256 x^{14} + 2560 x^{12} - 4096 x^{10} - 3072 x^{8} + 20480 x^{6} - 12288 x^{4} - 16384 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{44}\cdot 3^{16}\cdot 5077^{8}$ |
$3$ |
$37.9209022775$ |
$369.8239522562059$ |
✓ |
|
|
$C_2^5:S_4$ (as 32T34907) |
$[4, 4]$ |
$12$ |
$15$ |
$1000974895371.5886$ |
| 32.0.351...016.1 |
$x^{32} + 8 x^{24} + 64 x^{20} + 16 x^{16} + 1024 x^{12} + 2048 x^{8} + 65536$ |
$32$ |
[0,16] |
$2^{76}\cdot 17^{12}\cdot 41^{8}$ |
$3$ |
$37.9804887732$ |
$278.0832683343685$ |
✓ |
|
|
$C_2^6:S_4$ (as 32T96908) |
$[2, 24]$ |
$8$ |
$15$ |
$955272330542.1476$ |
| 32.0.361...000.1 |
$x^{32} + 2 x^{30} - 56 x^{28} - 824 x^{26} + 992 x^{24} + 23552 x^{22} + 121088 x^{20} + 560896 x^{18} + 1820416 x^{16} + 2243584 x^{14} + 1937408 x^{12} + 1507328 x^{10} + 253952 x^{8} - 843776 x^{6} - 229376 x^{4} + 32768 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{24}\cdot 29^{8}$ |
$4$ |
$38.0130418338$ |
$88.21290473450735$ |
✓ |
|
|
$C_2^4:C_4$ (as 32T262) |
not computed |
$30$ |
$15$ |
|
| 32.0.361...000.2 |
$x^{32} - 2 x^{30} - 56 x^{28} + 824 x^{26} + 992 x^{24} - 23552 x^{22} + 121088 x^{20} - 560896 x^{18} + 1820416 x^{16} - 2243584 x^{14} + 1937408 x^{12} - 1507328 x^{10} + 253952 x^{8} + 843776 x^{6} - 229376 x^{4} - 32768 x^{2} + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 5^{24}\cdot 29^{8}$ |
$4$ |
$38.0130418338$ |
$88.21290473450735$ |
✓ |
|
|
$C_2^4:C_4$ (as 32T262) |
not computed |
$30$ |
$15$ |
|
| 32.0.368...256.1 |
$x^{32} - 6 x^{28} + 49 x^{24} - 248 x^{20} + 1072 x^{16} - 3968 x^{12} + 12544 x^{8} - 24576 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{64}\cdot 41^{4}\cdot 1277^{8}$ |
$3$ |
$38.036951056$ |
$915.266081530393$ |
✓ |
|
|
$C_2^6:S_4$ (as 32T96908) |
$[4, 8]$ |
$8$ |
$15$ |
$747032345387.1615$ |
| 32.0.385...576.1 |
$x^{32} + 40 x^{24} + 16 x^{20} + 784 x^{16} + 256 x^{12} + 10240 x^{8} + 65536$ |
$32$ |
[0,16] |
$2^{72}\cdot 17^{4}\cdot 997^{8}$ |
$3$ |
$38.088809183$ |
$637.429922686193$ |
✓ |
|
|
$C_2^6:S_4$ (as 32T96908) |
$[2, 20]$ |
$8$ |
$15$ |
$901078689200.9504$ |
| 32.0.480...776.1 |
$x^{32} + 20 x^{30} + 236 x^{28} + 1948 x^{26} + 12276 x^{24} + 58148 x^{22} + 212422 x^{20} + 567784 x^{18} + 1013620 x^{16} + 772588 x^{14} + 788932 x^{12} + 1345276 x^{10} + 364625 x^{8} - 228564 x^{6} + 145744 x^{4} - 25856 x^{2} + 4096$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 13^{8}\cdot 17^{16}$ |
$4$ |
$38.354464152$ |
$102.99514551666987$ |
✓ |
|
|
$C_2^4:D_4$ (as 32T1369) |
$[2, 2, 4]$ |
$12$ |
$15$ |
$2205277237958.931$ |
| 32.0.480...776.2 |
$x^{32} + 3 x^{28} + 13 x^{24} - 108 x^{20} - 384 x^{16} - 1728 x^{12} + 3328 x^{8} + 12288 x^{4} + 65536$ |
$32$ |
[0,16] |
$2^{48}\cdot 3^{16}\cdot 13^{8}\cdot 17^{16}$ |
$4$ |
$38.354464152$ |
$102.99514551666987$ |
✓ |
|
|
$C_2^4:D_4$ (as 32T1369) |
$[2, 4, 8]$ |
$12$ |
$15$ |
$950005676337.5021$ |
