| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 12.0.47738317081.1 |
$x^{12} - 3 x^{11} + x^{10} + 7 x^{9} - 8 x^{8} - 4 x^{7} + 13 x^{6} - 4 x^{5} - 8 x^{4} + 7 x^{3} + x^{2} - 3 x + 1$ |
$12$ |
(0, 6) |
$7^{10}\cdot 13^{2}$ |
$2$ |
$7.76078392578$ |
$18.248200448594663$ |
|
|
✓ |
$C_2^2 \times A_4$ (as 12T25) |
trivial |
trivial |
$14$ |
$5$ |
$8.9159604909$ |
$0$ |
$13$ |
| 12.0.144627327488.1 |
$x^{12} - 3 x^{11} + 3 x^{10} + 2 x^{9} - 10 x^{8} + 11 x^{7} - x^{6} - 11 x^{5} + 18 x^{4} - 16 x^{3} + 10 x^{2} - 4 x + 1$ |
$12$ |
(0, 6) |
$2^{9}\cdot 7^{10}$ |
$2$ |
$8.51178927698$ |
$14.315066180821045$ |
|
|
? |
$D_4 \times C_3$ (as 12T14) |
trivial |
trivial |
$14$ |
$5$ |
$17.8850263478$ |
$0$ |
$7$ |
| 12.0.198015149549.1 |
$x^{12} - 5 x^{11} + 13 x^{10} - 19 x^{9} + 16 x^{8} - 6 x^{7} + 6 x^{6} - 23 x^{5} + 43 x^{4} - 44 x^{3} + 26 x^{2} - 8 x + 1$ |
$12$ |
(0, 6) |
$7^{10}\cdot 701$ |
$2$ |
$8.73758743869$ |
$134.00079521809832$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
trivial |
$14$ |
$5$ |
$22.4274702703$ |
$0$ |
$701$ |
| 12.0.524274062144.1 |
$x^{12} - 4 x^{11} + 3 x^{10} + 5 x^{9} - 3 x^{8} - 11 x^{7} + 6 x^{6} + 11 x^{5} - 3 x^{4} - 5 x^{3} + 3 x^{2} + 4 x + 1$ |
$12$ |
(0, 6) |
$2^{6}\cdot 7^{10}\cdot 29$ |
$3$ |
$9.476105001248202$ |
$77.08899060875882$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
trivial |
$14$ |
$5$ |
$36.64040293826498$ |
$0$ |
$29$ |
| 12.0.524274062144.2 |
$x^{12} - 3 x^{11} + x^{10} + 6 x^{8} + 3 x^{7} - 8 x^{6} - 11 x^{5} - x^{4} + 7 x^{3} + 8 x^{2} + 4 x + 1$ |
$12$ |
(0, 6) |
$2^{6}\cdot 7^{10}\cdot 29$ |
$3$ |
$9.476105001248202$ |
$77.08899060875882$ |
|
|
|
$C_2\wr C_6$ (as 12T134) |
trivial |
trivial |
$14$ |
$5$ |
$41.12872053146278$ |
$0$ |
$29$ |
| 12.0.1157018619904.1 |
$x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{12}\cdot 7^{10}$ |
$2$ |
$10.1222803696$ |
$10.122280369592772$ |
✓ |
✓ |
✓ |
$C_6\times C_2$ (as 12T2) |
trivial |
trivial |
$28$ |
$5$ |
$123.252731541$ |
$0$ |
$7$ |
| 12.0.1157018619904.3 |
$x^{12} + 5 x^{10} + 11 x^{8} + 13 x^{6} + 9 x^{4} + 3 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{12}\cdot 7^{10}$ |
$2$ |
$10.1222803696$ |
$17.023578553967216$ |
|
|
✓ |
$C_2^2 \times A_4$ (as 12T25) |
trivial |
trivial |
$14$ |
$5$ |
$59.4583386625$ |
$0$ |
$7$ |
| 12.0.4413675765625.1 |
$x^{12} - x^{11} + 2 x^{10} - 3 x^{9} + 5 x^{8} - 8 x^{7} + 13 x^{6} + 8 x^{5} + 5 x^{4} + 3 x^{3} + 2 x^{2} + x + 1$ |
$12$ |
(0, 6) |
$5^{6}\cdot 7^{10}$ |
$2$ |
$11.3170534969$ |
$11.317053496860568$ |
✓ |
✓ |
? |
$C_6\times C_2$ (as 12T2) |
trivial |
trivial |
$14$ |
$5$ |
$104.882003477$ |
$0$ |
$7$ |
| 12.6.5559960326067.1 |
$x^{12} - 5 x^{11} + 6 x^{10} + 9 x^{9} - 26 x^{8} + 15 x^{7} - x^{6} + 12 x^{5} - 6 x^{4} - 16 x^{3} + 5 x^{2} + 6 x + 1$ |
$12$ |
(6, 3) |
$-\,3^{9}\cdot 7^{10}$ |
$2$ |
$11.5369047675$ |
$11.53690476748077$ |
|
|
? |
$D_4 \times C_3$ (as 12T14) |
trivial |
$[2]$ |
$2$ |
$8$ |
$48.1439095362$ |
$5$ |
$7$ |
| 12.4.6889288847861.1 |
$x^{12} - x^{10} - 7 x^{9} + x^{8} + 13 x^{6} + x^{4} - 7 x^{3} - x^{2} + 1$ |
$12$ |
(4, 4) |
$7^{10}\cdot 29^{3}$ |
$2$ |
$11.7448605908$ |
$63.24800991823296$ |
|
|
✓ |
$C_4^3:C_6$ (as 12T141) |
trivial |
$[2]$ |
$2$ |
$7$ |
$43.8363058097$ |
$3$ |
$29$ |
| 12.0.6889288847861.1 |
$x^{12} - 5 x^{11} + 20 x^{10} - 54 x^{9} + 121 x^{8} - 216 x^{7} + 321 x^{6} - 394 x^{5} + 400 x^{4} - 331 x^{3} + 215 x^{2} - 106 x + 29$ |
$12$ |
(0, 6) |
$7^{10}\cdot 29^{3}$ |
$2$ |
$11.7448605908$ |
$27.255074007139722$ |
|
|
? |
$D_4\times A_4$ (as 12T51) |
trivial |
trivial |
$14$ |
$5$ |
$154.400112617$ |
$0$ |
$29$ |
| 12.4.8067775586689.1 |
$x^{12} - 2 x^{11} + x^{10} - 3 x^{9} + 3 x^{8} + 3 x^{7} - x^{6} - 5 x^{5} - 15 x^{4} + 10 x^{3} - 3 x^{2} - 3 x + 1$ |
$12$ |
(4, 4) |
$7^{10}\cdot 13^{4}$ |
$2$ |
$11.9004344759$ |
$18.248200448594663$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T26) |
trivial |
$[2]$ |
$2$ |
$7$ |
$47.1747110525$ |
$3$ |
$13$ |
| 12.4.8067775586689.2 |
$x^{12} - 4 x^{11} + 4 x^{10} + 4 x^{9} - x^{8} - 9 x^{7} - 15 x^{6} + 25 x^{5} + 10 x^{4} - 11 x^{3} - 6 x^{2} + 2 x + 1$ |
$12$ |
(4, 4) |
$7^{10}\cdot 13^{4}$ |
$2$ |
$11.9004344759$ |
$18.248200448594663$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T26) |
trivial |
$[2]$ |
$2$ |
$7$ |
$47.1747110525$ |
$3$ |
$13$ |
| 12.0.9256148959232.1 |
$x^{12} - 8 x^{10} + 29 x^{8} - 57 x^{6} + 64 x^{4} - 36 x^{2} + 8$ |
$12$ |
(0, 6) |
$2^{15}\cdot 7^{10}$ |
$2$ |
$12.0374878356$ |
$24.0749756711442$ |
|
|
? |
$D_4\times A_4$ (as 12T51) |
trivial |
trivial |
$14$ |
$5$ |
$177.995845189$ |
$0$ |
$7$ |
| 12.0.16135268698129.1 |
$x^{12} - 5 x^{11} + 9 x^{10} - 7 x^{9} + 3 x^{8} - x^{7} - x^{6} - 2 x^{5} + 12 x^{4} - 56 x^{3} + 144 x^{2} - 160 x + 64$ |
$12$ |
(0, 6) |
$7^{10}\cdot 239^{2}$ |
$2$ |
$12.6080527405$ |
$78.24332848791921$ |
✓ |
|
|
$C_2^2 \times A_4$ (as 12T25) |
trivial |
trivial |
$14$ |
$5$ |
$284.14484878$ |
$0$ |
$239$ |
| 12.6.34389384239007.1 |
$x^{12} - 3 x^{11} + x^{10} + 7 x^{9} - 22 x^{8} + 38 x^{7} - 43 x^{6} + 38 x^{5} - 22 x^{4} + 7 x^{3} + x^{2} - 3 x + 1$ |
$12$ |
(6, 3) |
$-\,3^{6}\cdot 7^{10}\cdot 167$ |
$3$ |
$13.428743132309783$ |
$113.28364897482143$ |
|
|
✓ |
$C_2\wr C_6$ (as 12T134) |
trivial |
$[2]$ |
$2$ |
$8$ |
$133.49146191302214$ |
$5$ |
$167$ |
| 12.8.34801233152049.1 |
$x^{12} - 3 x^{11} - 4 x^{10} + 16 x^{9} + 4 x^{8} - 24 x^{7} - x^{6} - 4 x^{5} - 10 x^{4} + 26 x^{3} + 31 x^{2} + 10 x + 1$ |
$12$ |
(8, 2) |
$3^{6}\cdot 7^{10}\cdot 13^{2}$ |
$3$ |
$13.442072066$ |
$31.606810323667133$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T25) |
trivial |
$[2]$ |
$2$ |
$9$ |
$185.836401127$ |
$7$ |
$13$ |
| 12.4.40147924665121.1 |
$x^{12} - x^{11} - 3 x^{10} + 5 x^{8} + 9 x^{7} - 15 x^{6} + 8 x^{5} + 3 x^{4} - 35 x^{3} + 37 x^{2} + 5 x - 13$ |
$12$ |
(4, 4) |
$7^{10}\cdot 13^{2}\cdot 29^{2}$ |
$3$ |
$13.603121957827904$ |
$98.26956684930803$ |
|
|
? |
$C_2^2\wr C_3$ (as 12T90) |
trivial |
$[2]$ |
$2$ |
$7$ |
$115.66791686017758$ |
$3$ |
$29$ |
| 12.8.40147924665121.1 |
$x^{12} - 5 x^{11} + 6 x^{10} + 9 x^{9} - 33 x^{8} + 36 x^{7} + 6 x^{6} - 51 x^{5} + 22 x^{4} + 19 x^{3} - 2 x^{2} - 8 x + 1$ |
$12$ |
(8, 2) |
$7^{10}\cdot 13^{2}\cdot 29^{2}$ |
$3$ |
$13.6031219578$ |
$98.26956684930803$ |
|
|
? |
$C_2^2\wr C_3$ (as 12T90) |
trivial |
$[2]$ |
$2$ |
$9$ |
$209.650751578$ |
$7$ |
$29$ |
| 12.4.74049191673856.1 |
$x^{12} - 4 x^{11} + 4 x^{10} - 10 x^{9} + 41 x^{8} - 58 x^{7} + 48 x^{6} - 80 x^{5} + 122 x^{4} - 102 x^{3} + 50 x^{2} - 12 x + 1$ |
$12$ |
(4, 4) |
$2^{18}\cdot 7^{10}$ |
$2$ |
$14.3150661808$ |
$17.023578553967216$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T26) |
trivial |
$[2]$ |
$2$ |
$7$ |
$172.005517567$ |
$3$ |
$7$ |
| 12.8.74049191673856.1 |
$x^{12} - 2 x^{11} - 6 x^{10} + 4 x^{9} + 10 x^{8} + 10 x^{7} + 34 x^{6} + 2 x^{5} - 71 x^{4} - 60 x^{3} - 10 x^{2} + 4 x + 1$ |
$12$ |
(8, 2) |
$2^{18}\cdot 7^{10}$ |
$2$ |
$14.3150661808$ |
$17.023578553967216$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T25) |
trivial |
$[2]$ |
$2$ |
$9$ |
$303.668194733$ |
$7$ |
$7$ |
| 12.0.74049191673856.1 |
$x^{12} - 2 x^{10} + 4 x^{8} - 8 x^{6} + 16 x^{4} - 32 x^{2} + 64$ |
$12$ |
(0, 6) |
$2^{18}\cdot 7^{10}$ |
$2$ |
$14.3150661808$ |
$14.315066180821045$ |
✓ |
✓ |
? |
$C_6\times C_2$ (as 12T2) |
trivial |
trivial |
$14$ |
$5$ |
$450.986245646$ |
$0$ |
$7$ |
| 12.4.74049191673856.2 |
$x^{12} - 4 x^{11} + 4 x^{10} + 18 x^{9} - 71 x^{8} + 124 x^{7} - 120 x^{6} + 74 x^{5} - 46 x^{4} + 38 x^{3} - 20 x^{2} + 2 x + 1$ |
$12$ |
(4, 4) |
$2^{18}\cdot 7^{10}$ |
$2$ |
$14.3150661808$ |
$17.023578553967216$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T26) |
trivial |
$[2]$ |
$2$ |
$7$ |
$172.005517567$ |
$3$ |
$7$ |
| 12.0.74049191673856.3 |
$x^{12} - 6 x^{11} + 18 x^{10} - 28 x^{9} + 26 x^{8} - 16 x^{7} + 20 x^{6} - 22 x^{5} + 17 x^{4} - 14 x^{3} + 2 x^{2} + 2 x + 1$ |
$12$ |
(0, 6) |
$2^{18}\cdot 7^{10}$ |
$2$ |
$14.3150661808$ |
$17.023578553967216$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T25) |
$[2]$ |
$[2]$ |
$4$ |
$5$ |
$100.980899762$ |
$0$ |
$7$ |
| 12.0.74049191673856.6 |
$x^{12} + 10 x^{10} + 44 x^{8} + 104 x^{6} + 144 x^{4} + 96 x^{2} + 64$ |
$12$ |
(0, 6) |
$2^{18}\cdot 7^{10}$ |
$2$ |
$14.3150661808$ |
$24.0749756711442$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T25) |
trivial |
trivial |
$14$ |
$5$ |
$522.101791055$ |
$0$ |
$7$ |
| 12.8.127996597203125.1 |
$x^{12} - 5 x^{11} + 6 x^{10} + 16 x^{9} - 61 x^{8} + 64 x^{7} + 27 x^{6} - 107 x^{5} + 57 x^{4} + 19 x^{3} - 16 x^{2} - x + 1$ |
$12$ |
(8, 2) |
$5^{6}\cdot 7^{10}\cdot 29$ |
$3$ |
$14.983037575428522$ |
$60.944198211752$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$[2]$ |
$2$ |
$9$ |
$390.57625621745353$ |
$7$ |
$29$ |
| 12.4.167044845723889.1 |
$x^{12} - 3 x^{11} + x^{10} + 7 x^{9} - 15 x^{8} + 10 x^{7} + 6 x^{6} - 11 x^{5} - x^{4} + x^{2} + 4 x + 1$ |
$12$ |
(4, 4) |
$7^{10}\cdot 769^{2}$ |
$2$ |
$15.3192001354$ |
$424.81442954934494$ |
|
|
? |
$A_4\wr C_3$ (as 12T265) |
trivial |
$[2]$ |
$2$ |
$7$ |
$262.003655505$ |
$3$ |
$769$ |
| 12.10.172770619021119.1 |
$x^{12} - x^{11} - 10 x^{10} + 7 x^{9} + 33 x^{8} - 12 x^{7} - 50 x^{6} + x^{5} + 38 x^{4} + 7 x^{3} - 12 x^{2} - 2 x + 1$ |
$12$ |
(10, 1) |
$-\,3^{6}\cdot 7^{10}\cdot 839$ |
$3$ |
$15.3622852214$ |
$253.91594535376217$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$[2]$ |
$2$ |
$10$ |
$629.155687023$ |
$9$ |
$839$ |
| 12.4.346159011411801.1 |
$x^{12} - 2 x^{11} - 5 x^{10} + 14 x^{9} + 10 x^{8} - 55 x^{7} + 27 x^{6} + 86 x^{5} - 142 x^{4} + 49 x^{3} + 88 x^{2} - 113 x + 43$ |
$12$ |
(4, 4) |
$3^{6}\cdot 7^{10}\cdot 41^{2}$ |
$3$ |
$16.2781971293$ |
$56.13075998354003$ |
|
|
? |
$C_2^4:A_4$ (as 12T87) |
trivial |
$[2]$ |
$2$ |
$7$ |
$312.665380261$ |
$3$ |
$41$ |
| 12.8.346159011411801.2 |
$x^{12} - 4 x^{11} + x^{10} + 7 x^{9} - x^{8} + 4 x^{7} - 22 x^{6} - 3 x^{5} + 34 x^{4} - 7 x^{3} - 13 x^{2} + 3 x + 1$ |
$12$ |
(8, 2) |
$3^{6}\cdot 7^{10}\cdot 41^{2}$ |
$3$ |
$16.2781971293$ |
$56.13075998354003$ |
|
|
? |
$C_2^4:A_4$ (as 12T87) |
trivial |
$[2]$ |
$2$ |
$9$ |
$645.979966156$ |
$7$ |
$41$ |
| 12.0.500422134593689.1 |
$x^{12} - x^{11} - 2 x^{10} + 5 x^{9} + x^{8} - 16 x^{7} + 13 x^{6} - 48 x^{5} + 9 x^{4} + 135 x^{3} - 162 x^{2} - 243 x + 729$ |
$12$ |
(0, 6) |
$7^{10}\cdot 11^{6}$ |
$2$ |
$16.7859030044$ |
$16.785903004359604$ |
✓ |
✓ |
? |
$C_6\times C_2$ (as 12T2) |
trivial |
trivial |
$14$ |
$5$ |
$706.974937058$ |
$0$ |
$11$ |
| 12.4.843466573910016.1 |
$x^{12} + 5 x^{10} + 4 x^{8} - 8 x^{6} - 5 x^{4} + 3 x^{2} + 1$ |
$12$ |
(4, 4) |
$2^{12}\cdot 3^{6}\cdot 7^{10}$ |
$3$ |
$17.5323038886$ |
$33.57798344383965$ |
|
|
✓ |
$C_2^4:A_4$ (as 12T87) |
trivial |
$[2]$ |
$2$ |
$7$ |
$424.566232381$ |
$3$ |
$7$ |
| 12.0.843466573910016.1 |
$x^{12} + 13 x^{10} + 64 x^{8} + 146 x^{6} + 148 x^{4} + 48 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{12}\cdot 3^{6}\cdot 7^{10}$ |
$3$ |
$17.5323038886$ |
$17.532303888591755$ |
✓ |
✓ |
✓ |
$C_6\times C_2$ (as 12T2) |
$[2]$ |
$[2]$ |
$4$ |
$5$ |
$140.798796005$ |
$0$ |
$7$ |
| 12.12.843466573910016.1 |
$x^{12} - 11 x^{10} + 44 x^{8} - 78 x^{6} + 60 x^{4} - 16 x^{2} + 1$ |
$12$ |
(12, 0) |
$2^{12}\cdot 3^{6}\cdot 7^{10}$ |
$3$ |
$17.5323038886$ |
$17.532303888591755$ |
|
✓ |
✓ |
$C_6\times C_2$ (as 12T2) |
trivial |
$[2]$ |
$2$ |
$11$ |
$2121.69295548$ |
$11$ |
$7$ |
| 12.8.843466573910016.1 |
$x^{12} - x^{10} - 6 x^{8} + 6 x^{6} + 8 x^{4} - 8 x^{2} + 1$ |
$12$ |
(8, 2) |
$2^{12}\cdot 3^{6}\cdot 7^{10}$ |
$3$ |
$17.532303888591755$ |
$33.57798344383965$ |
|
|
✓ |
$C_2^4:A_4$ (as 12T87) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1093.8251823149478$ |
$7$ |
$7$ |
| 12.0.843466573910016.3 |
$x^{12} + 3 x^{10} + 9 x^{8} + 27 x^{6} + 81 x^{4} + 243 x^{2} + 729$ |
$12$ |
(0, 6) |
$2^{12}\cdot 3^{6}\cdot 7^{10}$ |
$3$ |
$17.5323038886$ |
$17.532303888591755$ |
✓ |
✓ |
? |
$C_6\times C_2$ (as 12T2) |
$[2]$ |
$[2]$ |
$14$ |
$5$ |
$553.066702068$ |
$0$ |
$7$ |
| 12.0.973052659339264.1 |
$x^{12} - 15 x^{10} + 99 x^{8} - 379 x^{6} + 897 x^{4} - 1247 x^{2} + 841$ |
$12$ |
(0, 6) |
$2^{12}\cdot 7^{10}\cdot 29^{2}$ |
$3$ |
$17.74235897761322$ |
$91.67477612031394$ |
|
|
? |
$C_2^4:A_4$ (as 12T87) |
trivial |
trivial |
$14$ |
$5$ |
$2026.5926296700356$ |
$0$ |
$29$ |
| 12.0.973052659339264.2 |
$x^{12} + 12 x^{10} + 39 x^{8} - 22 x^{6} - 264 x^{4} - 116 x^{2} + 841$ |
$12$ |
(0, 6) |
$2^{12}\cdot 7^{10}\cdot 29^{2}$ |
$3$ |
$17.74235897761322$ |
$91.67477612031394$ |
|
|
? |
$C_2^4:A_4$ (as 12T87) |
trivial |
trivial |
$14$ |
$5$ |
$1734.534911069972$ |
$0$ |
$29$ |
| 12.0.1129900996000000.1 |
$x^{12} - 4 x^{11} + 3 x^{10} + 12 x^{9} - 38 x^{8} + 38 x^{7} + 27 x^{6} - 150 x^{5} + 284 x^{4} - 334 x^{3} + 325 x^{2} - 192 x + 99$ |
$12$ |
(0, 6) |
$2^{8}\cdot 5^{6}\cdot 7^{10}$ |
$3$ |
$17.9647026261$ |
$17.964702626096855$ |
|
|
|
$C_6\times S_3$ (as 12T18) |
$[3]$ |
$[3]$ |
$2$ |
$5$ |
$236.383640887$ |
$0$ |
$7$ |
| 12.0.1363454074150441.1 |
$x^{12} - x^{11} + 4 x^{10} - 7 x^{9} + 19 x^{8} - 40 x^{7} + 97 x^{6} + 120 x^{5} + 171 x^{4} + 189 x^{3} + 324 x^{2} + 243 x + 729$ |
$12$ |
(0, 6) |
$7^{10}\cdot 13^{6}$ |
$2$ |
$18.2482004486$ |
$18.248200448594663$ |
✓ |
✓ |
? |
$C_6\times C_2$ (as 12T2) |
$[2, 2]$ |
$[2, 2]$ |
$14$ |
$5$ |
$562.775330001$ |
$0$ |
$13$ |
| 12.8.1363454074150441.1 |
$x^{12} - x^{11} - 12 x^{10} + 11 x^{9} + 40 x^{8} - 57 x^{7} - 36 x^{6} + 197 x^{5} + 82 x^{4} - 221 x^{3} - 124 x^{2} + 78 x + 43$ |
$12$ |
(8, 2) |
$7^{10}\cdot 13^{6}$ |
$2$ |
$18.2482004486$ |
$18.248200448594663$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T25) |
trivial |
$[2, 2]$ |
$2$ |
$9$ |
$1604.61145419$ |
$6$ |
$13$ |
| 12.0.1363454074150441.2 |
$x^{12} - x^{11} + 18 x^{10} - 14 x^{9} + 138 x^{8} - 82 x^{7} + 517 x^{6} - 202 x^{5} + 976 x^{4} - 392 x^{3} + 688 x^{2} - 128 x + 64$ |
$12$ |
(0, 6) |
$7^{10}\cdot 13^{6}$ |
$2$ |
$18.2482004486$ |
$18.248200448594663$ |
|
|
? |
$C_2^2 \times A_4$ (as 12T25) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$87.5418107547$ |
$0$ |
$13$ |
| 12.0.2758547353515625.1 |
$x^{12} - 5 x^{11} + 13 x^{10} - 40 x^{9} + 100 x^{8} - 195 x^{7} + 370 x^{6} - 590 x^{5} + 855 x^{4} - 870 x^{3} + 908 x^{2} - 400 x + 64$ |
$12$ |
(0, 6) |
$5^{10}\cdot 7^{10}$ |
$2$ |
$19.3518892669$ |
$19.351889266884974$ |
|
|
|
$C_6\times S_3$ (as 12T18) |
$[3]$ |
$[3]$ |
$2$ |
$5$ |
$357.383618201$ |
$0$ |
$7$ |
| 12.12.3111223068921856.1 |
$x^{12} - 2 x^{11} - 13 x^{10} + 32 x^{9} + 31 x^{8} - 102 x^{7} - 22 x^{6} + 114 x^{5} + 13 x^{4} - 46 x^{3} - 10 x^{2} + 4 x + 1$ |
$12$ |
(12, 0) |
$2^{12}\cdot 7^{10}\cdot 2689$ |
$3$ |
$19.54688670899614$ |
$524.8966045985147$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
$[2]$ |
$2$ |
$11$ |
$4431.635320173742$ |
$11$ |
$2689$ |
| 12.0.3217569633140625.1 |
$x^{12} - x^{11} + 11 x^{10} - 7 x^{9} + 40 x^{8} - 12 x^{7} + 62 x^{6} + 15 x^{5} + 31 x^{4} + 112 x^{3} - 40 x^{2} - 2 x + 211$ |
$12$ |
(0, 6) |
$3^{6}\cdot 5^{6}\cdot 7^{10}$ |
$3$ |
$19.6017116485$ |
$19.601711648537535$ |
✓ |
✓ |
? |
$C_6\times C_2$ (as 12T2) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$140.798796005$ |
$0$ |
$7$ |
| 12.12.3217569633140625.1 |
$x^{12} - x^{11} - 19 x^{10} + 18 x^{9} + 110 x^{8} - 92 x^{7} - 218 x^{6} + 155 x^{5} + 166 x^{4} - 88 x^{3} - 40 x^{2} + 8 x + 1$ |
$12$ |
(12, 0) |
$3^{6}\cdot 5^{6}\cdot 7^{10}$ |
$3$ |
$19.6017116485$ |
$19.601711648537535$ |
|
✓ |
? |
$C_6\times C_2$ (as 12T2) |
trivial |
$[2]$ |
$2$ |
$11$ |
$4500.30498389$ |
$11$ |
$7$ |
| 12.0.3217569633140625.3 |
$x^{12} - x^{11} - 3 x^{10} + 7 x^{9} + 5 x^{8} - 33 x^{7} + 13 x^{6} - 132 x^{5} + 80 x^{4} + 448 x^{3} - 768 x^{2} - 1024 x + 4096$ |
$12$ |
(0, 6) |
$3^{6}\cdot 5^{6}\cdot 7^{10}$ |
$3$ |
$19.6017116485$ |
$19.601711648537535$ |
✓ |
✓ |
|
$C_6\times C_2$ (as 12T2) |
$[2]$ |
$[2]$ |
$14$ |
$5$ |
$1378.58167933$ |
$0$ |
$7$ |
| 12.2.4053211077702843.1 |
$x^{12} + 3 x^{10} - 12 x^{8} - 57 x^{6} - 87 x^{4} - 72 x^{2} - 48$ |
$12$ |
(2, 5) |
$-\,3^{15}\cdot 7^{10}$ |
$2$ |
$19.9825052194$ |
$19.9825052193603$ |
|
|
? |
$(C_6\times C_2):C_2$ (as 12T13) |
$[3]$ |
$[6]$ |
$2$ |
$6$ |
$593.09296639$ |
$1$ |
$7$ |
| 12.8.4739148267126784.1 |
$x^{12} - 4 x^{10} - 5 x^{8} + 20 x^{6} + 11 x^{4} - 16 x^{2} + 1$ |
$12$ |
(8, 2) |
$2^{24}\cdot 7^{10}$ |
$2$ |
$20.2445607392$ |
$36.33309687806791$ |
|
|
? |
$C_2^4:A_4$ (as 12T87) |
trivial |
$[2]$ |
$2$ |
$9$ |
$2883.35772546$ |
$7$ |
$7$ |
| 12.0.4739148267126784.1 |
$x^{12} + 12 x^{10} + 53 x^{8} + 104 x^{6} + 86 x^{4} + 24 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{24}\cdot 7^{10}$ |
$2$ |
$20.2445607392$ |
$20.244560739185545$ |
✓ |
✓ |
✓ |
$C_6\times C_2$ (as 12T2) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$123.252731541$ |
$0$ |
$7$ |
