| 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 |
| 8.0.26265625.2 |
$x^{8} - 2 x^{7} + 10 x^{6} - 12 x^{5} + 29 x^{4} - 18 x^{3} + 25 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$5^{6}\cdot 41^{2}$ |
$2$ |
$8.46103452991$ |
$21.410136276713814$ |
|
|
✓ |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$9.63994557572$ |
| 8.0.58140625.1 |
$x^{8} - 2 x^{7} + x^{6} + 4 x^{5} + 4 x^{4} - 28 x^{3} + 59 x^{2} - 54 x + 31$ |
$8$ |
[0,4] |
$5^{6}\cdot 61^{2}$ |
$2$ |
$9.34458377794$ |
$26.115143751039085$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$14.7059087656$ |
| 8.0.159390625.2 |
$x^{8} - x^{7} - 7 x^{6} + 10 x^{5} + 21 x^{4} - 30 x^{3} - 28 x^{2} + 48 x + 41$ |
$8$ |
[0,4] |
$5^{6}\cdot 101^{2}$ |
$2$ |
$10.6000483617$ |
$33.60378443921746$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$17.149972868$ |
| 8.4.268435456.1 |
$x^{8} - 4 x^{6} - 2 x^{4} + 12 x^{2} + 1$ |
$8$ |
[4,2] |
$2^{28}$ |
$1$ |
$11.313708499$ |
$14.050017282986396$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$21.1232074946$ |
| 8.4.324000000.1 |
$x^{8} - 3 x^{6} - x^{4} + 3 x^{2} + 1$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$11.5829218529$ |
$19.480074928505935$ |
|
|
✓ |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$14.3863096369$ |
| 8.4.324000000.4 |
$x^{8} - x^{6} - 4 x^{4} + 4 x^{2} + 1$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$11.5829218529$ |
$19.480074928505935$ |
|
|
✓ |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$16.9978390201$ |
| 8.0.484000000.7 |
$x^{8} - 12 x^{6} + 64 x^{4} - 143 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$12.1788328563$ |
$37.301503595352386$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$35.2057397082$ |
| 8.0.484000000.8 |
$x^{8} - 11 x^{6} + 51 x^{4} - 121 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$12.1788328563$ |
$37.301503595352386$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$60.1386480197$ |
| 8.0.484000000.10 |
$x^{8} + 11 x^{6} + 51 x^{4} + 121 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$12.1788328563$ |
$37.301503595352386$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$60.0737331615$ |
| 8.0.484000000.11 |
$x^{8} + 12 x^{6} + 64 x^{4} + 143 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$12.1788328563$ |
$37.301503595352386$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$48.4178812304$ |
| 8.0.511890625.2 |
$x^{8} - x^{7} - 7 x^{6} + 10 x^{5} + 21 x^{4} - 50 x^{3} - 38 x^{2} + 138 x + 131$ |
$8$ |
[0,4] |
$5^{6}\cdot 181^{2}$ |
$2$ |
$12.2644237355$ |
$44.98490324139099$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$32.0249946959$ |
| 8.0.907515625.2 |
$x^{8} - 2 x^{7} - 14 x^{6} + 34 x^{5} + 49 x^{4} - 148 x^{3} - x^{2} + 21 x + 181$ |
$8$ |
[0,4] |
$5^{6}\cdot 241^{2}$ |
$2$ |
$13.1744278653$ |
$51.90820660442091$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$63.3812441526$ |
| 8.4.1024000000.4 |
$x^{8} - 2 x^{6} - 6 x^{4} + 2 x^{2} + 1$ |
$8$ |
[4,2] |
$2^{16}\cdot 5^{6}$ |
$2$ |
$13.3748060995$ |
$18.914832180063517$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$29.0423408322$ |
| 8.4.1024000000.5 |
$x^{8} - 4 x^{6} + x^{4} + 6 x^{2} + 1$ |
$8$ |
[4,2] |
$2^{16}\cdot 5^{6}$ |
$2$ |
$13.3748060995$ |
$18.914832180063517$ |
|
|
✓ |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$39.1647068077$ |
| 8.4.1064390625.1 |
$x^{8} - 3 x^{7} + x^{6} - 4 x^{5} - x^{4} - 2 x^{3} - 6 x^{2} + 4 x + 1$ |
$8$ |
[4,2] |
$3^{4}\cdot 5^{6}\cdot 29^{2}$ |
$3$ |
$13.4396398271$ |
$31.187971562966524$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$28.2661752771$ |
| 8.4.1064390625.2 |
$x^{8} - x^{7} + x^{6} + 4 x^{5} - 9 x^{4} - 10 x^{3} - 20 x^{2} - 20 x - 5$ |
$8$ |
[4,2] |
$3^{4}\cdot 5^{6}\cdot 29^{2}$ |
$3$ |
$13.4396398271$ |
$31.187971562966524$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$32.747131008$ |
| 8.4.1212153856.4 |
$x^{8} - 8 x^{6} + 12 x^{4} - 24 x^{3} - 28 x^{2} + 24 x + 31$ |
$8$ |
[4,2] |
$2^{22}\cdot 17^{2}$ |
$2$ |
$13.6598118814$ |
$27.736837922354518$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$85.5081560743$ |
| 8.0.1212153856.11 |
$x^{8} - 4 x^{7} + 6 x^{6} - 3 x^{4} + 6 x^{2} + 4 x + 7$ |
$8$ |
[0,4] |
$2^{22}\cdot 17^{2}$ |
$2$ |
$13.6598118814$ |
$27.736837922354518$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$3$ |
$23.5697232166$ |
| 8.4.1216265625.2 |
$x^{8} - 3 x^{7} + x^{6} + 11 x^{5} - 31 x^{4} + 28 x^{3} + 24 x^{2} - 56 x + 16$ |
$8$ |
[4,2] |
$3^{4}\cdot 5^{6}\cdot 31^{2}$ |
$3$ |
$13.6655952658$ |
$32.24548975496266$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$29.9069034439$ |
| 8.4.1216265625.3 |
$x^{8} - x^{7} - 2 x^{6} + 10 x^{5} - 9 x^{4} - 10 x^{3} + 22 x^{2} - 17 x + 1$ |
$8$ |
[4,2] |
$3^{4}\cdot 5^{6}\cdot 31^{2}$ |
$3$ |
$13.6655952658$ |
$32.24548975496266$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$35.5868245569$ |
| 8.0.1233765625.2 |
$x^{8} - 2 x^{7} - 14 x^{6} + 29 x^{5} + 64 x^{4} - 158 x^{3} - 136 x^{2} + 371 x + 341$ |
$8$ |
[0,4] |
$5^{6}\cdot 281^{2}$ |
$2$ |
$13.6900200197$ |
$56.05065127531708$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$76.6446161648$ |
| 8.4.1444000000.4 |
$x^{8} - 2 x^{7} + x^{6} + 4 x^{5} - 11 x^{4} + 12 x^{3} - 16 x^{2} + 16 x - 4$ |
$8$ |
[4,2] |
$2^{8}\cdot 5^{6}\cdot 19^{2}$ |
$3$ |
$13.9619442377$ |
$29.149714088647936$ |
|
|
|
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$43.4590157699$ |
| 8.4.1444000000.7 |
$x^{8} - 3 x^{6} - 10 x^{5} - x^{4} + 20 x^{3} + 23 x^{2} + 10 x + 1$ |
$8$ |
[4,2] |
$2^{8}\cdot 5^{6}\cdot 19^{2}$ |
$3$ |
$13.9619442377$ |
$29.149714088647936$ |
|
|
✓ |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$27.7923606864$ |
| 8.0.1816890625.6 |
$x^{8} - x^{7} - 17 x^{6} + 10 x^{5} + 121 x^{4} - 40 x^{3} - 388 x^{2} + 58 x + 461$ |
$8$ |
[0,4] |
$5^{6}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$14.3686543636$ |
$61.745411988561074$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$51.2643387767$ |
| 8.0.1816890625.7 |
$x^{8} - 3 x^{7} - 14 x^{6} + 41 x^{5} + 89 x^{4} - 247 x^{3} - 196 x^{2} + 419 x + 331$ |
$8$ |
[0,4] |
$5^{6}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$14.3686543636$ |
$61.745411988561074$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$46.0546627272$ |
| 8.0.1816890625.8 |
$x^{8} - x^{7} - 14 x^{6} + 14 x^{5} + 81 x^{4} - 90 x^{3} - 270 x^{2} + 225 x + 505$ |
$8$ |
[0,4] |
$5^{6}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$14.3686543636$ |
$61.745411988561074$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$68.9009646943$ |
| 8.0.1816890625.9 |
$x^{8} - 3 x^{7} - 15 x^{6} + 42 x^{5} + 79 x^{4} - 162 x^{3} - 220 x^{2} + 48 x + 571$ |
$8$ |
[0,4] |
$5^{6}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$14.3686543636$ |
$61.745411988561074$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$43.50849549$ |
| 8.0.2127515625.4 |
$x^{8} - 3 x^{7} - 16 x^{6} + 43 x^{5} + 111 x^{4} - 245 x^{3} - 300 x^{2} + 355 x + 505$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{6}\cdot 41^{2}$ |
$3$ |
$14.6549416904$ |
$37.083443828241876$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$67.5169116564$ |
| 8.0.2512515625.2 |
$x^{8} - x^{7} - 17 x^{6} + 15 x^{5} + 116 x^{4} - 85 x^{3} - 413 x^{2} + 188 x + 701$ |
$8$ |
[0,4] |
$5^{6}\cdot 401^{2}$ |
$2$ |
$14.962824993$ |
$66.95757085563274$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$73.6242654777$ |
| 8.0.2769390625.2 |
$x^{8} - 3 x^{7} + 25 x^{6} - 63 x^{5} + 224 x^{4} - 417 x^{3} + 805 x^{2} - 877 x + 961$ |
$8$ |
[0,4] |
$5^{6}\cdot 421^{2}$ |
$2$ |
$15.1460026059$ |
$68.607019266523$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$70.9967718291$ |
| 8.0.3178140625.1 |
$x^{8} - 3 x^{7} - 6 x^{6} + 33 x^{5} + 51 x^{4} - 125 x^{3} - 80 x^{2} + 505 x + 655$ |
$8$ |
[0,4] |
$5^{6}\cdot 11^{2}\cdot 41^{2}$ |
$3$ |
$15.4089000714$ |
$71.0093887402365$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$82.966822886$ |
| 8.0.3178140625.3 |
$x^{8} - 2 x^{7} + 12 x^{6} - 20 x^{5} + 111 x^{4} - 10 x^{3} + 543 x^{2} + 139 x + 881$ |
$8$ |
[0,4] |
$5^{6}\cdot 11^{2}\cdot 41^{2}$ |
$3$ |
$15.4089000714$ |
$71.0093887402365$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$82.6261050011$ |
| 8.0.3320640625.1 |
$x^{8} - x^{7} + 21 x^{6} - 16 x^{5} + 171 x^{4} - 80 x^{3} + 600 x^{2} - 130 x + 755$ |
$8$ |
[0,4] |
$5^{6}\cdot 461^{2}$ |
$2$ |
$15.4936140937$ |
$71.79231635862584$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$82.7920813231$ |
| 8.0.3844000000.1 |
$x^{8} - 22 x^{6} + 194 x^{4} - 713 x^{2} + 961$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 31^{2}$ |
$3$ |
$15.7796702107$ |
$62.619679802828685$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$157.092910973$ |
| 8.0.3844000000.2 |
$x^{8} - 19 x^{6} + 151 x^{4} - 589 x^{2} + 961$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 31^{2}$ |
$3$ |
$15.7796702107$ |
$62.619679802828685$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$174.079516126$ |
| 8.0.3844000000.6 |
$x^{8} + 19 x^{6} + 151 x^{4} + 589 x^{2} + 961$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 31^{2}$ |
$3$ |
$15.7796702107$ |
$62.619679802828685$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$174.39771168$ |
| 8.0.3844000000.7 |
$x^{8} + 22 x^{6} + 194 x^{4} + 713 x^{2} + 961$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 31^{2}$ |
$3$ |
$15.7796702107$ |
$62.619679802828685$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$10$ |
$3$ |
$84.2551614337$ |
| 8.4.4030726144.1 |
$x^{8} - 4 x^{7} + 2 x^{6} - 4 x^{5} + 7 x^{4} + 8 x^{3} - 16 x^{2} + 8$ |
$8$ |
[4,2] |
$2^{22}\cdot 31^{2}$ |
$2$ |
$15.8735078659$ |
$37.455304749449176$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$165.255361838$ |
| 8.0.4059346369.1 |
$x^{8} - x^{7} + 5 x^{6} - 8 x^{5} + 37 x^{4} - 58 x^{3} + 80 x^{2} - 38 x + 9$ |
$8$ |
[0,4] |
$13^{6}\cdot 29^{2}$ |
$2$ |
$15.8875530497$ |
$36.868588674506164$ |
|
|
|
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$3$ |
$97.9900959685$ |
| 8.4.4079249161.1 |
$x^{8} - 2 x^{7} - 3 x^{6} + 2 x^{5} - 9 x^{4} + 2 x^{3} - 3 x^{2} - 2 x + 1$ |
$8$ |
[4,2] |
$13^{2}\cdot 17^{6}$ |
$2$ |
$15.8972692216$ |
$30.186194580660594$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$55.4374811595$ |
| 8.0.4241265625.2 |
$x^{8} - x^{7} + 23 x^{6} - 15 x^{5} + 196 x^{4} - 65 x^{3} + 727 x^{2} - 82 x + 991$ |
$8$ |
[0,4] |
$5^{6}\cdot 521^{2}$ |
$2$ |
$15.974855339$ |
$76.32140644266818$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$96.5540024709$ |
| 8.4.4405640625.1 |
$x^{8} - 2 x^{7} - 5 x^{6} + 8 x^{5} - 6 x^{4} + 22 x^{3} - 5 x^{2} - 28 x + 31$ |
$8$ |
[4,2] |
$3^{4}\cdot 5^{6}\cdot 59^{2}$ |
$3$ |
$16.0509644744$ |
$44.48505546908213$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$48.6572550752$ |
| 8.4.4405640625.2 |
$x^{8} - 3 x^{7} - x^{6} + 18 x^{5} - 29 x^{4} + 60 x^{2} - 90 x + 45$ |
$8$ |
[4,2] |
$3^{4}\cdot 5^{6}\cdot 59^{2}$ |
$3$ |
$16.0509644744$ |
$44.48505546908213$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$2$ |
$5$ |
$40.7092694147$ |
| 8.4.4539390625.1 |
$x^{8} - 3 x^{7} - 3 x^{6} + 20 x^{5} - 19 x^{4} - 20 x^{3} + 58 x^{2} - 44 x + 11$ |
$8$ |
[4,2] |
$5^{6}\cdot 7^{4}\cdot 11^{2}$ |
$3$ |
$16.1110814984$ |
$29.34086180290925$ |
|
|
✓ |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$89.0845661356$ |
| 8.4.4539390625.3 |
$x^{8} - 2 x^{7} + 8 x^{5} - 21 x^{4} + 2 x^{3} + 15 x^{2} + 7 x + 1$ |
$8$ |
[4,2] |
$5^{6}\cdot 7^{4}\cdot 11^{2}$ |
$3$ |
$16.1110814984$ |
$29.34086180290925$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$65.6555207605$ |
| 8.0.4573140625.2 |
$x^{8} - x^{7} + 11 x^{6} + 4 x^{5} + 81 x^{4} + 40 x^{3} + 430 x^{2} + 480 x + 1055$ |
$8$ |
[0,4] |
$5^{6}\cdot 541^{2}$ |
$2$ |
$16.126006092$ |
$77.7725136480552$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$94.6541036446$ |
| 8.4.4709390625.1 |
$x^{8} - x^{7} - 5 x^{6} - 9 x^{5} + 4 x^{4} + 31 x^{3} - 15 x^{2} - 21 x + 31$ |
$8$ |
[4,2] |
$3^{4}\cdot 5^{6}\cdot 61^{2}$ |
$3$ |
$16.185293879$ |
$45.23275582376457$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$49.8375707721$ |
| 8.4.4709390625.2 |
$x^{8} - 3 x^{7} + 2 x^{6} - 14 x^{4} + 15 x^{3} - 12 x^{2} + 36 x - 9$ |
$8$ |
[4,2] |
$3^{4}\cdot 5^{6}\cdot 61^{2}$ |
$3$ |
$16.185293879$ |
$45.23275582376457$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$84.8366562454$ |
| 8.0.4709390625.4 |
$x^{8} - 3 x^{7} - 16 x^{6} + 58 x^{5} + 111 x^{4} - 410 x^{3} - 300 x^{2} + 1000 x + 880$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{6}\cdot 61^{2}$ |
$3$ |
$16.185293879$ |
$45.23275582376457$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$10$ |
$3$ |
$100.886439517$ |
| 8.4.4848615424.5 |
$x^{8} + 4 x^{6} - 8 x^{5} + 6 x^{4} + 8 x^{3} - 36 x^{2} - 24 x + 2$ |
$8$ |
[4,2] |
$2^{24}\cdot 17^{2}$ |
$2$ |
$16.244345479$ |
$32.984845004941285$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
trivial |
$2$ |
$5$ |
$99.6310651223$ |
