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 |
---|---|---|---|---|
15.1.723352547563839.1 | $x^{15} - x^{14} - 2 x^{13} + 2 x^{12} - 2 x^{11} + 2 x^{10} + 5 x^{9} - 5 x^{8} + 4 x^{7} - 5 x^{6} - 4 x^{5} + 5 x^{4} - 2 x^{3} + x^{2} + x + 1$ | $-\,3^{3}\cdot 6653\cdot 4026880369$ | $S_{15}$ (as 15T104) | trivial |
15.3.1788527348449625.1 | $x^{15} - 2 x^{14} + 4 x^{13} - 9 x^{12} + 13 x^{11} - 15 x^{10} + 18 x^{9} - 23 x^{8} + 33 x^{7} - 44 x^{6} + 48 x^{5} - 44 x^{4} + 30 x^{3} - 16 x^{2} + 6 x - 1$ | $5^{3}\cdot 7^{10}\cdot 37^{3}$ | $S_5 \times C_3$ (as 15T24) | trivial |
15.3.2164169497031757.1 | $x^{15} - 7 x^{14} + 23 x^{13} - 45 x^{12} + 54 x^{11} - 32 x^{10} - 14 x^{9} + 55 x^{8} - 72 x^{7} + 69 x^{6} - 57 x^{5} + 39 x^{4} - 21 x^{3} + 9 x^{2} - 4 x + 1$ | $3^{3}\cdot 69593\cdot 1151759887$ | $S_{15}$ (as 15T104) | trivial |
15.3.2354315214908549.1 | $x^{15} - x^{14} + x^{13} - x^{12} - x^{11} + 3 x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} - x^{6} + 2 x^{3} - x^{2} + 2 x - 1$ | $27765763\cdot 84792023$ | $S_{15}$ (as 15T104) | trivial |
15.3.2432060458605625.1 | $x^{15} - x^{14} - 2 x^{13} + x^{12} + 2 x^{11} - 4 x^{10} - 4 x^{9} + 3 x^{8} + 4 x^{7} - 2 x^{6} - 3 x^{5} + 5 x^{4} + 5 x^{3} - x^{2} - 4 x - 1$ | $5^{4}\cdot 19^{2}\cdot 47^{6}$ | $C_3\wr D_5$ (as 15T46) | trivial |
15.3.3276367268581097.1 | $x^{15} - 6 x^{13} - x^{12} + 16 x^{11} + 8 x^{10} - 20 x^{9} - 24 x^{8} + 4 x^{7} + 31 x^{6} + 15 x^{5} - 15 x^{4} - 14 x^{3} + x^{2} + 4 x + 1$ | $3276367268581097$ | $S_{15}$ (as 15T104) | trivial |
15.1.3703260525677583.1 | $x^{15} - 2 x^{14} + x^{13} - x^{12} - 5 x^{11} + 4 x^{10} - 3 x^{9} + 2 x^{8} + 6 x^{7} - 3 x^{6} + 3 x^{5} - 4 x^{4} - 5 x^{3} - 3 x^{2} - 3 x - 1$ | $-\,3\cdot 13^{3}\cdot 561866260913$ | $S_{15}$ (as 15T104) | trivial |
15.3.4864965285308625.1 | $x^{15} - 3 x^{14} + 6 x^{13} - 12 x^{12} + 14 x^{11} - 17 x^{10} + 24 x^{9} - 28 x^{8} + 31 x^{7} - 21 x^{6} + 18 x^{5} - 15 x^{4} + 16 x^{3} - 11 x^{2} + 5 x - 1$ | $3^{9}\cdot 5^{3}\cdot 7^{11}$ | $S_5 \times C_3$ (as 15T24) | trivial |
15.1.5976545641547631.1 | $x^{15} - 2 x^{14} + 5 x^{13} - 10 x^{12} + 13 x^{11} - 20 x^{10} + 23 x^{9} - 22 x^{8} + 22 x^{7} - 20 x^{6} + 18 x^{5} - 20 x^{4} + 21 x^{3} - 15 x^{2} + 6 x - 1$ | $-\,3\cdot 195479\cdot 10191283363$ | $S_{15}$ (as 15T104) | trivial |
15.3.6114596477365737.1 | $x^{15} - 3 x^{14} + 5 x^{13} - 2 x^{12} - 8 x^{11} + 18 x^{10} - 18 x^{9} + 20 x^{7} - 27 x^{6} + 15 x^{5} + 3 x^{4} - 11 x^{3} + 10 x^{2} - 5 x + 1$ | $3^{4}\cdot 15601\cdot 4838718377$ | $S_{15}$ (as 15T104) | trivial |
15.1.6401597515801839.1 | $x^{15} - x^{14} - x^{13} + 2 x^{12} - 4 x^{11} - x^{10} + 3 x^{9} + 3 x^{8} + 12 x^{7} - 2 x^{6} - 14 x^{5} + 7 x^{4} + 11 x^{3} - 6 x^{2} + 1$ | $-\,3^{9}\cdot 13^{3}\cdot 23^{6}$ | $S_5 \times S_3$ (as 15T29) | trivial |
15.5.8565893077528823.1 | $x^{15} - 6 x^{13} + 9 x^{11} - 18 x^{10} + x^{9} + 32 x^{8} - 17 x^{7} - 19 x^{6} + 24 x^{5} + 3 x^{4} - 15 x^{3} + 3 x^{2} + 4 x - 1$ | $-\,23^{5}\cdot 191^{4}$ | $C_5\wr S_3$ (as 15T32) | trivial |
15.5.10496055636998343.1 | $x^{15} - 4 x^{14} + 6 x^{13} - x^{12} - 11 x^{11} + 18 x^{10} - 10 x^{9} - 9 x^{8} + 19 x^{7} - 12 x^{6} - 3 x^{5} + 9 x^{4} - 5 x^{3} - x^{2} + 3 x - 1$ | $-\,3^{5}\cdot 157\cdot 2377\cdot 115742009$ | $S_{15}$ (as 15T104) | trivial |
15.3.10544075126076649.1 | $x^{15} - 6 x^{14} + 11 x^{13} - x^{12} - 10 x^{11} - 13 x^{10} + 18 x^{9} + 40 x^{8} - 30 x^{7} - 64 x^{6} + 42 x^{5} + 47 x^{4} - 27 x^{3} - 19 x^{2} + 9 x + 1$ | $37^{2}\cdot 43^{2}\cdot 1609^{3}$ | $C_3\wr S_5$ (as 15T78) | trivial |
15.3.11354350039657729.1 | $x^{15} - 4 x^{14} + 5 x^{13} + x^{12} - 7 x^{11} + x^{10} + 7 x^{9} - 2 x^{8} - 8 x^{7} + 22 x^{6} - 37 x^{5} + 35 x^{4} - 20 x^{3} + 11 x^{2} - 7 x + 1$ | $13^{2}\cdot 127^{2}\cdot 1609^{3}$ | $C_3\wr S_5$ (as 15T78) | trivial |
15.3.12853809661090929.1 | $x^{15} - x^{14} - x^{13} + 3 x^{12} - x^{10} - 4 x^{9} + 4 x^{8} + 2 x^{7} - 7 x^{6} - x^{5} + 2 x^{4} - x^{3} + 2 x + 1$ | $3\cdot 4284603220363643$ | $S_{15}$ (as 15T104) | trivial |
15.3.15315650494266781.1 | $x^{15} - 2 x^{14} + x^{13} - x^{12} + 7 x^{11} - 5 x^{10} - 10 x^{9} + 7 x^{8} + 16 x^{7} - 15 x^{6} - 19 x^{5} + 27 x^{4} - 2 x^{3} - 11 x^{2} + 6 x - 1$ | $127^{2}\cdot 9829^{3}$ | $C_3\wr S_5$ (as 15T78) | trivial |
15.3.16680932154277329.1 | $x^{15} - 2 x^{14} + 6 x^{13} - 14 x^{12} + 23 x^{11} - 35 x^{10} + 44 x^{9} - 41 x^{8} + 25 x^{7} - 4 x^{6} - 20 x^{5} + 34 x^{4} - 30 x^{3} + 17 x^{2} - 6 x + 1$ | $3\cdot 47\cdot 103\cdot 11057\cdot 103878739$ | $S_{15}$ (as 15T104) | trivial |
15.3.19664802801826816.1 | $x^{15} - 5 x^{14} + 14 x^{13} - 23 x^{12} + 19 x^{11} + 7 x^{10} - 41 x^{9} + 47 x^{8} - 10 x^{7} - 39 x^{6} + 50 x^{5} - 18 x^{4} - 16 x^{3} + 21 x^{2} - 9 x + 1$ | $2^{10}\cdot 79^{7}$ | $D_5\times S_3$ (as 15T7) | trivial |
15.3.21643467887730481.1 | $x^{15} - x^{14} - x^{13} + x^{12} - 7 x^{11} - 2 x^{10} + 18 x^{9} + 12 x^{8} - 17 x^{7} + 7 x^{6} - 11 x^{5} - 21 x^{4} + 22 x^{3} - 11 x^{2} - 2 x - 1$ | $13^{2}\cdot 47^{6}\cdot 109^{2}$ | $C_3\wr D_5$ (as 15T46) | trivial |
15.3.23713122135310336.1 | $x^{15} - 5 x^{14} + 10 x^{13} - 5 x^{12} - 15 x^{11} + 29 x^{10} - 8 x^{9} - 31 x^{8} + 36 x^{7} - 24 x^{5} + 12 x^{4} + 9 x^{3} - 9 x^{2} + 1$ | $2^{18}\cdot 67^{6}$ | $A_5$ (as 15T5) | trivial |
15.1.24118280788986467.1 | $x^{15} - 2 x^{14} + 6 x^{12} - 13 x^{11} + 13 x^{10} - x^{9} - 21 x^{8} + 40 x^{7} - 41 x^{6} + 29 x^{5} - 18 x^{4} + 13 x^{3} - 7 x^{2} + x + 1$ | $-\,59^{6}\cdot 83^{3}$ | $S_5 \times S_3$ (as 15T29) | trivial |
15.3.31123779291971584.1 | $x^{15} + x^{13} - x^{12} - 5 x^{11} - 4 x^{10} - 5 x^{9} - x^{8} + 4 x^{7} + 2 x^{6} - 2 x^{5} - 4 x^{4} - 5 x^{3} - 4 x^{2} - 3 x - 1$ | $2^{18}\cdot 587^{4}$ | $S_6$ (as 15T28) | trivial |
15.5.35351257235385344.1 | $x^{15} - 3 x^{13} - 5 x^{12} + 8 x^{11} + x^{10} + 14 x^{9} - 13 x^{8} - 17 x^{7} + 4 x^{6} + x^{5} + 22 x^{4} - 2 x^{3} - 8 x^{2} - 3 x - 1$ | $-\,2^{10}\cdot 11^{13}$ | $S_3 \times C_5$ (as 15T4) | trivial |
15.3.39671359416303616.1 | $x^{15} - 7 x^{14} + 24 x^{13} - 47 x^{12} + 46 x^{11} + 18 x^{10} - 150 x^{9} + 296 x^{8} - 383 x^{7} + 371 x^{6} - 282 x^{5} + 171 x^{4} - 83 x^{3} + 31 x^{2} - 8 x + 1$ | $2^{18}\cdot 73^{6}$ | $A_5$ (as 15T5) | trivial |
15.1.44543599279432079.1 | $x^{15} - 4 x^{14} + 4 x^{13} + 4 x^{12} - 5 x^{11} - 13 x^{10} + 20 x^{9} + 4 x^{8} - 15 x^{7} - 13 x^{6} + 27 x^{5} - 4 x^{4} - 8 x^{3} - 2 x^{2} + 6 x - 1$ | $-\,239^{7}$ | $D_{15}$ (as 15T2) | trivial |
15.3.47090024679574321.1 | $x^{15} - x^{12} - x^{11} - x^{8} - 2 x^{7} + 2 x^{5} + 3 x^{4} + 2 x^{3} - x - 1$ | $14731^{4}$ | $S_6$ (as 15T28) | trivial |
15.3.57352136505929721.1 | $x^{15} - 2 x^{14} + 4 x^{13} - 10 x^{12} + 22 x^{11} - 33 x^{10} + 40 x^{9} - 63 x^{8} + 81 x^{7} - 81 x^{6} + 63 x^{5} - 69 x^{4} + 57 x^{3} - 24 x^{2} + 3$ | $3^{18}\cdot 23^{6}$ | $C_3^4:A_5$ (as 15T53) | trivial |
15.1.57477829056511319.1 | $x^{15} - 2 x^{14} + 3 x^{13} - 3 x^{12} - 3 x^{11} + 6 x^{10} - 14 x^{9} + 4 x^{8} - 9 x^{7} - 7 x^{6} + 7 x^{5} - 15 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ | $-\,1609^{3}\cdot 13798511$ | $S_3^5.S_5$ (as 15T93) | trivial |
15.3.59463924292145152.1 | $x^{15} - x^{14} - 6 x^{13} + 15 x^{12} - 9 x^{11} - 13 x^{10} + 30 x^{9} - 31 x^{8} + 24 x^{7} - 14 x^{6} + 10 x^{5} - 18 x^{4} + 27 x^{3} - 21 x^{2} + 8 x - 1$ | $2^{12}\cdot 13^{9}\cdot 37^{2}$ | $C_3\wr F_5$ (as 15T56) | trivial |
15.1.59770508839234803.1 | $x^{15} - 2 x^{12} + 3 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 1609^{3}$ | $C_3^4:(C_2\times S_5)$ (as 15T70) | trivial |
15.1.59770508839234803.2 | $x^{15} - x^{9} - x^{6} + x^{3} + 1$ | $-\,3^{15}\cdot 1609^{3}$ | $C_3^4:(C_2\times S_5)$ (as 15T70) | trivial |
15.3.69184806150882304.1 | $x^{15} + x^{13} - 3 x^{12} - 3 x^{11} - 5 x^{10} - 2 x^{9} + 3 x^{8} + 7 x^{7} + 4 x^{6} + x^{5} + x^{4} + 3 x^{3} + x^{2} - 1$ | $2^{10}\cdot 47^{4}\cdot 61^{4}$ | $S_6$ (as 15T28) | trivial |
15.1.69378727128301847.1 | $x^{15} - 2 x^{14} + 2 x^{13} - 2 x^{12} + 2 x^{11} - 4 x^{10} + 3 x^{9} + 2 x^{8} + x^{7} - 5 x^{6} + 3 x^{5} + 3 x^{4} + 6 x^{3} + 2 x^{2} - 1$ | $-\,23^{5}\cdot 47^{6}$ | $D_5\times S_3$ (as 15T7) | trivial |
15.5.77595502265817783.1 | $x^{15} - 3 x^{13} - 2 x^{12} + x^{11} + 12 x^{10} + 3 x^{9} - 15 x^{8} - 10 x^{7} - 4 x^{6} + 20 x^{5} + 7 x^{4} - 3 x^{3} - 7 x^{2} - 4 x + 1$ | $-\,3\cdot 13^{3}\cdot 11772948303113$ | $S_{15}$ (as 15T104) | trivial |
15.1.96318312824155136.1 | $x^{15} - 6 x^{14} + 19 x^{13} - 39 x^{12} + 58 x^{11} - 67 x^{10} + 68 x^{9} - 69 x^{8} + 65 x^{7} - 52 x^{6} + 33 x^{5} - 20 x^{4} + 12 x^{3} - 4 x^{2} + 3 x - 1$ | $-\,2^{10}\cdot 11^{7}\cdot 13^{6}$ | $D_5\times S_3$ (as 15T7) | trivial |
15.3.98765528526263521.1 | $x^{15} - 3 x^{14} + 7 x^{13} - 12 x^{12} + 8 x^{11} - 2 x^{10} - 17 x^{9} + 36 x^{8} - 49 x^{7} + 54 x^{6} - 41 x^{5} + 30 x^{4} - 17 x^{3} + 8 x^{2} - 5 x + 3$ | $13^{3}\cdot 31^{6}\cdot 37^{3}$ | $S_5 \times S_3$ (as 15T29) | trivial |
15.3.126064044311049216.1 | $x^{15} - 4 x^{14} + 3 x^{13} + 15 x^{12} - 40 x^{11} + 23 x^{10} + 52 x^{9} - 111 x^{8} + 83 x^{7} - 67 x^{5} + 86 x^{4} - 62 x^{3} + 26 x^{2} - 7 x + 1$ | $2^{10}\cdot 3^{5}\cdot 47^{7}$ | $D_5\times S_3$ (as 15T7) | trivial |
15.3.137631064560062464.1 | $x^{15} - x^{14} - 2 x^{13} + 3 x^{12} + 11 x^{11} - 5 x^{10} - 14 x^{9} - 5 x^{8} - 10 x^{7} + 22 x^{6} + 14 x^{5} + 2 x^{4} - 13 x^{3} - 5 x^{2} + 1$ | $2^{12}\cdot 23^{6}\cdot 61^{3}$ | $S_5 \times S_3$ (as 15T29) | trivial |
15.3.146928604515779584.1 | $x^{15} - 2 x^{14} - 3 x^{13} + 9 x^{12} - x^{11} - 5 x^{10} + 4 x^{9} - x^{8} + x^{7} - x^{5} - x^{4} + 7 x^{3} - x^{2} + 1$ | $2^{10}\cdot 3461^{4}$ | $S_6$ (as 15T28) | trivial |
15.1.154669958288795403.1 | $x^{15} - x^{12} + 2 x^{9} - 3 x^{6} + 3 x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.2 | $x^{15} - 2 x^{12} + 2 x^{9} - x^{6} + 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.3 | $x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.4 | $x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.5 | $x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.6 | $x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.5.154972454814106259.1 | $x^{15} - x^{14} - 2 x^{13} + x^{12} + x^{11} - x^{10} + 2 x^{9} - 15 x^{8} + 8 x^{7} + 28 x^{6} - 34 x^{5} - 7 x^{4} + 27 x^{3} - 7 x^{2} - 3 x + 1$ | $-\,11^{13}\cdot 67^{2}$ | $C_7^3:C_6$ (as 15T44) | trivial |
15.1.196421600341796875.1 | $x^{15} - x^{10} + 1$ | $-\,5^{15}\cdot 23^{5}$ | $C_5^2:(C_4\times S_3)$ (as 15T27) | trivial |
15.3.274502366303440896.1 | $x^{15} - x^{14} - x^{13} - 5 x^{12} + 5 x^{11} - 5 x^{10} - x^{9} + 3 x^{8} + 7 x^{7} + x^{6} - 3 x^{5} + x^{4} - 13 x^{3} + 5 x^{2} - 3 x + 1$ | $2^{12}\cdot 3^{9}\cdot 23^{7}$ | $S_5 \times S_3$ (as 15T29) | trivial |
15.3.334095024862954369.1 | $x^{15} - 2 x^{14} + 3 x^{13} - 5 x^{12} + x^{11} - 19 x^{10} + 16 x^{9} - 26 x^{8} + 55 x^{7} - 78 x^{6} + 88 x^{5} - 54 x^{4} + 39 x^{3} - 52 x^{2} + 21 x - 1$ | $7^{12}\cdot 17^{6}$ | $D_5\times C_3$ (as 15T3) | trivial |