| 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 |
| 12.0.11709207984384.1 |
$x^{12} - 6 x^{11} + 15 x^{10} - 20 x^{9} + 22 x^{8} - 34 x^{7} + 47 x^{6} - 40 x^{5} + 38 x^{4} - 42 x^{3} + 27 x^{2} - 8 x + 1$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{6}\cdot 89^{4}$ |
$3$ |
$12.2756348091$ |
$28.44982682753188$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$6$ |
$5$ |
$73.1160095474$ |
| 12.0.42681865994496.1 |
$x^{12} - 6 x^{11} + 13 x^{10} - 8 x^{9} - 16 x^{8} + 32 x^{7} + 9 x^{6} - 106 x^{5} + 160 x^{4} - 114 x^{3} + 63 x^{2} - 54 x + 27$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{8}\cdot 71^{4}$ |
$3$ |
$13.6726789595$ |
$33.442143949031745$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$6$ |
$5$ |
$499.105495264$ |
| 12.4.107495424000000.1 |
$x^{12} + 3 x^{10} - 8 x^{9} - 6 x^{8} - 12 x^{7} + 45 x^{6} - 12 x^{5} - 6 x^{4} - 8 x^{3} + 3 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{20}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$14.7666675706$ |
$24.1776264427508$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$268.346530948$ |
| 12.4.115157043765625.1 |
$x^{12} - x^{10} + 2 x^{8} + 4 x^{6} - 3 x^{4} - 3 x^{2} + 1$ |
$12$ |
[4,4] |
$5^{6}\cdot 293^{4}$ |
$2$ |
$14.8516330053$ |
$38.27531841800928$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$166.230726614$ |
| 12.4.256000000000000.1 |
$x^{12} - 2 x^{11} - 4 x^{10} + 10 x^{9} - 5 x^{8} - 20 x^{7} + 40 x^{6} - 25 x^{4} + 30 x^{3} - 10 x + 5$ |
$12$ |
[4,4] |
$2^{20}\cdot 5^{12}$ |
$2$ |
$15.8740105197$ |
$28.57900880593445$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$506.047684117$ |
| 12.0.386869246296064.2 |
$x^{12} - 2 x^{10} + 3 x^{8} - 4 x^{6} + 19 x^{4} - 34 x^{2} + 49$ |
$12$ |
[0,6] |
$2^{26}\cdot 7^{8}$ |
$2$ |
$16.4297271307$ |
$31.90883292885454$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$4$ |
$5$ |
$2170.21948857$ |
| 12.4.625000000000000.1 |
$x^{12} - 6 x^{11} + 9 x^{10} + 10 x^{9} - 40 x^{8} + 28 x^{7} + 37 x^{6} - 78 x^{5} + 40 x^{4} + 40 x^{3} - 59 x^{2} + 24 x - 1$ |
$12$ |
[4,4] |
$2^{12}\cdot 5^{16}$ |
$2$ |
$17.0997594668$ |
$27.202271339006447$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$766.508857204$ |
| 12.4.834668212890625.1 |
$x^{12} - 4 x^{11} + 4 x^{10} - 5 x^{9} + 5 x^{8} - x^{7} + 9 x^{6} + x^{5} + 5 x^{4} + 5 x^{3} + 4 x^{2} + 4 x + 1$ |
$12$ |
[4,4] |
$5^{12}\cdot 43^{4}$ |
$2$ |
$17.5169903019$ |
$41.739739355256155$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$805.9904134616443$ |
| 12.4.1024000000000000.4 |
$x^{12} - 6 x^{11} + 11 x^{10} - 15 x^{8} - 6 x^{7} + 21 x^{6} + 24 x^{5} - 50 x^{4} + 20 x^{3} - 16 x^{2} + 16 x + 4$ |
$12$ |
[4,4] |
$2^{22}\cdot 5^{12}$ |
$2$ |
$17.8179743628$ |
$28.876817690785337$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$1988.84012499$ |
| 12.4.3421422626013184.4 |
$x^{12} + 2 x^{10} + 11 x^{8} + 7 x^{4} - 18 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{22}\cdot 13^{8}$ |
$2$ |
$19.7023135776$ |
$27.735947540541815$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$4228.65892661$ |
| 12.0.10000000000000000.1 |
$x^{12} - 6 x^{11} + 13 x^{10} - 10 x^{9} + 5 x^{8} - 26 x^{7} + 41 x^{6} - 8 x^{5} + 20 x^{4} - 70 x^{3} + 8 x^{2} + 32 x + 74$ |
$12$ |
[0,6] |
$2^{16}\cdot 5^{16}$ |
$2$ |
$21.5443469003$ |
$33.092176689024704$ |
|
|
? |
$S_5$ (as 12T74) |
$[2]$ |
$4$ |
$5$ |
$7191.07873858$ |
| 12.4.10000000000000000.1 |
$x^{12} - 4 x^{11} + 14 x^{10} - 20 x^{9} + 10 x^{8} + 24 x^{7} - 66 x^{6} - 24 x^{5} + 10 x^{4} + 20 x^{3} + 14 x^{2} + 4 x + 1$ |
$12$ |
[4,4] |
$2^{16}\cdot 5^{16}$ |
$2$ |
$21.5443469003$ |
$48.468937332853066$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$6122.98638806$ |
| 12.0.16384000000000000.6 |
$x^{12} - 4 x^{11} + 14 x^{10} - 40 x^{9} + 85 x^{8} - 156 x^{7} + 244 x^{6} - 344 x^{5} + 460 x^{4} - 480 x^{3} + 464 x^{2} - 256 x + 96$ |
$12$ |
[0,6] |
$2^{26}\cdot 5^{12}$ |
$2$ |
$22.4492409662$ |
$42.82013114405259$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$2$ |
$5$ |
$11595.82288$ |
| 12.0.16384000000000000.7 |
$x^{12} - 4 x^{11} + 8 x^{10} - 20 x^{9} + 25 x^{8} - 8 x^{7} + 32 x^{6} + 16 x^{5} - 140 x^{4} + 32 x^{2} + 112 x + 196$ |
$12$ |
[0,6] |
$2^{26}\cdot 5^{12}$ |
$2$ |
$22.4492409662$ |
$54.512172900649155$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$4$ |
$5$ |
$29499.8421143$ |
| 12.0.16384000000000000.8 |
$x^{12} + 15 x^{8} - 8 x^{7} + 40 x^{5} + 175 x^{4} + 40 x^{3} + 32 x^{2} + 120 x + 225$ |
$12$ |
[0,6] |
$2^{26}\cdot 5^{12}$ |
$2$ |
$22.4492409662$ |
$54.512172900649155$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$4$ |
$5$ |
$30373.0064339$ |
| 12.4.24414062500000000.1 |
$x^{12} - x^{11} - x^{10} + 20 x^{9} - 15 x^{8} - 7 x^{7} - 28 x^{6} + 197 x^{5} + 155 x^{4} - 60 x^{3} - 39 x^{2} - x - 1$ |
$12$ |
[4,4] |
$2^{8}\cdot 5^{20}$ |
$2$ |
$23.2079441681$ |
$36.616613186499904$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$2$ |
$7$ |
$4066.63246211$ |
| 12.4.40000000000000000.1 |
$x^{12} - 4 x^{11} + 4 x^{10} - 20 x^{9} + 25 x^{8} - 8 x^{7} + 2 x^{6} - 32 x^{5} + 30 x^{4} + 6 x^{2} - 4 x - 1$ |
$12$ |
[4,4] |
$2^{18}\cdot 5^{16}$ |
$2$ |
$24.1827117512$ |
$34.27271426496622$ |
|
|
? |
$S_5$ (as 12T74) |
$[4]$ |
$2$ |
$7$ |
$3577.34395433$ |
| 12.0.57541523968884736.5 |
$x^{12} - 2 x^{11} + 7 x^{10} - 20 x^{9} + 44 x^{8} - 76 x^{7} + 210 x^{6} - 216 x^{5} + 228 x^{4} - 176 x^{3} + 184 x^{2} - 96 x + 16$ |
$12$ |
[0,6] |
$2^{28}\cdot 11^{8}$ |
$2$ |
$24.9267187375$ |
$40.63282352308103$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$2$ |
$5$ |
$15035.0609716$ |
| 12.4.57541523968884736.6 |
$x^{12} - 2 x^{11} - 3 x^{10} - 6 x^{9} - 2 x^{8} + 14 x^{7} - 31 x^{6} + 58 x^{5} + 317 x^{4} + 220 x^{3} - 154 x^{2} - 220 x - 66$ |
$12$ |
[4,4] |
$2^{28}\cdot 11^{8}$ |
$2$ |
$24.9267187375$ |
$40.63282352308103$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$50075.7604852$ |
| 12.4.65536000000000000.4 |
$x^{12} - 32 x^{7} - 40 x^{6} - 80 x^{5} - 25 x^{4} + 80 x^{3} + 116 x^{2} + 160 x + 60$ |
$12$ |
[4,4] |
$2^{28}\cdot 5^{12}$ |
$2$ |
$25.1984209979$ |
$42.82013114405259$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$2$ |
$7$ |
$41418.133456$ |
| 12.0.65536000000000000.10 |
$x^{12} - 10 x^{10} + 5 x^{8} - 32 x^{7} + 100 x^{6} + 160 x^{5} + 190 x^{4} + 200 x^{3} + 176 x^{2} + 80 x + 40$ |
$12$ |
[0,6] |
$2^{28}\cdot 5^{12}$ |
$2$ |
$25.1984209979$ |
$42.82013114405259$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$2$ |
$5$ |
$16066.0113635$ |
| 12.0.65536000000000000.15 |
$x^{12} + 8 x^{10} + 10 x^{8} - 100 x^{6} + 25 x^{4} + 100 x^{2} + 100$ |
$12$ |
[0,6] |
$2^{28}\cdot 5^{12}$ |
$2$ |
$25.1984209979$ |
$54.512172900649155$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$5$ |
$24170.3510116$ |
| 12.4.75826372274028544.3 |
$x^{12} - 2 x^{11} - 7 x^{10} + 22 x^{9} + 5 x^{8} - 84 x^{7} + 50 x^{6} + 140 x^{5} - 130 x^{4} - 160 x^{3} + 112 x^{2} + 80 x + 8$ |
$12$ |
[4,4] |
$2^{28}\cdot 7^{10}$ |
$2$ |
$25.5065482212$ |
$34.04715710793443$ |
|
|
? |
$S_5$ (as 12T74) |
$[3]$ |
$2$ |
$7$ |
$13998.7348457$ |
| 12.0.82115019702009856.11 |
$x^{12} - 4 x^{11} + 9 x^{10} - 22 x^{9} + 45 x^{8} - 40 x^{7} + 27 x^{6} - 86 x^{5} + 22 x^{4} + 48 x^{3} + 96 x^{2} + 48 x + 16$ |
$12$ |
[0,6] |
$2^{20}\cdot 23^{8}$ |
$2$ |
$25.676464092$ |
$49.140804269668145$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$4$ |
$5$ |
$45251.6413102$ |
| 12.4.160000000000000000.4 |
$x^{12} - 2 x^{11} - 14 x^{10} + 30 x^{9} + 55 x^{8} - 120 x^{7} - 120 x^{6} + 340 x^{5} - 225 x^{4} + 50 x^{3} + 30 x^{2} - 10 x + 5$ |
$12$ |
[4,4] |
$2^{20}\cdot 5^{16}$ |
$2$ |
$27.1441761659$ |
$54.404542678012895$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$14985.7093727$ |
| 12.0.218...776.81 |
$x^{12} - 6 x^{11} + 13 x^{10} - 2 x^{9} - 36 x^{8} + 30 x^{7} + 187 x^{6} - 726 x^{5} + 1395 x^{4} - 1700 x^{3} + 1378 x^{2} - 716 x + 194$ |
$12$ |
[0,6] |
$2^{28}\cdot 13^{8}$ |
$2$ |
$27.8632790715$ |
$37.1930153725407$ |
|
|
? |
$S_5$ (as 12T74) |
$[3]$ |
$2$ |
$5$ |
$16151.7410422$ |
| 12.0.262144000000000000.4 |
$x^{12} - 8 x^{10} + 45 x^{8} - 120 x^{6} + 160 x^{4} - 112 x^{2} + 36$ |
$12$ |
[0,6] |
$2^{30}\cdot 5^{12}$ |
$2$ |
$28.2842712475$ |
$64.8262638677105$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$5$ |
$79127.1897572$ |
| 12.4.262144000000000000.4 |
$x^{12} + 8 x^{10} + 5 x^{8} - 80 x^{6} + 160 x^{4} - 128 x^{2} + 36$ |
$12$ |
[4,4] |
$2^{30}\cdot 5^{12}$ |
$2$ |
$28.2842712475$ |
$64.8262638677105$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$75753.2535473$ |
| 12.4.262144000000000000.6 |
$x^{12} - 4 x^{11} + 4 x^{10} - 20 x^{9} + 70 x^{8} - 76 x^{7} + 164 x^{6} - 364 x^{5} + 25 x^{4} + 400 x^{3} + 144 x^{2} - 576 x + 216$ |
$12$ |
[4,4] |
$2^{30}\cdot 5^{12}$ |
$2$ |
$28.2842712475$ |
$50.92200462185694$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$2$ |
$7$ |
$46699.5998277$ |
| 12.4.390625000000000000.1 |
$x^{12} - 2 x^{11} - 4 x^{10} + 40 x^{7} - 80 x^{6} + 40 x^{5} + 320 x^{2} + 160 x - 80$ |
$12$ |
[4,4] |
$2^{12}\cdot 5^{20}$ |
$2$ |
$29.2401773821$ |
$51.783710976517675$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$35076.0118501$ |
| 12.4.390625000000000000.2 |
$x^{12} - 2 x^{11} - 4 x^{10} + 25 x^{8} - 10 x^{7} - 30 x^{6} + 40 x^{5} - 125 x^{4} + 150 x^{3} + 30 x^{2} - 60 x - 20$ |
$12$ |
[4,4] |
$2^{12}\cdot 5^{20}$ |
$2$ |
$29.2401773821$ |
$65.24338750098681$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$30374.7743402$ |
| 12.4.401805558271246336.1 |
$x^{12} - 2 x^{11} - 4 x^{10} + 8 x^{9} + 18 x^{8} - 16 x^{7} - 64 x^{6} + 32 x^{5} + 72 x^{4} - 64 x^{3} - 64 x^{2} + 64 x + 64$ |
$12$ |
[4,4] |
$2^{16}\cdot 19^{10}$ |
$2$ |
$29.3090220978$ |
$32.89826497785412$ |
|
|
? |
$S_5$ (as 12T74) |
$[3]$ |
$2$ |
$7$ |
$50319.6102706$ |
| 12.4.415...936.56 |
$x^{12} - 12 x^{10} + 90 x^{8} - 308 x^{6} + 633 x^{4} - 432 x^{2} + 64$ |
$12$ |
[4,4] |
$2^{30}\cdot 3^{18}$ |
$2$ |
$29.3938769134$ |
$41.569219381653056$ |
|
|
|
$S_5$ (as 12T74) |
$[3]$ |
$2$ |
$7$ |
$77760.2839285$ |
| 12.0.524...536.12 |
$x^{12} - 4 x^{11} + 5 x^{10} + 2 x^{9} + 5 x^{8} - 72 x^{7} + 119 x^{6} + 82 x^{5} - 362 x^{4} + 48 x^{3} + 768 x^{2} - 976 x + 400$ |
$12$ |
[0,6] |
$2^{20}\cdot 29^{8}$ |
$2$ |
$29.9673719339$ |
$59.15321989923478$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$4$ |
$5$ |
$103520.549403$ |
| 12.4.638...504.23 |
$x^{12} - 12 x^{10} + 2 x^{8} + 172 x^{6} + 481 x^{4} - 384 x^{2} + 256$ |
$12$ |
[4,4] |
$2^{30}\cdot 29^{6}$ |
$2$ |
$30.4630924235$ |
$43.08131845707603$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$2$ |
$7$ |
$134869.936937$ |
| 12.0.640...000.11 |
$x^{12} - 2 x^{11} + 11 x^{10} - 20 x^{9} + 35 x^{8} - 58 x^{7} + 21 x^{6} - 28 x^{5} - 20 x^{4} + 60 x^{3} + 56 x^{2} - 32 x + 76$ |
$12$ |
[0,6] |
$2^{22}\cdot 5^{16}$ |
$2$ |
$30.4683075789$ |
$43.18091413946323$ |
|
|
? |
$S_5$ (as 12T74) |
$[4]$ |
$2$ |
$5$ |
$14046.790727$ |
| 12.4.640...000.13 |
$x^{12} - 18 x^{10} + 115 x^{8} - 360 x^{6} + 575 x^{4} - 422 x^{2} + 81$ |
$12$ |
[4,4] |
$2^{22}\cdot 5^{16}$ |
$2$ |
$30.4683075789$ |
$46.79940508206552$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$107506.253186$ |
| 12.4.935...856.66 |
$x^{12} - 6 x^{10} - 12 x^{9} + 48 x^{8} - 236 x^{6} + 648 x^{5} - 252 x^{4} - 1152 x^{3} + 1728 x^{2} - 864 x + 144$ |
$12$ |
[4,4] |
$2^{28}\cdot 3^{20}$ |
$2$ |
$31.4488967305$ |
$50.414421537552215$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$199092.076429$ |
| 12.4.172...296.3 |
$x^{12} + 6 x^{10} + 15 x^{8} + 20 x^{6} + 15 x^{4} - 110 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{12}\cdot 29^{10}$ |
$2$ |
$33.0898648921$ |
$37.142117525068365$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$35121.8177843$ |
| 12.12.184...000.1 |
$x^{12} - 24 x^{10} + 192 x^{8} - 664 x^{6} + 992 x^{4} - 512 x^{2} + 16$ |
$12$ |
[12,0] |
$2^{20}\cdot 5^{6}\cdot 103^{4}$ |
$3$ |
$33.2772479889$ |
$101.89087030315206$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$11$ |
$160256.354359$ |
| 12.0.209...144.3 |
$x^{12} + 14 x^{10} - 28 x^{9} + 89 x^{8} - 52 x^{7} - 226 x^{6} + 216 x^{5} + 285 x^{4} - 516 x^{3} + 308 x^{2} - 84 x + 9$ |
$12$ |
[0,6] |
$2^{22}\cdot 29^{8}$ |
$2$ |
$33.6372376834$ |
$44.533499491161095$ |
|
|
? |
$S_5$ (as 12T74) |
$[4]$ |
$2$ |
$5$ |
$11387.2151209$ |
| 12.4.210...176.1 |
$x^{12} - 6 x^{10} - 12 x^{9} - 21 x^{8} + 144 x^{7} + 316 x^{6} - 288 x^{5} - 1101 x^{4} + 48 x^{3} + 1506 x^{2} + 108 x - 599$ |
$12$ |
[4,4] |
$2^{26}\cdot 3^{22}$ |
$2$ |
$33.6475895466$ |
$50.414421537552215$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$421525.043508$ |
| 12.0.357...064.30 |
$x^{12} + 6 x^{10} - 4 x^{9} + 32 x^{8} - 64 x^{7} + 82 x^{6} - 16 x^{5} + 612 x^{4} + 128 x^{3} + 2872 x^{2} + 2432 x + 1392$ |
$12$ |
[0,6] |
$2^{22}\cdot 31^{8}$ |
$2$ |
$35.1665249371$ |
$46.817648399439314$ |
|
|
? |
$S_5$ (as 12T74) |
$[8]$ |
$2$ |
$5$ |
$17339.4529555$ |
| 12.4.374...424.135 |
$x^{12} + 54 x^{8} - 324 x^{6} + 729 x^{4} - 972 x^{2} + 324$ |
$12$ |
[4,4] |
$2^{30}\cdot 3^{20}$ |
$2$ |
$35.3001930412$ |
$59.95318879120351$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$282352.265485$ |
| 12.4.525...784.1 |
$x^{12} - 4 x^{11} + 2 x^{10} - 16 x^{9} + 64 x^{8} + 76 x^{7} - 436 x^{6} + 792 x^{5} - 2183 x^{4} + 4608 x^{3} - 5702 x^{2} + 4504 x - 1654$ |
$12$ |
[4,4] |
$2^{26}\cdot 23^{8}$ |
$2$ |
$36.3120037527$ |
$70.65263524866003$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$433524.405491$ |
| 12.0.625...000.6 |
$x^{12} - 4 x^{11} - x^{10} + 60 x^{9} - 205 x^{8} + 198 x^{7} + 758 x^{6} - 3508 x^{5} + 7390 x^{4} - 9520 x^{3} + 7856 x^{2} - 4224 x + 1504$ |
$12$ |
[0,6] |
$2^{16}\cdot 5^{20}$ |
$2$ |
$36.8403149864$ |
$65.24338750098681$ |
|
|
? |
$S_5$ (as 12T74) |
$[2, 2]$ |
$2$ |
$5$ |
$46350.8472599$ |
| 12.4.749...384.4 |
$x^{12} - 4 x^{11} + 2 x^{10} - 4 x^{9} + 101 x^{8} - 480 x^{7} + 996 x^{6} - 960 x^{5} + 404 x^{4} - 32 x^{3} + 32 x^{2} - 128 x + 64$ |
$12$ |
[4,4] |
$2^{30}\cdot 17^{8}$ |
$2$ |
$37.4002297495$ |
$52.89191214766356$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
$2$ |
$7$ |
$431398.06017$ |
| 12.0.842...704.125 |
$x^{12} - 6 x^{10} + 51 x^{8} - 72 x^{7} - 200 x^{6} + 216 x^{5} + 1338 x^{4} - 1488 x^{3} - 1032 x^{2} - 288 x + 2920$ |
$12$ |
[0,6] |
$2^{28}\cdot 3^{22}$ |
$2$ |
$37.7681422832$ |
$50.414421537552215$ |
|
|
|
$S_5$ (as 12T74) |
$[4]$ |
$2$ |
$5$ |
$285327.672941$ |
| 12.0.102...000.17 |
$x^{12} - 4 x^{11} + 14 x^{10} - 20 x^{9} + 115 x^{8} - 192 x^{7} + 138 x^{6} - 568 x^{5} + 770 x^{4} + 360 x^{3} + 1496 x^{2} - 1904 x + 824$ |
$12$ |
[0,6] |
$2^{26}\cdot 5^{16}$ |
$2$ |
$38.3876620733$ |
$81.51471130870617$ |
|
|
|
$S_5$ (as 12T74) |
$[2]$ |
$2$ |
$5$ |
$142977.462814$ |
| 12.12.205...841.1 |
$x^{12} - x^{11} - 20 x^{10} + 17 x^{9} + 140 x^{8} - 87 x^{7} - 408 x^{6} + 113 x^{5} + 464 x^{4} + 55 x^{3} - 106 x^{2} - 18 x + 1$ |
$12$ |
[12,0] |
$29^{6}\cdot 431^{4}$ |
$2$ |
$40.6778592244$ |
$111.79892664958818$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$2$ |
$11$ |
$972152.429669$ |
