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 |
12.0.46411484401953.1 |
$x^{12} - 4 x^{9} + 17 x^{6} - 4 x^{3} + 1$ |
$12$ |
[0,6] |
$3^{9}\cdot 11^{9}$ |
$2$ |
$13.7684627804$ |
$21.761357200260658$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$119.966636312$ |
12.0.58157342720000.1 |
$x^{12} - 2 x^{11} - 8 x^{9} + 10 x^{8} + 16 x^{6} + 8 x^{5} + 28 x^{4} + 8 x^{3} + 20 x^{2} + 4$ |
$12$ |
[0,6] |
$2^{16}\cdot 5^{4}\cdot 17^{5}$ |
$3$ |
$14.0297644495$ |
$30.37930199399368$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$4$ |
$5$ |
$212.982874279$ |
12.2.69259433447763.2 |
$x^{12} - x^{9} - x^{6} - x^{3} + 1$ |
$12$ |
[2,5] |
$-\,3^{15}\cdot 13^{6}$ |
$2$ |
$14.235517008$ |
$23.91555719607668$ |
|
|
✓ |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$154.445265134$ |
12.0.107567821094912.1 |
$x^{12} + 6 x^{10} - 2 x^{9} + 18 x^{8} - 14 x^{7} + 45 x^{6} - 20 x^{5} + 24 x^{4} - 6 x^{3} + x^{2} + 2 x + 1$ |
$12$ |
[0,6] |
$2^{18}\cdot 17^{7}$ |
$2$ |
$14.7674960818$ |
$29.98603852645895$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$121.960201024$ |
12.2.117231566641875.1 |
$x^{12} - 3 x^{11} + 3 x^{10} + 3 x^{9} - 9 x^{8} + 12 x^{7} - 3 x^{6} - 33 x^{5} + 72 x^{4} - 72 x^{3} + 60 x^{2} - 45 x + 15$ |
$12$ |
[2,5] |
$-\,3^{13}\cdot 5^{4}\cdot 7^{6}$ |
$3$ |
$14.8737466848$ |
$28.735837225253608$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$258.717712708$ |
12.0.143393766507472.1 |
$x^{12} - 5 x^{11} + 14 x^{10} - 28 x^{9} + 48 x^{8} - 69 x^{7} + 83 x^{6} - 87 x^{5} + 80 x^{4} - 61 x^{3} + 38 x^{2} - 20 x + 8$ |
$12$ |
[0,6] |
$2^{4}\cdot 13^{5}\cdot 17^{6}$ |
$3$ |
$15.1255388716$ |
$23.59841316812497$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$303.355053029$ |
12.0.169075682574336.1 |
$x^{12} + 4 x^{10} - 4 x^{9} + 10 x^{8} + 2 x^{6} + 16 x^{5} - 4 x^{4} + 4 x^{3} + 12 x^{2} + 3$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{9}$ |
$2$ |
$15.3346345019$ |
$24.23672593327708$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$503.338702385$ |
12.0.179359981764608.2 |
$x^{12} - 4 x^{10} + 18 x^{8} - 32 x^{6} + 57 x^{4} - 28 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{31}\cdot 17^{4}$ |
$2$ |
$15.4102776157$ |
$44.47661932088469$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$4$ |
$5$ |
$1054.43483881$ |
12.0.503060929445888.15 |
$x^{12} + 4 x^{10} + 2 x^{8} - 4 x^{6} + 9 x^{4} + 16 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{35}\cdot 11^{4}$ |
$2$ |
$16.7932614352$ |
$39.56869954598961$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$1497.62950611$ |
12.0.685529707511808.5 |
$x^{12} + 12 x^{10} - 2 x^{9} + 54 x^{8} - 18 x^{7} + 114 x^{6} - 54 x^{5} + 117 x^{4} - 62 x^{3} + 54 x^{2} - 24 x + 4$ |
$12$ |
[0,6] |
$2^{16}\cdot 3^{21}$ |
$2$ |
$17.2319935466$ |
$27.896364403879762$ |
|
|
|
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$6$ |
$5$ |
$1770.07675319$ |
12.0.1521681143169024.3 |
$x^{12} - 8 x^{9} + 16 x^{6} + 8$ |
$12$ |
[0,6] |
$2^{33}\cdot 3^{11}$ |
$2$ |
$18.4159292675$ |
$34.955407562927284$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$1367.45863609$ |
12.0.1721085137518592.1 |
$x^{12} - 2 x^{11} + 3 x^{10} - 14 x^{9} + 32 x^{8} - 70 x^{7} + 141 x^{6} - 162 x^{5} + 128 x^{4} - 110 x^{3} + 67 x^{2} - 14 x + 3$ |
$12$ |
[0,6] |
$2^{22}\cdot 17^{7}$ |
$2$ |
$18.6058791677$ |
$37.780041142444276$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$1064.01224806$ |
12.2.2742118830047232.4 |
$x^{12} - 2 x^{9} - 2 x^{3} + 1$ |
$12$ |
[2,5] |
$-\,2^{18}\cdot 3^{21}$ |
$2$ |
$19.3422587728$ |
$27.896364403879762$ |
|
|
✓ |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$2174.26408337$ |
12.2.2869759708233728.1 |
$x^{12} - 4 x^{11} + 6 x^{10} - 12 x^{9} + x^{8} - 8 x^{7} - 8 x^{5} + x^{4} - 12 x^{3} + 6 x^{2} - 4 x + 1$ |
$12$ |
[2,5] |
$-\,2^{35}\cdot 17^{4}$ |
$2$ |
$19.4157331527$ |
$52.89191214766356$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$2634.80287989$ |
12.0.3423782572130304.4 |
$x^{12} + 6 x^{10} + 12 x^{6} + 21 x^{4} + 6 x^{2} + 6$ |
$12$ |
[0,6] |
$2^{31}\cdot 3^{13}$ |
$2$ |
$19.7034457018$ |
$24.987759659239007$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[2]$ |
$2$ |
$5$ |
$1405.06268937$ |
12.0.3537090251849728.1 |
$x^{12} + 2 x^{10} - 8 x^{9} + 17 x^{8} - 16 x^{7} + 24 x^{6} - 16 x^{5} + 17 x^{4} - 8 x^{3} + 2 x^{2} + 1$ |
$12$ |
[0,6] |
$2^{32}\cdot 7^{7}$ |
$2$ |
$19.7569777967$ |
$34.04715710793443$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[2]$ |
$2$ |
$5$ |
$1524.31181569$ |
12.2.3966492492169216.1 |
$x^{12} - 2 x^{10} - 29 x^{8} - 88 x^{6} - 128 x^{4} - 72 x^{2} - 4$ |
$12$ |
[2,5] |
$-\,2^{32}\cdot 31^{4}$ |
$2$ |
$19.946523809$ |
$66.38555910891195$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$3063.51849061$ |
12.0.6847565144260608.26 |
$x^{12} + 6 x^{10} - 8 x^{9} + 21 x^{8} - 48 x^{7} + 48 x^{6} - 96 x^{5} + 93 x^{4} - 104 x^{3} + 102 x^{2} + 25$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{13}$ |
$2$ |
$20.8750735528$ |
$24.987759659239007$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[2]$ |
$2$ |
$5$ |
$2721.94808262$ |
12.0.6847565144260608.30 |
$x^{12} - 4 x^{11} + 24 x^{9} - 14 x^{8} - 112 x^{7} + 164 x^{6} + 64 x^{5} - 218 x^{4} + 64 x^{3} + 144 x^{2} - 128 x + 32$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{13}$ |
$2$ |
$20.8750735528$ |
$50.414421537552215$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$3851.22972153$ |
12.0.10271347716390912.5 |
$x^{12} - 6 x^{10} + 24 x^{8} - 48 x^{6} + 45 x^{4} - 18 x^{2} + 18$ |
$12$ |
[0,6] |
$2^{31}\cdot 3^{14}$ |
$2$ |
$21.5924680659$ |
$30.93861708477606$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[2]$ |
$4$ |
$5$ |
$5837.13405799$ |
12.2.11277990709674579.1 |
$x^{12} - 15 x^{9} - 16 x^{6} - 15 x^{3} + 1$ |
$12$ |
[2,5] |
$-\,3^{14}\cdot 11^{9}$ |
$2$ |
$21.7613572003$ |
$21.761357200260658$ |
|
|
|
$\SOPlus(4,2)$ (as 12T36) |
$[3]$ |
$2$ |
$6$ |
$2759.04846544$ |
12.2.14280872991653888.1 |
$x^{12} + 6 x^{10} + 3 x^{8} + 32 x^{6} + 23 x^{4} - 230 x^{2} - 23$ |
$12$ |
[2,5] |
$-\,2^{22}\cdot 23^{7}$ |
$2$ |
$22.1936924282$ |
$48.602826013129224$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$2144.01575742$ |
12.0.15543550148214784.6 |
$x^{12} - 3 x^{11} + 9 x^{9} - 23 x^{7} + 33 x^{6} - 58 x^{5} + 168 x^{4} - 350 x^{3} + 404 x^{2} - 274 x + 106$ |
$12$ |
[0,6] |
$2^{17}\cdot 17^{9}$ |
$2$ |
$22.3509430284$ |
$29.834929532638093$ |
|
|
|
$\SOPlus(4,2)$ (as 12T36) |
$[2]$ |
$2$ |
$5$ |
$1815.6866528$ |
12.2.20542695432781824.21 |
$x^{12} - 6 x^{10} - 16 x^{9} - 15 x^{8} - 24 x^{7} - 24 x^{6} - 24 x^{5} - 15 x^{4} - 16 x^{3} - 6 x^{2} + 1$ |
$12$ |
[2,5] |
$-\,2^{32}\cdot 3^{14}$ |
$2$ |
$22.8764230319$ |
$30.93861708477606$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$7694.69688611$ |
12.2.41085390865563648.27 |
$x^{12} - 24 x^{8} - 92 x^{6} - 123 x^{4} - 36 x^{2} - 2$ |
$12$ |
[2,5] |
$-\,2^{33}\cdot 3^{14}$ |
$2$ |
$24.2367259333$ |
$24.23672593327708$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[3]$ |
$2$ |
$6$ |
$5766.66279094$ |
12.0.43873901280755712.19 |
$x^{12} + 12 x^{10} - 4 x^{9} + 54 x^{8} - 36 x^{7} + 120 x^{6} - 108 x^{5} + 153 x^{4} - 148 x^{3} + 108 x^{2} - 120 x + 52$ |
$12$ |
[0,6] |
$2^{22}\cdot 3^{21}$ |
$2$ |
$24.3697189804$ |
$39.4514168808688$ |
|
|
|
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$6$ |
$5$ |
$19615.2324223$ |
12.0.61628086298345472.16 |
$x^{12} - 12 x^{10} - 16 x^{9} + 36 x^{8} + 120 x^{7} + 92 x^{6} - 72 x^{5} - 102 x^{4} + 24 x^{3} + 72 x^{2} + 144 x + 132$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{15}$ |
$2$ |
$25.0696472715$ |
$44.62120719642371$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$16645.3813689$ |
12.0.61628086298345472.17 |
$x^{12} + 12 x^{10} - 8 x^{9} + 54 x^{8} - 72 x^{7} + 144 x^{6} - 216 x^{5} + 297 x^{4} - 328 x^{3} + 324 x^{2} - 336 x + 164$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{15}$ |
$2$ |
$25.0696472715$ |
$44.62120719642371$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[3]$ |
$2$ |
$5$ |
$7062.02301849$ |
12.0.66060088129912832.2 |
$x^{12} - x^{11} + 5 x^{10} - x^{9} + 19 x^{8} - 11 x^{7} + 28 x^{6} + 40 x^{5} + 53 x^{4} - 35 x^{3} + 56 x^{2} + 50 x + 52$ |
$12$ |
[0,6] |
$2^{15}\cdot 17^{10}$ |
$2$ |
$25.2151523046$ |
$29.98603852645895$ |
|
|
|
$\SOPlus(4,2)$ (as 12T36) |
$[3]$ |
$2$ |
$5$ |
$9999.40082606$ |
12.0.92442129447518208.45 |
$x^{12} - 4 x^{9} + 36 x^{8} - 108 x^{7} + 200 x^{6} - 468 x^{5} + 753 x^{4} - 884 x^{3} + 1584 x^{2} - 2136 x + 1076$ |
$12$ |
[0,6] |
$2^{31}\cdot 3^{16}$ |
$2$ |
$25.9311928538$ |
$47.429446013156884$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$4$ |
$5$ |
$28092.659112$ |
12.2.164...592.16 |
$x^{12} - 16 x^{9} + 18 x^{8} - 48 x^{7} - 52 x^{6} + 120 x^{5} - 54 x^{4} - 224 x^{3} - 120 x^{2} - 96 x - 56$ |
$12$ |
[2,5] |
$-\,2^{35}\cdot 3^{14}$ |
$2$ |
$27.2048050354$ |
$36.79242356556043$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$29270.4133053$ |
12.0.164...592.79 |
$x^{12} - 4 x^{11} + 18 x^{10} - 60 x^{9} + 169 x^{8} - 400 x^{7} + 844 x^{6} - 1456 x^{5} + 2116 x^{4} - 2328 x^{3} + 1752 x^{2} - 784 x + 166$ |
$12$ |
[0,6] |
$2^{35}\cdot 3^{14}$ |
$2$ |
$27.2048050354$ |
$59.95318879120351$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[2]$ |
$2$ |
$5$ |
$18048.5946466$ |
12.0.164...592.81 |
$x^{12} - 8 x^{9} + 18 x^{8} + 4 x^{6} - 120 x^{5} + 138 x^{4} + 312 x^{2} - 288 x + 264$ |
$12$ |
[0,6] |
$2^{35}\cdot 3^{14}$ |
$2$ |
$27.2048050354$ |
$36.79242356556043$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[2]$ |
$2$ |
$5$ |
$13466.2777242$ |
12.2.175...848.27 |
$x^{12} - 8 x^{9} + 6 x^{6} - 8 x^{3} + 1$ |
$12$ |
[2,5] |
$-\,2^{24}\cdot 3^{21}$ |
$2$ |
$27.3540846835$ |
$39.4514168808688$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$16250.4292995$ |
12.2.184884258895036416.4 |
$x^{12} + 12 x^{10} - 8 x^{9} + 36 x^{8} - 96 x^{7} + 4 x^{6} - 144 x^{5} + 54 x^{4} + 296 x^{3} + 144 x^{2} - 240 x - 100$ |
$12$ |
[2,5] |
$-\,2^{32}\cdot 3^{16}$ |
$2$ |
$27.4731418213$ |
$47.429446013156884$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[2]$ |
$2$ |
$6$ |
$13675.4283482$ |
12.0.221...224.10 |
$x^{12} - 4 x^{11} + 22 x^{10} - 76 x^{9} + 239 x^{8} - 568 x^{7} + 1328 x^{6} - 2216 x^{5} + 3553 x^{4} - 4108 x^{3} + 4198 x^{2} - 2388 x + 1103$ |
$12$ |
[0,6] |
$2^{35}\cdot 23^{5}$ |
$2$ |
$27.8862908292$ |
$38.36665218650175$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[6]$ |
$2$ |
$5$ |
$2119.03888242$ |
12.2.264240352519651328.8 |
$x^{12} - x^{10} - 35 x^{8} - 81 x^{6} - 60 x^{4} - 30 x^{2} - 2$ |
$12$ |
[2,5] |
$-\,2^{17}\cdot 17^{10}$ |
$2$ |
$28.3030515042$ |
$37.780041142444276$ |
|
|
|
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$15684.3779837$ |
12.0.497393604742873088.7 |
$x^{12} - 2 x^{11} + 5 x^{10} - 14 x^{9} + 34 x^{8} - 18 x^{7} + 79 x^{6} - 58 x^{5} + 28 x^{4} + 142 x^{3} + 583 x^{2} + 974 x + 919$ |
$12$ |
[0,6] |
$2^{22}\cdot 17^{9}$ |
$2$ |
$29.8349295326$ |
$29.834929532638093$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[12]$ |
$2$ |
$5$ |
$2814.11997512$ |
12.0.606610978192228352.4 |
$x^{12} + 2 x^{10} + 18 x^{8} + 64 x^{6} + 100 x^{4} + 200 x^{2} + 8$ |
$12$ |
[0,6] |
$2^{31}\cdot 7^{10}$ |
$2$ |
$30.3325686238$ |
$34.04715710793443$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[3, 6]$ |
$2$ |
$5$ |
$4282.63636183$ |
12.2.831...872.39 |
$x^{12} + 12 x^{10} + 54 x^{8} + 68 x^{6} - 159 x^{4} - 360 x^{2} - 32$ |
$12$ |
[2,5] |
$-\,2^{31}\cdot 3^{18}$ |
$2$ |
$31.1417277899$ |
$44.62120719642371$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$42468.7435699$ |
12.2.831...872.42 |
$x^{12} + 12 x^{10} + 54 x^{8} + 100 x^{6} + 33 x^{4} - 72 x^{2} - 32$ |
$12$ |
[2,5] |
$-\,2^{31}\cdot 3^{18}$ |
$2$ |
$31.1417277899$ |
$44.62120719642371$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$6$ |
$85833.8288488$ |
12.2.147...328.11 |
$x^{12} + 12 x^{10} + 54 x^{8} + 44 x^{6} - 303 x^{4} - 576 x^{2} - 128$ |
$12$ |
[2,5] |
$-\,2^{35}\cdot 3^{16}$ |
$2$ |
$32.6712557253$ |
$56.40343465948361$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[2]$ |
$2$ |
$6$ |
$40835.556576$ |
12.0.147...328.68 |
$x^{12} - 12 x^{10} - 16 x^{9} + 54 x^{8} + 144 x^{7} - 24 x^{6} - 432 x^{5} - 423 x^{4} + 328 x^{3} + 756 x^{2} + 312 x + 38$ |
$12$ |
[0,6] |
$2^{35}\cdot 3^{16}$ |
$2$ |
$32.6712557253$ |
$56.40343465948361$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[3]$ |
$2$ |
$5$ |
$27225.5707975$ |
12.12.203...888.1 |
$x^{12} - 6 x^{11} - 9 x^{10} + 74 x^{9} + 48 x^{8} - 270 x^{7} - 117 x^{6} + 360 x^{5} + 84 x^{4} - 172 x^{3} - 9 x^{2} + 12 x + 1$ |
$12$ |
[12,0] |
$2^{16}\cdot 3^{13}\cdot 11^{7}$ |
$3$ |
$33.5531851372$ |
$69.0391438702834$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$11$ |
$279893.771548$ |
12.2.332...488.128 |
$x^{12} - 16 x^{9} + 56 x^{6} + 160 x^{3} - 8$ |
$12$ |
[2,5] |
$-\,2^{33}\cdot 3^{18}$ |
$2$ |
$34.9554075629$ |
$34.955407562927284$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[3]$ |
$2$ |
$6$ |
$34178.8560928$ |
12.0.352...416.19 |
$x^{12} - 4 x^{11} + 6 x^{10} - 4 x^{9} + 25 x^{8} - 72 x^{7} + 8 x^{6} + 240 x^{5} - 218 x^{4} - 528 x^{3} + 1400 x^{2} - 1184 x + 392$ |
$12$ |
[0,6] |
$2^{33}\cdot 17^{7}$ |
$2$ |
$35.1232228225$ |
$71.31922073282139$ |
|
|
|
$\SOPlus(4,2)$ (as 12T36) |
$[4]$ |
$2$ |
$5$ |
$34859.5759199$ |
12.0.499...232.27 |
$x^{12} - 12 x^{10} - 8 x^{9} + 90 x^{8} + 120 x^{7} - 272 x^{6} - 648 x^{5} + 81 x^{4} + 1704 x^{3} + 2268 x^{2} + 1296 x + 396$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{19}$ |
$2$ |
$36.1566880051$ |
$72.71017779983123$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$158684.543593$ |
12.0.499...232.41 |
$x^{12} + 24 x^{10} - 8 x^{9} + 252 x^{8} - 96 x^{7} + 1312 x^{6} - 432 x^{5} + 3204 x^{4} + 192 x^{3} + 2592 x^{2} + 1728 x + 288$ |
$12$ |
[0,6] |
$2^{32}\cdot 3^{19}$ |
$2$ |
$36.1566880051$ |
$72.71017779983123$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
trivial |
$2$ |
$5$ |
$98614.0055855$ |
12.0.508...152.15 |
$x^{12} + 16 x^{10} + 108 x^{8} + 448 x^{6} + 1252 x^{4} + 2112 x^{2} + 1568$ |
$12$ |
[0,6] |
$2^{35}\cdot 23^{6}$ |
$2$ |
$36.2132974624$ |
$38.36665218650175$ |
|
|
? |
$\SOPlus(4,2)$ (as 12T36) |
$[6]$ |
$2$ |
$5$ |
$79352.3565534$ |
12.0.542...728.3 |
$x^{12} - 20 x^{10} + 113 x^{8} - 124 x^{6} + 264 x^{4} - 122 x^{2} + 32$ |
$12$ |
[0,6] |
$2^{17}\cdot 23^{10}$ |
$2$ |
$36.4109790858$ |
$48.602826013129224$ |
|
|
|
$\SOPlus(4,2)$ (as 12T36) |
$[3]$ |
$2$ |
$5$ |
$44155.2665747$ |