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 |
---|---|---|---|---|
8.4.15243125.1 | $x^{8} - x^{7} - 3 x^{6} + 3 x^{5} + 3 x^{4} - 6 x^{3} - 2 x^{2} + 3 x + 1$ | $5^{4}\cdot 29^{3}$ | $C_4\wr C_2$ (as 8T17) | trivial |
8.4.15297613.1 | $x^{8} - 2 x^{7} - x^{6} + 5 x^{5} - 2 x^{4} - 6 x^{3} + 3 x^{2} + 2 x - 1$ | $37\cdot 643^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.4.15908237.1 | $x^{8} - x^{6} - x^{5} - 3 x^{4} + 4 x^{2} - 1$ | $43\cdot 369959$ | $S_8$ (as 8T50) | trivial |
8.4.16324589.1 | $x^{8} - 5 x^{6} - x^{5} + 7 x^{4} + 4 x^{3} - 2 x^{2} - 4 x - 1$ | $149\cdot 331^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.4.16374773.1 | $x^{8} - x^{7} - x^{6} - 2 x^{4} + 2 x^{3} + 4 x^{2} - x - 1$ | $1753\cdot 9341$ | $S_8$ (as 8T50) | trivial |
8.4.16526789.1 | $x^{8} - 3 x^{6} - x^{3} + 3 x^{2} - 1$ | $19\cdot 607\cdot 1433$ | $S_8$ (as 8T50) | trivial |
8.4.16623109.1 | $x^{8} - 2 x^{7} - x^{6} + 5 x^{5} - 3 x^{4} - 2 x^{3} + 3 x^{2} - x - 1$ | $16623109$ | $S_8$ (as 8T50) | trivial |
8.4.16643125.1 | $x^{8} - x^{7} - 2 x^{6} + 2 x^{5} - x^{3} + x + 1$ | $5^{4}\cdot 31\cdot 859$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.4.16706269.1 | $x^{8} - 2 x^{7} + x^{6} - x^{5} + x^{4} + 2 x^{3} - 4 x^{2} + 1$ | $73\cdot 228853$ | $S_8$ (as 8T50) | trivial |
8.4.16877741.1 | $x^{8} - 3 x^{7} + 2 x^{6} + x^{5} + x^{3} - 4 x^{2} + 1$ | $16877741$ | $S_8$ (as 8T50) | trivial |
8.4.16981229.1 | $x^{8} - 3 x^{7} + 4 x^{6} - x^{5} - 4 x^{4} + 5 x^{3} - 2 x^{2} - 2 x + 1$ | $3329\cdot 5101$ | $S_8$ (as 8T50) | trivial |
8.4.17025973.1 | $x^{8} - 3 x^{7} + 2 x^{6} + 4 x^{5} - 8 x^{4} + 3 x^{3} + 3 x^{2} - 4 x + 1$ | $67\cdot 254119$ | $S_8$ (as 8T50) | trivial |
8.4.17129069.1 | $x^{8} - 2 x^{7} + x^{5} - x^{3} + x^{2} + 2 x - 1$ | $17129069$ | $S_8$ (as 8T50) | trivial |
8.4.17238125.1 | $x^{8} - x^{7} - 2 x^{6} + x^{5} + 3 x^{4} - 3 x^{3} - 3 x^{2} + 2 x + 1$ | $5^{4}\cdot 27581$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.4.17318125.1 | $x^{8} - 2 x^{7} + x^{6} + 3 x^{5} - 7 x^{4} + 4 x^{3} - 4 x^{2} + 4 x - 1$ | $5^{4}\cdot 11^{2}\cdot 229$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.4.17383253.1 | $x^{8} - x^{6} - x^{5} - 2 x^{4} + x^{2} + 2 x + 1$ | $17383253$ | $S_8$ (as 8T50) | trivial |
8.4.17592581.1 | $x^{8} - 2 x^{7} + 3 x^{5} - 4 x^{4} - x^{3} + 4 x^{2} + x - 1$ | $137\cdot 128413$ | $S_8$ (as 8T50) | trivial |
8.4.17712197.1 | $x^{8} - 2 x^{7} + 2 x^{5} - 2 x^{3} - 3 x^{2} + 2 x + 1$ | $17712197$ | $S_8$ (as 8T50) | trivial |
8.4.17919197.1 | $x^{8} - x^{6} - x^{5} - 3 x^{4} + 3 x^{3} + 2 x^{2} - 3 x + 1$ | $17919197$ | $S_8$ (as 8T50) | trivial |
8.4.17949581.1 | $x^{8} - 2 x^{7} + x^{6} + x^{5} - 4 x^{4} + 3 x^{3} - 2 x + 1$ | $13\cdot 71\cdot 19447$ | $S_8$ (as 8T50) | trivial |
8.4.18031373.1 | $x^{8} - x^{7} - 3 x^{6} + 5 x^{5} + x^{4} - 7 x^{3} + 2 x^{2} + 2 x - 1$ | $17\cdot 71\cdot 14939$ | $S_8$ (as 8T50) | trivial |
8.4.18340381.1 | $x^{8} - 4 x^{6} - x^{5} + 5 x^{4} + x^{3} - 4 x^{2} + 1$ | $229\cdot 283^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.4.18416197.1 | $x^{8} - x^{7} - x^{6} + x^{3} - x^{2} + x + 1$ | $18416197$ | $S_8$ (as 8T50) | trivial |
8.4.18441341.1 | $x^{8} - x^{7} - 2 x^{6} + 3 x^{4} + x^{3} - 3 x^{2} + x + 1$ | $18441341$ | $S_8$ (as 8T50) | trivial |
8.4.18553789.1 | $x^{8} - x^{7} - x^{6} + 4 x^{5} - 4 x^{4} - 4 x^{3} + 4 x^{2} + x - 1$ | $59\cdot 157\cdot 2003$ | $S_8$ (as 8T50) | trivial |
8.4.18660737.1 | $x^{8} - 3 x^{6} - 4 x^{5} + 5 x^{4} + 4 x^{3} - 3 x^{2} + 1$ | $233\cdot 283^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.4.19009909.1 | $x^{8} - x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} - 3 x^{3} + 3 x^{2} - 1$ | $197\cdot 96497$ | $S_8$ (as 8T50) | trivial |
8.4.19129013.1 | $x^{8} - 2 x^{7} + 4 x^{5} - 5 x^{4} + x^{3} + 3 x^{2} - 4 x + 1$ | $131\cdot 146023$ | $S_8$ (as 8T50) | trivial |
8.4.19268125.1 | $x^{8} - 2 x^{7} + x^{6} + x^{5} - 5 x^{4} + 4 x^{3} + 4 x^{2} - 2 x - 1$ | $5^{4}\cdot 30829$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.4.19360000.1 | $x^{8} - 3 x^{6} + 3 x^{4} - 3 x^{2} + 1$ | $2^{8}\cdot 5^{4}\cdot 11^{2}$ | $C_2^2 \wr C_2$ (as 8T18) | trivial |
8.4.19824653.1 | $x^{8} - x^{7} - 3 x^{6} + 4 x^{5} + x^{4} - 4 x^{3} + 3 x^{2} + x - 1$ | $19824653$ | $S_8$ (as 8T50) | trivial |
8.4.19885949.1 | $x^{8} - 3 x^{7} + 3 x^{6} + 3 x^{5} - 7 x^{4} + 3 x^{3} + 4 x^{2} - 2 x - 1$ | $19885949$ | $S_8$ (as 8T50) | trivial |
8.4.20013373.1 | $x^{8} - x^{7} - 2 x^{6} + 2 x^{4} + x^{3} + x - 1$ | $20013373$ | $S_8$ (as 8T50) | trivial |
8.4.20030653.1 | $x^{8} - 2 x^{7} - x^{6} + 5 x^{5} - 2 x^{4} - 6 x^{3} + 4 x^{2} + 3 x - 1$ | $37\cdot 541369$ | $S_8$ (as 8T50) | trivial |
8.4.20099501.1 | $x^{8} - 3 x^{7} + 2 x^{6} + x^{5} - 2 x^{4} + 3 x^{3} - 2 x^{2} - 2 x + 1$ | $31\cdot 648371$ | $S_8$ (as 8T50) | trivial |
8.4.20182493.1 | $x^{8} - x^{7} - 3 x^{6} + 5 x^{5} - x^{4} - 4 x^{3} + 3 x^{2} - 1$ | $20182493$ | $S_8$ (as 8T50) | trivial |
8.4.20262517.1 | $x^{8} - 2 x^{6} - 3 x^{5} - x^{4} + 9 x^{3} + x^{2} - 5 x + 1$ | $11\cdot 23\cdot 283^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.4.20268125.1 | $x^{8} - x^{7} - x^{6} + 2 x^{5} - 3 x^{4} - 4 x^{3} + x^{2} + 3 x + 1$ | $5^{4}\cdot 32429$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.4.20493125.1 | $x^{8} - x^{7} + 3 x^{5} - 3 x^{4} + 2 x^{2} - 2 x - 1$ | $5^{4}\cdot 32789$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.4.20502784.1 | $x^{8} - x^{6} + 4 x^{4} - 4 x^{2} + 1$ | $2^{8}\cdot 283^{2}$ | $C_2^3:S_4$ (as 8T39) | trivial |
8.4.20613077.1 | $x^{8} - x^{7} - x^{6} + x^{5} - 2 x^{4} - 2 x^{3} + 3 x^{2} + x - 1$ | $20613077$ | $S_8$ (as 8T50) | trivial |
8.4.20993125.1 | $x^{8} - x^{7} - 2 x^{5} + x^{3} + x^{2} + 2 x - 1$ | $5^{4}\cdot 33589$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.4.21543941.1 | $x^{8} - x^{7} + 2 x^{6} - 7 x^{5} + 4 x^{4} - 5 x^{3} + 6 x^{2} + 2 x - 1$ | $269\cdot 283^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.4.21550625.1 | $x^{8} - x^{7} - x^{6} - 2 x^{5} + 3 x^{4} + 4 x^{3} - 4 x^{2} - 2 x + 1$ | $5^{4}\cdot 29^{2}\cdot 41$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.4.22974464.1 | $x^{8} - 2 x^{7} + x^{6} - 4 x^{4} + 6 x^{3} - 6 x^{2} + 4 x - 1$ | $2^{12}\cdot 71\cdot 79$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.4.23040000.1 | $x^{8} - 2 x^{7} - x^{6} - 5 x^{4} - x^{2} - 2 x + 1$ | $2^{12}\cdot 3^{2}\cdot 5^{4}$ | $Q_8:C_2$ (as 8T11) | trivial |
8.4.23643125.1 | $x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 5 x^{4} + 3 x^{3} + x^{2} - 3 x + 1$ | $5^{4}\cdot 11\cdot 19\cdot 181$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.4.24212981.1 | $x^{8} - x^{7} - 3 x^{6} + 4 x^{5} + 3 x^{4} - 4 x^{3} - 3 x^{2} + x + 1$ | $13\cdot 17\cdot 331^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.4.25338125.1 | $x^{8} - 3 x^{7} + 3 x^{6} - x^{5} - 3 x^{4} + 6 x^{3} - 5 x^{2} + 4 x - 1$ | $5^{4}\cdot 71\cdot 571$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.4.25388213.1 | $x^{8} - 3 x^{7} + 3 x^{6} + 4 x^{5} - 7 x^{4} - 4 x^{3} + 3 x^{2} + 3 x + 1$ | $283^{2}\cdot 317$ | $C_2 \wr S_4$ (as 8T44) | trivial |