| 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 |
| 12.0.1157018619904.2 |
$x^{12} - 5 x^{10} + 11 x^{8} - 13 x^{6} + 9 x^{4} - 3 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 7^{10}$ |
$2$ |
$10.1222803696$ |
$14.315066180821045$ |
|
|
✓ |
$A_4 \times C_2$ (as 12T7) |
trivial |
$14$ |
$5$ |
$70.4864492171$ |
| 12.0.1511207993344.2 |
$x^{12} - 2 x^{11} + 2 x^{10} + 2 x^{9} + 3 x^{8} - 4 x^{6} + 3 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 7^{8}$ |
$2$ |
$10.350079528$ |
$12.308388215503062$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$4$ |
$5$ |
$20.7514845804$ |
| 12.0.1586874322944.5 |
$x^{12} + 6 x^{10} + 15 x^{8} + 19 x^{6} + 12 x^{4} + 3 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{18}$ |
$2$ |
$10.3923048454$ |
$14.696938456699069$ |
|
|
✓ |
$A_4 \times C_2$ (as 12T7) |
trivial |
$18$ |
$5$ |
$151.463499998$ |
| 12.0.8067775586689.1 |
$x^{12} - 5 x^{11} + 18 x^{10} - 48 x^{9} + 100 x^{8} - 178 x^{7} + 267 x^{6} - 336 x^{5} + 364 x^{4} - 329 x^{3} + 245 x^{2} - 147 x + 49$ |
$12$ |
[0,6] |
$7^{10}\cdot 13^{4}$ |
$2$ |
$11.9004344759$ |
$18.248200448594663$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
$[2]$ |
$14$ |
$5$ |
$118.411290819$ |
| 12.0.11284439629824.2 |
$x^{12} - 4 x^{9} + 15 x^{8} - 12 x^{7} + 8 x^{6} - 12 x^{5} + 15 x^{4} - 4 x^{3} + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 3^{16}$ |
$2$ |
$12.2378934159$ |
$14.553389922872519$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$4$ |
$5$ |
$63.8033404215$ |
| 12.4.12745792515625.1 |
$x^{12} - 3 x^{11} + 8 x^{10} - 15 x^{9} + 18 x^{8} - 19 x^{7} - 8 x^{6} + 18 x^{5} - 7 x^{4} + 15 x^{3} - 15 x^{2} + x + 1$ |
$12$ |
[4,4] |
$5^{6}\cdot 13^{8}$ |
$2$ |
$12.3627163157$ |
$12.362716315674692$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$73.2101878921$ |
| 12.0.17213603549184.2 |
$x^{12} - x^{10} + 3 x^{8} + 5 x^{4} - 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{12}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$12.6762068204$ |
$17.926863604818365$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$6$ |
$5$ |
$153.96121657$ |
| 12.4.27825593350009.1 |
$x^{12} - 3 x^{11} + 2 x^{10} - 3 x^{9} + 8 x^{8} - 3 x^{7} - 28 x^{6} + 24 x^{5} + x^{4} + 45 x^{3} - 61 x^{2} + 3 x + 1$ |
$12$ |
[4,4] |
$7^{8}\cdot 13^{6}$ |
$2$ |
$13.1938143701$ |
$13.193814370085985$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$92.1299826393$ |
| 12.0.32357746661769.1 |
$x^{12} - 6 x^{11} + 12 x^{10} - 3 x^{9} - 18 x^{8} - 3 x^{7} + 67 x^{6} - 39 x^{5} - 39 x^{4} - 12 x^{3} + 36 x^{2} + 12 x + 1$ |
$12$ |
[0,6] |
$3^{18}\cdot 17^{4}$ |
$2$ |
$13.3607710668$ |
$21.42428528562855$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[2]$ |
$18$ |
$5$ |
$404.15700628$ |
| 12.4.74049191673856.3 |
$x^{12} - 2 x^{11} - 2 x^{10} + 16 x^{9} - 13 x^{8} - 28 x^{7} + 50 x^{6} - 62 x^{4} + 26 x^{3} + 12 x^{2} - 54 x - 27$ |
$12$ |
[4,4] |
$2^{18}\cdot 7^{10}$ |
$2$ |
$14.3150661808$ |
$17.023578553967216$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$185.388043669$ |
| 12.4.86161557405625.1 |
$x^{12} - 5 x^{10} + 18 x^{8} - 20 x^{6} - 7 x^{4} - 15 x^{2} + 1$ |
$12$ |
[4,4] |
$5^{4}\cdot 13^{10}$ |
$2$ |
$14.4969328872$ |
$18.957066304919827$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$167.924001727$ |
| 12.0.96717311574016.3 |
$x^{12} + 4 x^{10} - x^{8} - x^{4} + 4 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{24}\cdot 7^{8}$ |
$2$ |
$14.6372228401$ |
$17.406689545317608$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$5$ |
$71.267658558$ |
| 12.4.96717311574016.4 |
$x^{12} - 4 x^{10} - x^{8} - x^{4} - 4 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{24}\cdot 7^{8}$ |
$2$ |
$14.6372228401$ |
$17.406689545317608$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$245.785554293$ |
| 12.4.101559956668416.2 |
$x^{12} - 6 x^{10} - 16 x^{9} + 3 x^{8} + 42 x^{7} + 28 x^{6} - 6 x^{5} - 24 x^{4} - 36 x^{3} - 36 x^{2} - 18 x - 3$ |
$12$ |
[4,4] |
$2^{18}\cdot 3^{18}$ |
$2$ |
$14.6969384567$ |
$17.477703781463642$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$332.146241747$ |
| 12.0.213838914125824.1 |
$x^{12} - 6 x^{11} + 18 x^{10} - 34 x^{9} + 53 x^{8} - 76 x^{7} + 80 x^{6} - 34 x^{5} - 10 x^{4} - 8 x^{3} + 32 x^{2} + 8 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 13^{8}$ |
$2$ |
$15.6377366496$ |
$18.59650768627035$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[3]$ |
$4$ |
$5$ |
$188.005900914$ |
| 12.0.371667309755625.1 |
$x^{12} - x^{11} + 2 x^{10} + 7 x^{9} - x^{8} + 9 x^{6} - x^{4} + 7 x^{3} + 2 x^{2} - x + 1$ |
$12$ |
[0,6] |
$3^{6}\cdot 5^{4}\cdot 13^{8}$ |
$3$ |
$16.3749329489$ |
$21.412852778309286$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[2]$ |
$6$ |
$5$ |
$265.862081831$ |
| 12.4.564668382613504.3 |
$x^{12} + 6 x^{10} + 2 x^{8} - 19 x^{6} + 2 x^{4} + 6 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{12}\cdot 13^{10}$ |
$2$ |
$16.9557155647$ |
$23.97900291135148$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$475.372736414$ |
| 12.4.722204136308736.9 |
$x^{12} - 6 x^{10} + 21 x^{8} - 44 x^{6} + 54 x^{4} - 36 x^{2} + 9$ |
$12$ |
[4,4] |
$2^{24}\cdot 3^{16}$ |
$2$ |
$17.3069948437$ |
$20.58160140743025$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$594.937841602$ |
| 12.0.722204136308736.14 |
$x^{12} + 6 x^{10} + 21 x^{8} + 44 x^{6} + 54 x^{4} + 36 x^{2} + 9$ |
$12$ |
[0,6] |
$2^{24}\cdot 3^{16}$ |
$2$ |
$17.3069948437$ |
$20.58160140743025$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
$[3]$ |
$2$ |
$5$ |
$341.881314243$ |
| 12.4.1039043198361249.1 |
$x^{12} - 3 x^{11} + 3 x^{10} - 7 x^{9} + 18 x^{8} - 18 x^{7} - 31 x^{6} + 12 x^{5} + 72 x^{4} + 60 x^{3} - 108 x^{2} - 27 x + 9$ |
$12$ |
[4,4] |
$3^{16}\cdot 17^{6}$ |
$2$ |
$17.8396419506$ |
$17.839641950637386$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$989.16216967$ |
| 12.4.1101670627147776.3 |
$x^{12} - 2 x^{11} - 6 x^{10} - 2 x^{9} - 13 x^{8} - 48 x^{7} + 28 x^{6} + 48 x^{5} - 13 x^{4} + 2 x^{3} - 6 x^{2} + 2 x + 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$17.9268636048$ |
$21.31875374853333$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$669.474843374$ |
| 12.0.1363454074150441.3 |
$x^{12} - x^{11} + 14 x^{10} - 13 x^{9} + 83 x^{8} - 70 x^{7} + 232 x^{6} - 119 x^{5} + 244 x^{4} - 97 x^{3} + 70 x^{2} - 8 x + 1$ |
$12$ |
[0,6] |
$7^{10}\cdot 13^{6}$ |
$2$ |
$18.2482004486$ |
$18.248200448594663$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[2, 2]$ |
$2$ |
$5$ |
$96.4796484344$ |
| 12.0.1998099208210609.1 |
$x^{12} - 3 x^{11} + 13 x^{10} - 23 x^{9} + 36 x^{8} - 26 x^{7} + 19 x^{6} + 8 x^{5} + 16 x^{4} - 4 x^{3} + 34 x^{2} + 5 x + 1$ |
$12$ |
[0,6] |
$7^{6}\cdot 19^{8}$ |
$2$ |
$18.8387212751$ |
$18.838721275076466$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
$[4]$ |
$2$ |
$5$ |
$186.316655752$ |
| 12.0.2025170913606201.1 |
$x^{12} - 6 x^{10} + 33 x^{8} - 87 x^{6} + 360 x^{4} + 219 x^{2} + 289$ |
$12$ |
[0,6] |
$3^{16}\cdot 19^{6}$ |
$2$ |
$18.859860385$ |
$18.859860385004858$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[4]$ |
$2$ |
$5$ |
$84.5285670343$ |
| 12.4.2154038935140625.3 |
$x^{12} - x^{11} - 10 x^{10} + 6 x^{9} + 32 x^{8} - 12 x^{7} - 41 x^{6} - 16 x^{5} - 24 x^{4} - 19 x^{3} + 9 x^{2} + 9 x + 1$ |
$12$ |
[4,4] |
$5^{6}\cdot 13^{10}$ |
$2$ |
$18.9570663049$ |
$18.957066304919827$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
$[2]$ |
$2$ |
$7$ |
$861.443546399$ |
| 12.4.2572632521265625.1 |
$x^{12} - x^{11} - 7 x^{10} + 2 x^{9} + 7 x^{8} - 2 x^{7} - 127 x^{6} - 77 x^{5} + 98 x^{4} + 28 x^{3} + 49$ |
$12$ |
[4,4] |
$5^{6}\cdot 7^{8}\cdot 13^{4}$ |
$3$ |
$19.2396933714$ |
$29.50226581402583$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$709.275411867$ |
| 12.4.3429038075724121.1 |
$x^{12} - 3 x^{11} - 2 x^{10} + x^{9} + 36 x^{8} - 23 x^{7} - 116 x^{6} - 10 x^{5} + 319 x^{4} + 209 x^{3} - 473 x^{2} - 247 x + 169$ |
$12$ |
[4,4] |
$7^{8}\cdot 29^{6}$ |
$2$ |
$19.7059643282$ |
$19.705964328162043$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$1824.19500337$ |
| 12.0.3493441689358336.14 |
$x^{12} - 6 x^{11} + 13 x^{10} - 10 x^{9} - 21 x^{8} + 78 x^{7} - 73 x^{6} - 30 x^{5} + 169 x^{4} - 210 x^{3} - 101 x^{2} + 190 x + 202$ |
$12$ |
[0,6] |
$2^{12}\cdot 31^{8}$ |
$2$ |
$19.7365448064$ |
$19.736544806437948$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
$[4]$ |
$4$ |
$5$ |
$1160.75122176$ |
| 12.0.4452139149819904.5 |
$x^{12} + 10 x^{10} + 21 x^{8} + 66 x^{6} + 110 x^{4} + 116 x^{2} + 49$ |
$12$ |
[0,6] |
$2^{18}\cdot 19^{8}$ |
$2$ |
$20.1394401761$ |
$23.949965549560982$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$4$ |
$5$ |
$725.564838933$ |
| 12.0.4739148267126784.13 |
$x^{12} - 7 x^{8} + 14 x^{6} + 98 x^{4} + 294 x^{2} + 49$ |
$12$ |
[0,6] |
$2^{24}\cdot 7^{10}$ |
$2$ |
$20.2445607392$ |
$24.0749756711442$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[4]$ |
$2$ |
$5$ |
$206.655401464$ |
| 12.4.4739148267126784.22 |
$x^{12} - 7 x^{8} - 14 x^{6} + 98 x^{4} - 294 x^{2} + 49$ |
$12$ |
[4,4] |
$2^{24}\cdot 7^{10}$ |
$2$ |
$20.2445607392$ |
$24.0749756711442$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$1734.39318931$ |
| 12.4.5881408402696281.3 |
$x^{12} - 13 x^{10} + 22 x^{8} - 104 x^{6} + x^{4} - 195 x^{2} + 1$ |
$12$ |
[4,4] |
$3^{6}\cdot 7^{10}\cdot 13^{4}$ |
$3$ |
$20.6121571445$ |
$31.606810323667133$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[2]$ |
$2$ |
$7$ |
$726.081873929$ |
| 12.0.6499837226778624.43 |
$x^{12} + 12 x^{10} + 54 x^{8} + 132 x^{6} + 189 x^{4} + 162 x^{2} + 81$ |
$12$ |
[0,6] |
$2^{24}\cdot 3^{18}$ |
$2$ |
$20.7846096908$ |
$24.717205726885414$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[2]$ |
$2$ |
$5$ |
$487.631648098$ |
| 12.4.6499837226778624.45 |
$x^{12} - 12 x^{10} + 54 x^{8} - 132 x^{6} + 189 x^{4} - 162 x^{2} + 81$ |
$12$ |
[4,4] |
$2^{24}\cdot 3^{18}$ |
$2$ |
$20.7846096908$ |
$24.717205726885414$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$3192.36943943$ |
| 12.0.9291682743890625.2 |
$x^{12} - 2 x^{11} - 4 x^{10} + x^{9} + 19 x^{8} - 3 x^{7} + 41 x^{6} + 36 x^{5} + 121 x^{4} - 13 x^{3} + 176 x^{2} - 16 x + 64$ |
$12$ |
[0,6] |
$3^{6}\cdot 5^{6}\cdot 13^{8}$ |
$3$ |
$21.4128527783$ |
$21.412852778309286$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
$[2, 2]$ |
$2$ |
$5$ |
$414.598522146$ |
| 12.0.9351388785251241.3 |
$x^{12} + 24 x^{8} + 13 x^{6} + 144 x^{4} + 156 x^{2} + 361$ |
$12$ |
[0,6] |
$3^{18}\cdot 17^{6}$ |
$2$ |
$21.4242852856$ |
$21.42428528562855$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[2, 2]$ |
$2$ |
$5$ |
$331.041902445$ |
| 12.0.9845005879332009.3 |
$x^{12} + 18 x^{10} - 32 x^{9} + 267 x^{8} - 324 x^{7} + 1168 x^{6} - 384 x^{5} + 2799 x^{4} - 228 x^{3} + 4545 x^{2} + 2052 x + 3249$ |
$12$ |
[0,6] |
$3^{18}\cdot 71^{4}$ |
$2$ |
$21.5163201807$ |
$43.78355855797927$ |
✓ |
|
? |
$A_4 \times C_2$ (as 12T7) |
$[4]$ |
$18$ |
$5$ |
$3039.60843665$ |
| 12.4.13685690504052736.12 |
$x^{12} - 2 x^{10} - 6 x^{8} - 30 x^{6} - 7 x^{4} - 28 x^{2} + 25$ |
$12$ |
[4,4] |
$2^{24}\cdot 13^{8}$ |
$2$ |
$22.1150992547$ |
$26.299433382699032$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$2659.85170055$ |
| 12.0.13685690504052736.17 |
$x^{12} + 2 x^{10} - 6 x^{8} + 30 x^{6} - 7 x^{4} + 28 x^{2} + 25$ |
$12$ |
[0,6] |
$2^{24}\cdot 13^{8}$ |
$2$ |
$22.1150992547$ |
$26.299433382699032$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$5$ |
$743.28971555$ |
| 12.0.20284857552156561.2 |
$x^{12} - 6 x^{11} + 17 x^{10} - 30 x^{9} + 94 x^{8} - 262 x^{7} + 374 x^{6} - 265 x^{5} + 566 x^{4} - 969 x^{3} + 580 x^{2} - 100 x + 1000$ |
$12$ |
[0,6] |
$3^{6}\cdot 7^{8}\cdot 13^{6}$ |
$3$ |
$22.8523568346$ |
$22.852356834621286$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
$[2, 4]$ |
$2$ |
$5$ |
$219.255307646$ |
| 12.0.25112847391952896.2 |
$x^{12} + 2 x^{10} + 8 x^{8} + 12 x^{6} + 22 x^{4} - 11 x^{2} + 49$ |
$12$ |
[0,6] |
$2^{12}\cdot 19^{10}$ |
$2$ |
$23.2625862551$ |
$32.89826497785412$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$5$ |
$2425.67745873$ |
| 12.0.33045608803078144.1 |
$x^{12} + 18 x^{10} + 114 x^{8} + 260 x^{6} + 1859 x^{4} - 4394 x^{2} + 28561$ |
$12$ |
[0,6] |
$2^{12}\cdot 7^{10}\cdot 13^{4}$ |
$3$ |
$23.8008689519$ |
$51.61370512661073$ |
✓ |
|
? |
$A_4 \times C_2$ (as 12T7) |
$[2, 4]$ |
$14$ |
$5$ |
$1615.30314445$ |
| 12.0.36138776487264256.2 |
$x^{12} - 2 x^{11} - 4 x^{10} + 14 x^{9} - 15 x^{8} + 90 x^{7} + 50 x^{6} - 644 x^{5} + 1098 x^{4} - 1152 x^{3} + 822 x^{2} - 230 x + 25$ |
$12$ |
[0,6] |
$2^{18}\cdot 13^{10}$ |
$2$ |
$23.9790029114$ |
$28.516000872850142$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
$[2]$ |
$2$ |
$5$ |
$981.852738997$ |
| 12.12.52206766144000000.1 |
$x^{12} - 15 x^{10} + 76 x^{8} - 148 x^{6} + 99 x^{4} - 19 x^{2} + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 5^{6}\cdot 13^{8}$ |
$3$ |
$24.7254326313$ |
$34.96704216279658$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$11$ |
$27689.0510913$ |
| 12.12.113...864.1 |
$x^{12} - 15 x^{10} + 74 x^{8} - 136 x^{6} + 92 x^{4} - 18 x^{2} + 1$ |
$12$ |
[12,0] |
$2^{12}\cdot 7^{8}\cdot 13^{6}$ |
$3$ |
$26.3876287402$ |
$37.31774244321726$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$11$ |
$34885.4965388$ |
| 12.0.209824841467085056.5 |
$x^{12} + 2 x^{10} + 12 x^{8} + 26 x^{6} + 115 x^{4} + 36 x^{2} + 64$ |
$12$ |
[0,6] |
$2^{8}\cdot 31^{10}$ |
$2$ |
$27.7643861065$ |
$34.980934492937045$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
$[18]$ |
$2$ |
$5$ |
$31367.7469501$ |
| 12.0.219708209445758929.3 |
$x^{12} - 5 x^{11} + 33 x^{10} - 107 x^{9} + 337 x^{8} - 651 x^{7} + 1205 x^{6} + 1204 x^{5} + 1632 x^{4} - 1608 x^{3} + 44000 x^{2} + 119712 x + 118336$ |
$12$ |
[0,6] |
$7^{10}\cdot 167^{4}$ |
$2$ |
$27.8710837978$ |
$65.40434523039623$ |
✓ |
|
|
$A_4 \times C_2$ (as 12T7) |
$[16]$ |
$14$ |
$5$ |
$2950.17006547$ |
| 12.0.223...504.10 |
$x^{12} - 6 x^{11} + 17 x^{10} - 24 x^{9} - 7 x^{8} + 90 x^{7} - 85 x^{6} - 60 x^{5} + 331 x^{4} - 234 x^{3} + 215 x^{2} + 36 x + 4$ |
$12$ |
[0,6] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$27.911689339648817$ |
✓ |
|
|
$A_4 \times C_2$ (as 12T7) |
$[2]$ |
$2$ |
$5$ |
$7504.4041113$ |
| 12.4.223...504.33 |
$x^{12} - 6 x^{11} + 23 x^{10} - 60 x^{9} + 95 x^{8} - 86 x^{7} - 63 x^{6} + 304 x^{5} - 467 x^{4} + 414 x^{3} - 75 x^{2} - 80 x + 46$ |
$12$ |
[4,4] |
$2^{18}\cdot 31^{8}$ |
$2$ |
$27.9116893396$ |
$27.911689339648817$ |
|
|
|
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$52798.990549$ |
| 12.4.284...856.24 |
$x^{12} - 8 x^{10} + 23 x^{8} - 56 x^{6} + 207 x^{4} - 648 x^{2} + 729$ |
$12$ |
[4,4] |
$2^{24}\cdot 19^{8}$ |
$2$ |
$28.4814694356$ |
$33.87036609855754$ |
|
|
? |
$A_4 \times C_2$ (as 12T7) |
trivial |
$2$ |
$7$ |
$18235.0066012$ |
