| 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 |
| 15.5.257...000.1 |
$x^{15} - 5 x^{13} - 5 x^{12} - 20 x^{11} - 10 x^{10} + 30 x^{9} + 70 x^{8} + 95 x^{7} + 110 x^{6} + 85 x^{5} + 185 x^{4} + 45 x^{3} + 50 x^{2} - 25 x - 5$ |
$15$ |
(5, 5) |
$-\,2^{12}\cdot 5^{17}\cdot 7^{7}$ |
$3$ |
$26.7527903869$ |
$30.937664227835434$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
trivial |
trivial |
$2$ |
$9$ |
$184544.05094$ |
$5$ |
| 15.3.283...000.1 |
$x^{15} - 5 x^{14} + 10 x^{13} - 20 x^{12} + 15 x^{11} - 21 x^{10} + 175 x^{9} - 295 x^{8} + 785 x^{7} - 845 x^{6} + 1247 x^{5} - 2065 x^{4} + 2675 x^{3} - 1225 x^{2} + 40 x + 72$ |
$15$ |
(3, 6) |
$2^{21}\cdot 5^{17}\cdot 11^{6}$ |
$3$ |
$42.6741690112$ |
|
|
|
? |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
trivial |
trivial |
$2$ |
$8$ |
$25661881.7232$ |
$3$ |
| 15.3.283...000.2 |
$x^{15} - 5 x^{14} - 5 x^{13} + 35 x^{12} + 145 x^{11} - 263 x^{10} - 540 x^{9} - 180 x^{8} + 1900 x^{7} + 800 x^{6} - 977 x^{5} - 925 x^{4} - 965 x^{3} + 835 x^{2} - 5 x + 89$ |
$15$ |
(3, 6) |
$2^{21}\cdot 5^{17}\cdot 11^{6}$ |
$3$ |
$42.6741690112$ |
|
|
|
? |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
trivial |
trivial |
$2$ |
$8$ |
$19160065.1923$ |
$3$ |
| 15.3.293...000.1 |
$x^{15} - 15 x^{13} - 40 x^{12} + 720 x^{10} - 2480 x^{9} + 11700 x^{8} - 42150 x^{7} + 89040 x^{6} - 228150 x^{5} + 327600 x^{4} - 478980 x^{3} + 412200 x^{2} - 279300 x + 94480$ |
$15$ |
(3, 6) |
$2^{28}\cdot 3^{15}\cdot 5^{17}$ |
$3$ |
$67.79691278772712$ |
$121.94367865849007$ |
|
|
|
$S_5 \times S_3$ (as 15T29) |
trivial |
trivial |
$2$ |
$8$ |
$1044480146.3607405$ |
$3$ |
| 18.6.507...000.1 |
$x^{18} - 12 x^{16} - 20 x^{15} + 45 x^{14} + 240 x^{13} + 180 x^{12} - 900 x^{11} - 2385 x^{10} - 940 x^{9} + 6210 x^{8} + 13260 x^{7} + 6025 x^{6} - 18540 x^{5} - 30390 x^{4} - 4840 x^{3} + 21600 x^{2} + 16080 x + 3100$ |
$18$ |
(6, 6) |
$2^{34}\cdot 3^{18}\cdot 5^{17}$ |
$3$ |
$50.8009467626$ |
|
|
|
? |
$C_3\wr S_5:C_2$ (as 18T845) |
trivial |
trivial |
$2$ |
$11$ |
$1235939083.08$ |
$6$ |
| 18.6.126...000.1 |
$x^{18} - 30 x^{16} - 20 x^{15} + 360 x^{14} + 420 x^{13} - 3230 x^{12} - 7200 x^{11} + 8490 x^{10} + 43140 x^{9} + 87660 x^{8} + 149820 x^{7} + 175670 x^{6} + 147600 x^{5} + 82800 x^{4} + 26360 x^{3} + 9000 x^{2} + 4800 x - 200$ |
$18$ |
(6, 6) |
$2^{34}\cdot 3^{18}\cdot 5^{19}$ |
$3$ |
$60.7484414158$ |
$121.94367865849007$ |
|
|
? |
$S_3\times S_5$ (as 18T227) |
trivial |
trivial |
$2$ |
$11$ |
$6503790952.27$ |
$6$ |
| 20.0.243...000.1 |
$x^{20} - 20 x^{18} + 220 x^{16} - 48 x^{15} - 520 x^{14} + 1040 x^{13} - 6670 x^{12} - 8680 x^{11} + 82648 x^{10} + 80240 x^{9} - 335920 x^{8} - 172960 x^{7} + 1105960 x^{6} + 399184 x^{5} - 1904775 x^{4} + 1283240 x^{3} + 8424540 x^{2} + 8752080 x + 3070180$ |
$20$ |
(0, 10) |
$2^{59}\cdot 5^{22}\cdot 11^{6}$ |
$3$ |
$93.1801268908$ |
|
|
|
? |
$C_2^{10}.C_3^4:(S_3\times F_5)$ (as 20T1032) |
trivial |
trivial |
$2$ |
$9$ |
$962178480689$ |
$0$ |
| 20.0.219...000.1 |
$x^{20} - 40 x^{18} - 80 x^{17} + 540 x^{16} + 1920 x^{15} - 1120 x^{14} - 12280 x^{13} + 54950 x^{12} + 91520 x^{11} - 398016 x^{10} + 528960 x^{9} + 1490240 x^{8} - 4294560 x^{7} + 2844720 x^{6} + 12388192 x^{5} + 10739860 x^{4} - 24257280 x^{3} + 11562000 x^{2} + 174841920 x + 234225072$ |
$20$ |
(0, 10) |
$2^{59}\cdot 3^{2}\cdot 5^{22}\cdot 11^{6}$ |
$4$ |
$104.000498982$ |
|
|
|
? |
$C_2^{10}.C_3^4:(S_3\times F_5)$ (as 20T1032) |
$[4]$ |
$[4]$ |
$2$ |
$9$ |
$1013484687050$ |
$0$ |
| 20.4.242...000.1 |
$x^{20} - 5 x^{19} - 25 x^{18} + 35 x^{17} + 1000 x^{16} - 2478 x^{15} - 12250 x^{14} + 74190 x^{13} - 130285 x^{12} + 136445 x^{11} - 388435 x^{10} + 970665 x^{9} + 1784260 x^{8} - 11407390 x^{7} + 21264310 x^{6} - 16392250 x^{5} - 5760615 x^{4} - 4392785 x^{3} + 55965075 x^{2} - 26870825 x + 8792410$ |
$20$ |
(4, 8) |
$2^{55}\cdot 5^{22}\cdot 7^{10}$ |
$3$ |
$104.531820218$ |
|
|
|
|
$C_2^8.(S_3\times F_5)$ (as 20T559) |
trivial |
trivial |
$2$ |
$11$ |
$93637547912100$ |
$4$ |
| 20.0.388...000.1 |
$x^{20} - 40 x^{17} + 500 x^{16} + 4208 x^{15} + 22860 x^{14} + 89480 x^{13} + 347650 x^{12} + 1383720 x^{11} + 5121684 x^{10} + 15240040 x^{9} + 34578120 x^{8} + 57142880 x^{7} + 70268380 x^{6} + 71884872 x^{5} + 72196265 x^{4} + 62435320 x^{3} + 40912340 x^{2} + 18112880 x + 3773156$ |
$20$ |
(0, 10) |
$2^{59}\cdot 5^{22}\cdot 7^{10}$ |
$3$ |
$120.075529929$ |
|
|
|
? |
$C_2^8.(F_5\times S_4)$ (as 20T811) |
$[4]$ |
$[4]$ |
$2$ |
$9$ |
$3399389331400$ |
$0$ |
| 20.4.506...000.1 |
$x^{20} - 60 x^{18} - 160 x^{17} + 870 x^{16} + 4320 x^{15} - 3520 x^{14} - 54960 x^{13} - 68265 x^{12} + 307840 x^{11} + 947856 x^{10} - 307920 x^{9} - 4643510 x^{8} - 3997440 x^{7} + 8299980 x^{6} + 8363824 x^{5} - 19541415 x^{4} - 16312320 x^{3} + 14352120 x^{2} - 23055840 x - 39496248$ |
$20$ |
(4, 8) |
$2^{55}\cdot 3^{20}\cdot 5^{22}\cdot 13^{2}$ |
$4$ |
$153.184591509$ |
|
|
|
? |
$C_2^8.(F_5\times S_4)$ (as 20T811) |
$[2, 2]$ |
$[2, 4]$ |
$2$ |
$11$ |
$222617324287000$ |
$3$ |
| 20.4.149...000.1 |
$x^{20} - 30 x^{18} - 80 x^{17} + 555 x^{16} + 1920 x^{15} - 1000 x^{14} + 40560 x^{13} - 964695 x^{12} + 2689760 x^{11} + 14821146 x^{10} - 92071680 x^{9} + 74473325 x^{8} + 647709600 x^{7} - 2618033400 x^{6} + 10090345424 x^{5} - 50448894465 x^{4} + 169568098560 x^{3} - 318768052590 x^{2} + 310434398640 x - 122509757583$ |
$20$ |
(4, 8) |
$2^{51}\cdot 3^{20}\cdot 5^{22}\cdot 23^{2}\cdot 389^{2}$ |
$5$ |
$256.31999868$ |
|
|
|
|
$C_2^8.(F_5\times S_4)$ (as 20T811) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$72532444830100000$ |
$3$ |
