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 |
12.0.15203947802176.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 22 x^{9} + 32 x^{8} - 30 x^{7} + 57 x^{6} - 56 x^{5} - 14 x^{3} + 14 x^{2} + 14 x + 7$ |
$12$ |
[0,6] |
$2^{6}\cdot 7^{10}\cdot 29^{2}$ |
$3$ |
$12.5457423473$ |
$77.08899060875882$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$14$ |
$5$ |
$320.143524163$ |
12.0.15203947802176.3 |
$x^{12} - 4 x^{11} + 6 x^{10} - 12 x^{9} + 44 x^{8} - 98 x^{7} + 134 x^{6} - 168 x^{5} + 249 x^{4} - 310 x^{3} + 262 x^{2} - 146 x + 43$ |
$12$ |
[0,6] |
$2^{6}\cdot 7^{10}\cdot 29^{2}$ |
$3$ |
$12.5457423473$ |
$77.08899060875882$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$14$ |
$5$ |
$306.194604814$ |
12.4.75753088140625.1 |
$x^{12} - x^{11} - 2 x^{10} - 8 x^{8} + x^{7} - 11 x^{6} + x^{5} - 8 x^{4} - 2 x^{2} - x + 1$ |
$12$ |
[4,4] |
$5^{6}\cdot 7^{8}\cdot 29^{2}$ |
$3$ |
$14.3422304079$ |
$44.06387579995631$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$137.573943409$ |
12.8.151416101265625.1 |
$x^{12} - 2 x^{11} - 4 x^{10} + 3 x^{9} + 10 x^{8} + 13 x^{7} - 21 x^{6} - 27 x^{5} + 25 x^{4} + 20 x^{3} - 10 x^{2} - 8 x - 1$ |
$12$ |
[8,2] |
$5^{6}\cdot 7^{8}\cdot 41^{2}$ |
$3$ |
$15.1943107755$ |
$52.393284371934335$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$423.834397821$ |
12.4.242810410640625.2 |
$x^{12} - 3 x^{11} - 6 x^{8} + 3 x^{7} - 9 x^{6} + 3 x^{5} - 6 x^{4} - 3 x + 1$ |
$12$ |
[4,4] |
$3^{16}\cdot 5^{6}\cdot 19^{2}$ |
$3$ |
$15.8041912046$ |
$42.17192986702622$ |
|
|
✓ |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$297.144632588$ |
12.8.368947264000000.2 |
$x^{12} - 5 x^{10} + 2 x^{8} + 17 x^{6} - 19 x^{4} + 2 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{12}\cdot 5^{6}\cdot 7^{8}$ |
$3$ |
$16.3649126361$ |
$30.013382108043007$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$690.069334247$ |
12.4.564668382613504.2 |
$x^{12} + 2 x^{10} - 7 x^{8} - 19 x^{6} - 8 x^{4} + 5 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{12}\cdot 13^{10}$ |
$2$ |
$16.9557155647$ |
$31.096919456532316$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$436.632563589$ |
12.8.564668382613504.3 |
$x^{12} - 5 x^{10} + 5 x^{8} + 6 x^{6} - 7 x^{4} - 2 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{12}\cdot 13^{10}$ |
$2$ |
$16.9557155647$ |
$31.096919456532316$ |
|
|
✓ |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$942.874445517$ |
12.4.860374847629609.1 |
$x^{12} - 3 x^{11} + 2 x^{10} + 10 x^{9} - 48 x^{8} + 109 x^{7} - 193 x^{6} + 245 x^{5} - 250 x^{4} + 250 x^{3} - 202 x^{2} + 105 x - 25$ |
$12$ |
[4,4] |
$13^{10}\cdot 79^{2}$ |
$2$ |
$17.5613261536$ |
$75.35284821191699$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$524.301439397$ |
12.4.2950947586890625.1 |
$x^{12} - 3 x^{11} + x^{10} + 19 x^{9} - 36 x^{8} + 28 x^{7} + 3 x^{6} - 14 x^{5} + 96 x^{4} - 163 x^{3} + 81 x^{2} - 41 x + 29$ |
$12$ |
[4,4] |
$5^{6}\cdot 7^{8}\cdot 181^{2}$ |
$3$ |
$19.4609240614$ |
$110.08369108484274$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$775.245730506$ |
12.8.4739148267126784.5 |
$x^{12} - 6 x^{10} + 8 x^{8} + 8 x^{6} - 13 x^{4} - 6 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{24}\cdot 7^{10}$ |
$2$ |
$20.2445607392$ |
$32.60366934501777$ |
|
|
✓ |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$3598.32322043$ |
12.4.4739148267126784.13 |
$x^{12} + 2 x^{10} - 10 x^{8} - 20 x^{6} - 5 x^{4} + 4 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{24}\cdot 7^{10}$ |
$2$ |
$20.2445607392$ |
$32.60366934501777$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$1749.48542816$ |
12.12.5674816059390625.1 |
$x^{12} - 3 x^{11} - 14 x^{10} + 34 x^{9} + 88 x^{8} - 114 x^{7} - 301 x^{6} + 26 x^{5} + 408 x^{4} + 340 x^{3} + 117 x^{2} + 18 x + 1$ |
$12$ |
[12,0] |
$5^{6}\cdot 7^{8}\cdot 251^{2}$ |
$3$ |
$20.5508275891$ |
$129.63448785201967$ |
|
|
✓ |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$11$ |
$6151.25064962$ |
12.8.6189907940737024.2 |
$x^{12} - 2 x^{10} - 9 x^{8} + 14 x^{6} + 10 x^{4} - 8 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{30}\cdot 7^{8}$ |
$2$ |
$20.7001590559$ |
$33.33740602939541$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$4788.14752655$ |
12.4.6189907940737024.6 |
$x^{12} - 4 x^{10} - 8 x^{8} + 14 x^{6} + 27 x^{4} + 10 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{30}\cdot 7^{8}$ |
$2$ |
$20.7001590559$ |
$33.33740602939541$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$2271.15178361$ |
12.8.6499837226778624.3 |
$x^{12} - 15 x^{8} - 2 x^{6} + 36 x^{4} - 12 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{24}\cdot 3^{18}$ |
$2$ |
$20.7846096908$ |
$33.473412960414905$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$6390.13442863$ |
12.4.6499837226778624.29 |
$x^{12} - 12 x^{8} - 14 x^{6} + 9 x^{4} + 12 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{24}\cdot 3^{18}$ |
$2$ |
$20.7846096908$ |
$33.473412960414905$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$2915.1114474$ |
12.12.26635831223765625.1 |
$x^{12} - 3 x^{11} - 15 x^{10} + 55 x^{9} + 48 x^{8} - 303 x^{7} + 90 x^{6} + 516 x^{5} - 312 x^{4} - 278 x^{3} + 153 x^{2} + 48 x - 19$ |
$12$ |
[12,0] |
$3^{16}\cdot 5^{6}\cdot 199^{2}$ |
$3$ |
$23.3770041818$ |
$136.48131973068624$ |
|
|
✓ |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$11$ |
$16635.8219018$ |
12.8.46221064723759104.2 |
$x^{12} - 6 x^{10} + 3 x^{8} + 30 x^{6} - 42 x^{4} + 12 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{30}\cdot 3^{16}$ |
$2$ |
$24.4757868319$ |
$39.41801805957117$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$13263.9231209$ |
12.4.46221064723759104.12 |
$x^{12} - 6 x^{10} - 3 x^{8} + 30 x^{6} + 36 x^{4} + 12 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{30}\cdot 3^{16}$ |
$2$ |
$24.4757868319$ |
$39.41801805957117$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$4523.69850917$ |
12.0.52456210366771264.2 |
$x^{12} - 5 x^{11} + 10 x^{10} - 14 x^{9} + 4 x^{8} + 34 x^{7} - 47 x^{6} + 45 x^{5} + 32 x^{4} - 68 x^{3} + 20 x^{2} + 36 x + 16$ |
$12$ |
[0,6] |
$2^{6}\cdot 31^{10}$ |
$2$ |
$24.7352559922$ |
$49.470511984396374$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
$[9]$ |
$2$ |
$5$ |
$5007.63993466$ |
12.4.303305489096114176.2 |
$x^{12} + 16 x^{10} + 88 x^{8} + 190 x^{6} + 121 x^{4} - 38 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{30}\cdot 7^{10}$ |
$2$ |
$28.6301323616$ |
$46.108551370852055$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$18039.9289201$ |
12.8.303305489096114176.3 |
$x^{12} - 6 x^{10} - 13 x^{8} + 106 x^{6} - 104 x^{4} + 8 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{30}\cdot 7^{10}$ |
$2$ |
$28.6301323616$ |
$46.108551370852055$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$35458.0805586$ |
12.8.415989582513831936.6 |
$x^{12} - 6 x^{10} - 9 x^{8} + 78 x^{6} - 18 x^{4} - 108 x^{2} + 9$ |
$12$ |
[8,2] |
$2^{30}\cdot 3^{18}$ |
$2$ |
$29.3938769134$ |
$47.33855458753409$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$60287.1772797$ |
12.4.415...936.19 |
$x^{12} + 6 x^{10} - 21 x^{8} - 188 x^{6} - 285 x^{4} + 30 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{30}\cdot 3^{18}$ |
$2$ |
$29.3938769134$ |
$47.33855458753409$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$30994.8576366$ |
12.0.839299365868340224.2 |
$x^{12} - 3 x^{10} + 27 x^{8} - 49 x^{6} + 92 x^{4} - 68 x^{2} + 16$ |
$12$ |
[0,6] |
$2^{10}\cdot 31^{10}$ |
$2$ |
$31.1644696991$ |
$69.96186898587409$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
$[9]$ |
$2$ |
$5$ |
$47570.5723119$ |
12.8.875884192259375104.1 |
$x^{12} - 2 x^{10} - 13 x^{8} + 14 x^{6} + 26 x^{4} - 28 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{30}\cdot 13^{8}$ |
$2$ |
$31.2754732992$ |
$50.36884737557236$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$44602.7411646$ |
12.4.875...104.12 |
$x^{12} + 8 x^{10} - 38 x^{6} - 39 x^{4} - 6 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{30}\cdot 13^{8}$ |
$2$ |
$31.2754732992$ |
$50.36884737557236$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$21419.6350311$ |
12.0.335...896.10 |
$x^{12} - 12 x^{10} + 60 x^{8} - 98 x^{6} + 147 x^{4} - 130 x^{2} + 64$ |
$12$ |
[0,6] |
$2^{12}\cdot 31^{10}$ |
$2$ |
$34.9809344929$ |
$69.96186898587409$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
$[18]$ |
$2$ |
$5$ |
$22402.7593676$ |
12.0.335...896.14 |
$x^{12} - 6 x^{10} + 15 x^{8} - 82 x^{6} + 480 x^{4} - 1184 x^{2} + 1024$ |
$12$ |
[0,6] |
$2^{12}\cdot 31^{10}$ |
$2$ |
$34.9809344929$ |
$69.96186898587409$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
$[18]$ |
$2$ |
$5$ |
$25262.3625398$ |
12.0.335...896.16 |
$x^{12} + 5 x^{10} - 18 x^{8} - 20 x^{6} + 344 x^{4} - 960 x^{2} + 1024$ |
$12$ |
[0,6] |
$2^{12}\cdot 31^{10}$ |
$2$ |
$34.9809344929$ |
$49.470511984396374$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
$[2, 18]$ |
$2$ |
$5$ |
$69157.3741111$ |
12.0.134...584.22 |
$x^{12} - 6 x^{10} + 15 x^{8} + 42 x^{6} - 140 x^{4} + 56 x^{2} + 1024$ |
$12$ |
[0,6] |
$2^{14}\cdot 31^{10}$ |
$2$ |
$39.2647713827$ |
$69.96186898587409$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
$[18]$ |
$2$ |
$5$ |
$145139.663993$ |
12.0.134...584.38 |
$x^{12} + 9 x^{10} + 26 x^{8} + 52 x^{6} + 136 x^{4} + 32 x^{2} + 256$ |
$12$ |
[0,6] |
$2^{14}\cdot 31^{10}$ |
$2$ |
$39.2647713827$ |
$69.96186898587409$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
$[18]$ |
$2$ |
$5$ |
$145504.628318$ |
12.8.182...784.2 |
$x^{12} - 10 x^{10} + 23 x^{8} + 22 x^{6} - 94 x^{4} + 16 x^{2} + 49$ |
$12$ |
[8,2] |
$2^{30}\cdot 19^{8}$ |
$2$ |
$40.2788803522$ |
$64.86874738888089$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$272582.854584$ |
12.4.182...784.21 |
$x^{12} + 6 x^{10} - 13 x^{8} - 92 x^{6} - 69 x^{4} + 62 x^{2} + 49$ |
$12$ |
[4,4] |
$2^{30}\cdot 19^{8}$ |
$2$ |
$40.2788803522$ |
$64.86874738888089$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$207414.242214$ |
12.0.537...336.46 |
$x^{12} + 14 x^{10} + 61 x^{8} + 52 x^{6} + 308 x^{4} - 192 x^{2} + 256$ |
$12$ |
[0,6] |
$2^{16}\cdot 31^{10}$ |
$2$ |
$44.0732157126$ |
$69.96186898587409$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
$[2, 18]$ |
$2$ |
$5$ |
$68501.2845348$ |
12.8.102...016.3 |
$x^{12} - 6 x^{10} - 4 x^{8} + 56 x^{6} - 61 x^{4} - 6 x^{2} + 1$ |
$12$ |
[8,2] |
$2^{24}\cdot 19^{10}$ |
$2$ |
$46.5251725102$ |
$74.92834051998875$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$508428.854995$ |
12.4.102...016.8 |
$x^{12} - 4 x^{10} - 25 x^{8} - 20 x^{6} + 10 x^{4} + 10 x^{2} + 1$ |
$12$ |
[4,4] |
$2^{24}\cdot 19^{10}$ |
$2$ |
$46.5251725102$ |
$74.92834051998875$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$195533.18316$ |
12.8.148...576.4 |
$x^{12} - 8 x^{10} - 8 x^{8} + 202 x^{6} - 449 x^{4} - 50 x^{2} + 625$ |
$12$ |
[8,2] |
$2^{30}\cdot 13^{10}$ |
$2$ |
$47.9580058227$ |
$77.23590471702916$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
$[2]$ |
$2$ |
$9$ |
$1367926.32557$ |
12.4.148...576.24 |
$x^{12} + 6 x^{10} - 37 x^{8} - 266 x^{6} - 284 x^{4} + 500 x^{2} + 625$ |
$12$ |
[4,4] |
$2^{30}\cdot 13^{10}$ |
$2$ |
$47.9580058227$ |
$77.23590471702916$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
$[2]$ |
$2$ |
$7$ |
$260226.572826$ |
12.8.366...536.1 |
$x^{12} - 10 x^{10} + 15 x^{8} + 76 x^{6} - 164 x^{4} - 16 x^{2} + 4$ |
$12$ |
[8,2] |
$2^{32}\cdot 31^{8}$ |
$2$ |
$62.6596239759$ |
$102.38052790852275$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$26170228.8757$ |
12.8.366...536.4 |
$x^{12} - 14 x^{10} - 107 x^{8} + 1516 x^{6} - 1910 x^{4} + 592 x^{2} + 16$ |
$12$ |
[8,2] |
$2^{32}\cdot 31^{8}$ |
$2$ |
$62.6596239759$ |
$102.38052790852275$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$20522359.3551$ |
12.8.366...536.5 |
$x^{12} + 6 x^{10} - 131 x^{8} + 428 x^{6} - 462 x^{4} + 96 x^{2} + 64$ |
$12$ |
[8,2] |
$2^{32}\cdot 31^{8}$ |
$2$ |
$62.6596239759$ |
$102.38052790852275$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$18762949.2549$ |
12.8.366...536.7 |
$x^{12} - 10 x^{10} - 33 x^{8} + 396 x^{6} - 4 x^{4} - 2768 x^{2} + 2116$ |
$12$ |
[8,2] |
$2^{32}\cdot 31^{8}$ |
$2$ |
$62.6596239759$ |
$102.38052790852275$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$18281652.4878$ |
12.4.366...536.12 |
$x^{12} - 14 x^{10} + 17 x^{8} + 152 x^{6} + 198 x^{4} + 96 x^{2} + 16$ |
$12$ |
[4,4] |
$2^{32}\cdot 31^{8}$ |
$2$ |
$62.6596239759$ |
$102.38052790852275$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$7829913.71559$ |
12.4.366...536.16 |
$x^{12} + 16 x^{10} - 100 x^{8} - 1320 x^{6} - 1028 x^{4} + 656 x^{2} + 16$ |
$12$ |
[4,4] |
$2^{32}\cdot 31^{8}$ |
$2$ |
$62.6596239759$ |
$102.38052790852275$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$10852566.9425$ |
12.4.366...536.17 |
$x^{12} + 30 x^{10} + 135 x^{8} + 56 x^{6} - 512 x^{4} - 576 x^{2} + 64$ |
$12$ |
[4,4] |
$2^{32}\cdot 31^{8}$ |
$2$ |
$62.6596239759$ |
$102.38052790852275$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$8325812.53378$ |
12.4.366...536.39 |
$x^{12} - 4 x^{10} - 134 x^{8} - 136 x^{6} + 1608 x^{4} + 1408 x^{2} + 256$ |
$12$ |
[4,4] |
$2^{32}\cdot 31^{8}$ |
$2$ |
$62.6596239759$ |
$102.38052790852275$ |
|
|
|
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$6883827.8094$ |
12.8.658...024.4 |
$x^{12} - 26 x^{10} + 231 x^{8} - 790 x^{6} + 620 x^{4} + 876 x^{2} + 121$ |
$12$ |
[8,2] |
$2^{30}\cdot 19^{10}$ |
$2$ |
$65.7965299557$ |
$105.96467536947762$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$9$ |
$8725038.14989$ |
12.4.658...024.14 |
$x^{12} + 8 x^{10} - 100 x^{8} - 1018 x^{6} - 2101 x^{4} - 662 x^{2} + 121$ |
$12$ |
[4,4] |
$2^{30}\cdot 19^{10}$ |
$2$ |
$65.7965299557$ |
$105.96467536947762$ |
|
|
? |
$C_2^3:A_4$ (as 12T58) |
trivial |
$2$ |
$7$ |
$3000629.41451$ |