Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 8.0.144...464.4 | $x^{8} - 4 x^{7} + 2422 x^{6} - 7252 x^{5} + 2205833 x^{4} - 4399584 x^{3} + 895316528 x^{2} - 893117944 x + 136648520446$ | $2^{22}\cdot 2423^{4}$ | $C_4\times C_2$ (as 8T2) | $[11, 98340]$ |
| 8.0.150...224.4 | $x^{8} - 4 x^{7} + 2446 x^{6} - 7324 x^{5} + 2249705 x^{4} - 4487208 x^{3} + 922122440 x^{2} - 919880056 x + 142122972958$ | $2^{22}\cdot 2447^{4}$ | $C_4\times C_2$ (as 8T2) | $[4, 20, 12580]$ |
| 8.0.374...449.2 | $x^{8} - 2 x^{7} + 170 x^{6} - 308 x^{5} + 16593 x^{4} - 8850 x^{3} + 940388 x^{2} + 123912 x + 21525984$ | $73^{6}\cdot 223^{4}$ | $C_4\times C_2$ (as 8T2) | $[2, 8, 65520]$ |
| 8.0.444...336.4 | $x^{8} + 4536 x^{6} + 6429780 x^{4} + 2916548208 x^{2} + 416343691009$ | $2^{24}\cdot 2269^{4}$ | $C_4\times C_2$ (as 8T2) | $[1044870]$ |
| 8.0.467...096.4 | $x^{8} + 4592 x^{6} + 6589520 x^{4} + 3025907584 x^{2} + 437250240001$ | $2^{24}\cdot 2297^{4}$ | $C_4\times C_2$ (as 8T2) | $[14, 80080]$ |
| 8.0.539...936.4 | $x^{8} + 4760 x^{6} + 7080500 x^{4} + 3370318000 x^{2} + 504712205761$ | $2^{24}\cdot 2381^{4}$ | $C_4\times C_2$ (as 8T2) | $[1010990]$ |
| 8.0.550...816.4 | $x^{8} + 4784 x^{6} + 7152080 x^{4} + 3421555072 x^{2} + 514951195201$ | $2^{24}\cdot 2393^{4}$ | $C_4\times C_2$ (as 8T2) | $[5, 10, 20400]$ |
| 8.0.627...256.4 | $x^{8} + 4944 x^{6} + 7638480 x^{4} + 3776464512 x^{2} + 587247875041$ | $2^{24}\cdot 2473^{4}$ | $C_4\times C_2$ (as 8T2) | $[10, 131360]$ |
| 8.0.724...129.1 | $x^{8} - 2 x^{7} + 210 x^{6} - 368 x^{5} + 23373 x^{4} - 14510 x^{3} + 1466208 x^{2} + 76192 x + 37558784$ | $73^{6}\cdot 263^{4}$ | $C_4\times C_2$ (as 8T2) | $[1091961]$ |
| 8.0.816...009.1 | $x^{8} - 2 x^{7} + 218 x^{6} - 380 x^{5} + 24873 x^{4} - 15786 x^{3} + 1590908 x^{2} + 60840 x + 41606784$ | $73^{6}\cdot 271^{4}$ | $C_4\times C_2$ (as 8T2) | $[1354309]$ |
| 8.0.928...968.4 | $x^{8} + 6488 x^{6} + 13154420 x^{4} + 8534587696 x^{2} + 865193827682$ | $2^{31}\cdot 811^{4}$ | $C_8$ (as 8T1) | $[1016306]$ |
| 8.0.975...288.4 | $x^{8} + 6568 x^{6} + 13480820 x^{4} + 8854202576 x^{2} + 908662539362$ | $2^{31}\cdot 821^{4}$ | $C_8$ (as 8T1) | $[1151954]$ |
| 8.0.985...168.4 | $x^{8} + 6584 x^{6} + 13546580 x^{4} + 8919068272 x^{2} + 917549148482$ | $2^{31}\cdot 823^{4}$ | $C_8$ (as 8T1) | $[2, 610706]$ |
| 8.0.100...568.4 | $x^{8} + 6616 x^{6} + 13678580 x^{4} + 9049748528 x^{2} + 935517754082$ | $2^{31}\cdot 827^{4}$ | $C_8$ (as 8T1) | $[1440002]$ |
| 8.0.112...264.1 | $x^{8} + 6612 x^{6} + 10929636 x^{4} + 6022229436 x^{2} + 829562104809$ | $2^{24}\cdot 3^{6}\cdot 19^{4}\cdot 29^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 362, 362]$ |
| 8.0.113...888.4 | $x^{8} + 6824 x^{6} + 14552180 x^{4} + 9930407632 x^{2} + 1058829713762$ | $2^{31}\cdot 853^{4}$ | $C_8$ (as 8T1) | $[9, 120402]$ |
| 8.0.115...448.4 | $x^{8} + 6856 x^{6} + 14688980 x^{4} + 10070764688 x^{2} + 1078830667202$ | $2^{31}\cdot 857^{4}$ | $C_8$ (as 8T1) | $[2, 539746]$ |
| 8.0.119...928.4 | $x^{8} + 6904 x^{6} + 14895380 x^{4} + 10283770352 x^{2} + 1109361726722$ | $2^{31}\cdot 863^{4}$ | $C_8$ (as 8T1) | $[2, 2, 4, 62948]$ |
| 8.0.119...504.1 | $x^{8} + 6708 x^{6} + 11249316 x^{4} + 6288367644 x^{2} + 878799378249$ | $2^{24}\cdot 3^{6}\cdot 13^{4}\cdot 43^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 378, 378]$ |
| 8.0.122...904.1 | $x^{8} + 6756 x^{6} + 11410884 x^{4} + 6424327692 x^{2} + 904224122649$ | $2^{24}\cdot 3^{6}\cdot 563^{4}$ | $Q_8$ (as 8T5) | $[2, 750, 750]$ |
| 8.0.125...489.2 | $x^{8} - x^{7} + 1608 x^{6} - 3250 x^{5} + 188893 x^{4} + 474767 x^{3} + 6289010 x^{2} + 15728420 x + 66111848$ | $73^{4}\cdot 89^{7}$ | $C_8$ (as 8T1) | $[2, 2, 2, 157522]$ |
| 8.0.127...368.4 | $x^{8} + 7016 x^{6} + 15382580 x^{4} + 10792418128 x^{2} + 1183118837282$ | $2^{31}\cdot 877^{4}$ | $C_8$ (as 8T1) | $[19, 57494]$ |
| 8.0.129...808.4 | $x^{8} + 7048 x^{6} + 15523220 x^{4} + 10940765456 x^{2} + 1204851795842$ | $2^{31}\cdot 881^{4}$ | $C_8$ (as 8T1) | $[2, 2, 6, 54966]$ |
| 8.0.132...928.4 | $x^{8} + 7096 x^{6} + 15735380 x^{4} + 11165825648 x^{2} + 1238010918722$ | $2^{31}\cdot 887^{4}$ | $C_8$ (as 8T1) | $[2, 571394]$ |
| 8.0.141...049.1 | $x^{8} - 2 x^{7} + 258 x^{6} - 440 x^{5} + 33093 x^{4} - 22886 x^{3} + 2322648 x^{2} - 50240 x + 66904064$ | $73^{6}\cdot 311^{4}$ | $C_4\times C_2$ (as 8T2) | $[7, 186732]$ |
| 8.0.145...248.4 | $x^{8} + 7256 x^{6} + 16452980 x^{4} + 11938282288 x^{2} + 1353502754402$ | $2^{31}\cdot 907^{4}$ | $C_8$ (as 8T1) | $[1243954]$ |
| 8.0.147...824.1 | $x^{8} + 7068 x^{6} + 12489156 x^{4} + 7356112884 x^{2} + 1083187622169$ | $2^{24}\cdot 3^{6}\cdot 19^{4}\cdot 31^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 410, 410]$ |
| 8.0.147...168.4 | $x^{8} + 7288 x^{6} + 16598420 x^{4} + 12096928496 x^{2} + 1377537732482$ | $2^{31}\cdot 911^{4}$ | $C_8$ (as 8T1) | $[2, 2, 2, 177986]$ |
| 8.0.153...000.1 | $x^{8} + 7140 x^{6} + 12744900 x^{4} + 7583215500 x^{2} + 1128003305625$ | $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 7^{4}\cdot 17^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 2, 2, 198, 198]$ |
| 8.0.159...064.1 | $x^{8} + 7212 x^{6} + 13003236 x^{4} + 7814944836 x^{2} + 1174195461609$ | $2^{24}\cdot 3^{6}\cdot 601^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 4, 180, 360]$ |
| 8.0.159...288.4 | $x^{8} + 7432 x^{6} + 17260820 x^{4} + 12828241424 x^{2} + 1489679535362$ | $2^{31}\cdot 929^{4}$ | $C_8$ (as 8T1) | $[2, 2, 2, 203524]$ |
| 8.0.161...489.1 | $x^{8} - 2 x^{7} + 84 x^{6} - 322 x^{5} + 8967 x^{4} + 16100 x^{3} + 604596 x^{2} + 1085296 x + 12178432$ | $113^{6}\cdot 167^{4}$ | $C_4\times C_2$ (as 8T2) | $[1290179]$ |
| 8.0.162...001.1 | $x^{8} - 2 x^{7} + 174 x^{6} - 148 x^{5} + 18561 x^{4} - 35530 x^{3} + 1250448 x^{2} - 2033504 x + 31533568$ | $89^{6}\cdot 239^{4}$ | $C_4\times C_2$ (as 8T2) | $[5, 5, 5, 11895]$ |
| 8.0.168...928.4 | $x^{8} + 7528 x^{6} + 17709620 x^{4} + 13331801936 x^{2} + 1568153202722$ | $2^{31}\cdot 941^{4}$ | $C_8$ (as 8T1) | $[3, 600342]$ |
| 8.0.172...504.1 | $x^{8} + 7356 x^{6} + 13527684 x^{4} + 8292470292 x^{2} + 1270821072249$ | $2^{24}\cdot 3^{6}\cdot 613^{4}$ | $Q_8$ (as 8T5) | $[2, 758, 758]$ |
| 8.0.172...688.4 | $x^{8} + 7576 x^{6} + 17936180 x^{4} + 13588449968 x^{2} + 1608532764962$ | $2^{31}\cdot 947^{4}$ | $C_8$ (as 8T1) | $[3, 594582]$ |
| 8.0.177...544.1 | $x^{8} + 7404 x^{6} + 13704804 x^{4} + 8455864068 x^{2} + 1304317032489$ | $2^{24}\cdot 3^{6}\cdot 617^{4}$ | $Q_8$ (as 8T5) | $[2, 806, 806]$ |
| 8.0.179...344.1 | $x^{8} + 7428 x^{6} + 13793796 x^{4} + 8538359724 x^{2} + 1321311167289$ | $2^{24}\cdot 3^{6}\cdot 619^{4}$ | $Q_8$ (as 8T5) | $[2, 826, 826]$ |
| 8.0.184...424.1 | $x^{8} + 7476 x^{6} + 13972644 x^{4} + 8704957212 x^{2} + 1355797085769$ | $2^{24}\cdot 3^{6}\cdot 7^{4}\cdot 89^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 374, 374]$ |
| 8.0.187...808.4 | $x^{8} + 7736 x^{6} + 18701780 x^{4} + 14467697008 x^{2} + 1748782875842$ | $2^{31}\cdot 967^{4}$ | $C_8$ (as 8T1) | $[2, 665026]$ |
| 8.0.191...784.1 | $x^{8} + 7548 x^{6} + 14243076 x^{4} + 8958894804 x^{2} + 1408786207929$ | $2^{24}\cdot 3^{6}\cdot 17^{4}\cdot 37^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 362, 362]$ |
| 8.0.193...344.1 | $x^{8} + 7572 x^{6} + 14333796 x^{4} + 9044625276 x^{2} + 1426789637289$ | $2^{24}\cdot 3^{6}\cdot 631^{4}$ | $Q_8$ (as 8T5) | $[2, 770, 770]$ |
| 8.0.198...000.1 | $x^{8} + 7620 x^{6} + 14516100 x^{4} + 9217723500 x^{2} + 1463313605625$ | $2^{24}\cdot 3^{6}\cdot 5^{4}\cdot 127^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 406, 406]$ |
| 8.0.200...608.4 | $x^{8} + 7864 x^{6} + 19325780 x^{4} + 15197793392 x^{2} + 1867428863042$ | $2^{31}\cdot 983^{4}$ | $C_8$ (as 8T1) | $[2, 769778]$ |
| 8.0.207...528.4 | $x^{8} + 7928 x^{6} + 19641620 x^{4} + 15571876336 x^{2} + 1928966181122$ | $2^{31}\cdot 991^{4}$ | $C_8$ (as 8T1) | $[2, 2, 4, 108868]$ |
| 8.0.209...864.1 | $x^{8} + 7716 x^{6} + 14884164 x^{4} + 9570517452 x^{2} + 1538460680409$ | $2^{24}\cdot 3^{6}\cdot 643^{4}$ | $Q_8$ (as 8T5) | $[2, 798, 798]$ |
| 8.0.212...488.4 | $x^{8} + 7976 x^{6} + 19880180 x^{4} + 15856431568 x^{2} + 1976107784162$ | $2^{31}\cdot 997^{4}$ | $C_8$ (as 8T1) | $[1529218]$ |
| 8.0.216...064.1 | $x^{8} + 7788 x^{6} + 15163236 x^{4} + 9840940164 x^{2} + 1596692541609$ | $2^{24}\cdot 3^{6}\cdot 11^{4}\cdot 59^{4}$ | $Q_8$ (as 8T5) | $[2, 2, 2, 374, 374]$ |
| 8.0.222...384.1 | $x^{8} + 7836 x^{6} + 15350724 x^{4} + 10024022772 x^{2} + 1636421717529$ | $2^{24}\cdot 3^{6}\cdot 653^{4}$ | $Q_8$ (as 8T5) | $[2, 710, 710]$ |
| 8.0.222...528.4 | $x^{8} + 8072 x^{6} + 20361620 x^{4} + 16435899664 x^{2} + 2072977845122$ | $2^{31}\cdot 1009^{4}$ | $C_8$ (as 8T1) | $[2, 2, 2, 169586]$ |