| 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 |
Max $p$ |
| 5.1.2085136.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 10 x^{2} + 17 x - 12$ |
$5$ |
(1, 2) |
$2^{4}\cdot 19^{4}$ |
$2$ |
$18.358063904$ |
$21.08787780747746$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$115.104690764$ |
$1$ |
$19$ |
| 5.1.6385729.1 |
$x^{5} - 19 x^{2} + 38 x - 95$ |
$5$ |
(1, 2) |
$7^{2}\cdot 19^{4}$ |
$2$ |
$22.9637122778$ |
$27.89664017835169$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$52.7711189868$ |
$1$ |
$19$ |
| 5.1.8340544.1 |
$x^{5} - x^{4} + 8 x^{3} - 32 x^{2} + 45 x - 17$ |
$5$ |
(1, 2) |
$2^{6}\cdot 19^{4}$ |
$2$ |
$24.2236105478$ |
$29.822762797001236$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$37.3886570798$ |
$1$ |
$19$ |
| 5.3.8731507.1 |
$x^{5} - x^{4} - 11 x^{3} + 6 x^{2} + 26 x - 17$ |
$5$ |
(3, 1) |
$-\,19^{4}\cdot 67$ |
$2$ |
$24.4465648034$ |
$86.30585953217158$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$72.2353914755$ |
$2$ |
$67$ |
| 5.1.8861828.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 10 x^{2} + 36 x - 88$ |
$5$ |
(1, 2) |
$2^{2}\cdot 17\cdot 19^{4}$ |
$3$ |
$24.5191078144$ |
$69.01031427929789$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$77.4405325976$ |
$1$ |
$19$ |
| 5.1.10556001.1 |
$x^{5} - 2 x^{4} + 13 x^{3} - 9 x^{2} + 36 x - 12$ |
$5$ |
(1, 2) |
$3^{4}\cdot 19^{4}$ |
$2$ |
$25.3921739481$ |
$37.987817647853376$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$204.981024337$ |
$1$ |
$19$ |
| 5.1.10556001.2 |
$x^{5} - 19 x^{2} + 57$ |
$5$ |
(1, 2) |
$3^{4}\cdot 19^{4}$ |
$2$ |
$25.3921739481$ |
$37.987817647853376$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$57.0180367174$ |
$1$ |
$19$ |
| 5.1.13032100.1 |
$x^{5} - x^{4} - 11 x^{3} + 6 x^{2} + 64 x - 74$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{2}\cdot 19^{4}$ |
$3$ |
$26.485177067$ |
$37.426097677043586$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$163.949828804$ |
$1$ |
$19$ |
| 5.1.15768841.1 |
$x^{5} - x^{4} + 8 x^{3} - 13 x^{2} + 7 x + 2$ |
$5$ |
(1, 2) |
$11^{2}\cdot 19^{4}$ |
$2$ |
$27.5143941798$ |
$34.970289156132615$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$110.813541037$ |
$1$ |
$19$ |
| 5.1.16290125.1 |
$x^{5} - x^{4} + 8 x^{3} + 6 x^{2} + 7 x + 2$ |
$5$ |
(1, 2) |
$5^{3}\cdot 19^{4}$ |
$2$ |
$27.6939486986$ |
$35.255784590695$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
trivial |
$2$ |
$2$ |
$130.253109803$ |
$1$ |
$19$ |
| 5.3.19157187.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 10 x^{2} - 2 x - 31$ |
$5$ |
(3, 1) |
$-\,3\cdot 7^{2}\cdot 19^{4}$ |
$3$ |
$28.6066068729$ |
$48.318398149372435$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$168.585463186$ |
$3$ |
$19$ |
| 5.1.21893928.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 29 x^{2} - 21 x + 45$ |
$5$ |
(1, 2) |
$2^{3}\cdot 3\cdot 7\cdot 19^{4}$ |
$4$ |
$29.3808757858$ |
$136.6650679499711$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$173.626798848$ |
$1$ |
$19$ |
| 5.3.25021632.1 |
$x^{5} - 2 x^{4} - 6 x^{3} - 28 x^{2} + 93 x - 50$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 3\cdot 19^{4}$ |
$3$ |
$30.1761011286$ |
$51.65454038648106$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$415.384202807$ |
$3$ |
$19$ |
| 5.1.29843509.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 10 x^{2} + 17 x + 7$ |
$5$ |
(1, 2) |
$19^{4}\cdot 229$ |
$2$ |
$31.2586326878$ |
$159.55874874704458$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$134.259377159$ |
$1$ |
$229$ |
| 5.3.31668003.1 |
$x^{5} - x^{4} - 11 x^{3} - 13 x^{2} + 7 x + 2$ |
$5$ |
(3, 1) |
$-\,3^{5}\cdot 19^{4}$ |
$2$ |
$31.6318167112$ |
$79.01784496234544$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$390.476970218$ |
$3$ |
$19$ |
| 5.1.31798324.1 |
$x^{5} - 2 x^{4} + 13 x^{3} - 28 x^{2} - 2 x + 26$ |
$5$ |
(1, 2) |
$2^{2}\cdot 19^{4}\cdot 61$ |
$3$ |
$31.6578083788$ |
$130.72373925743406$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$488.184998967$ |
$1$ |
$61$ |
| 5.3.36359559.1 |
$x^{5} - 2 x^{4} - 6 x^{3} - 9 x^{2} + 36 x + 45$ |
$5$ |
(3, 1) |
$-\,3^{2}\cdot 19^{4}\cdot 31$ |
$3$ |
$32.5179921152$ |
$101.68206443290325$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$284.4938858961103$ |
$3$ |
$31$ |
| 5.3.38965979.1 |
$x^{5} - x^{4} - 11 x^{3} - 13 x^{2} + 83 x - 36$ |
$5$ |
(3, 1) |
$-\,13\cdot 19^{4}\cdot 23$ |
$3$ |
$32.9713795242$ |
$182.32174756217856$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$291.0817050127638$ |
$2$ |
$23$ |
| 5.3.44830424.1 |
$x^{5} - x^{4} - 11 x^{3} - 32 x^{2} + 102 x + 135$ |
$5$ |
(3, 1) |
$-\,2^{3}\cdot 19^{4}\cdot 43$ |
$3$ |
$33.9089677502$ |
$195.5609336661764$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$391.588586658$ |
$3$ |
$43$ |
| 5.1.49131017.1 |
$x^{5} - 2 x^{4} + 13 x^{3} - 47 x^{2} + 55 x - 12$ |
$5$ |
(1, 2) |
$13\cdot 19^{4}\cdot 29$ |
$3$ |
$34.5359296354$ |
$204.72626149904954$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$426.33689108127305$ |
$1$ |
$29$ |
| 5.1.52128400.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 48 x^{2} - 40 x + 64$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{2}\cdot 19^{4}$ |
$3$ |
$34.9474006581$ |
$47.15392827872883$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$628.753661344$ |
$1$ |
$19$ |
| 5.1.55386425.1 |
$x^{5} - 2 x^{4} + 13 x^{3} + 10 x^{2} - 2 x + 45$ |
$5$ |
(1, 2) |
$5^{2}\cdot 17\cdot 19^{4}$ |
$3$ |
$35.3737145367$ |
$127.11808576800293$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$168.596613842$ |
$1$ |
$19$ |
| 5.3.56298672.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 48 x^{2} + 36 x - 126$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 3^{3}\cdot 19^{4}$ |
$3$ |
$35.489479519$ |
$41.84733622123886$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$488.422168332$ |
$3$ |
$19$ |
| 5.3.56298672.2 |
$x^{5} - 2 x^{4} - 6 x^{3} + 10 x^{2} - 2 x - 12$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 3^{3}\cdot 19^{4}$ |
$3$ |
$35.489479519$ |
$53.956712810953526$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$647.277944639$ |
$3$ |
$19$ |
| 5.1.68939809.1 |
$x^{5} - x^{4} - 11 x^{3} - 70 x^{2} - 107 x - 55$ |
$5$ |
(1, 2) |
$19^{4}\cdot 23^{2}$ |
$2$ |
$36.9567706846$ |
$50.56695457443357$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$514.680756026$ |
$1$ |
$23$ |
| 5.1.75064896.1 |
$x^{5} - 2 x^{4} + 13 x^{3} - 28 x^{2} + 74 x - 544$ |
$5$ |
(1, 2) |
$2^{6}\cdot 3^{2}\cdot 19^{4}$ |
$3$ |
$37.5913028129$ |
$51.65454038648106$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$1264.88779673$ |
$1$ |
$19$ |
| 5.1.75064896.2 |
$x^{5} - x^{4} + 8 x^{3} - 32 x^{2} + 64 x + 192$ |
$5$ |
(1, 2) |
$2^{6}\cdot 3^{2}\cdot 19^{4}$ |
$3$ |
$37.5913028129$ |
$51.65454038648106$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$127.065444315$ |
$1$ |
$19$ |
| 5.3.77150032.1 |
$x^{5} - 19 x^{3} - 38 x^{2} + 152 x + 190$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 19^{4}\cdot 37$ |
$3$ |
$37.797860871$ |
$161.61328961170548$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$681.231339825$ |
$3$ |
$37$ |
| 5.3.78583563.1 |
$x^{5} - 19 x^{3} + 19 x - 57$ |
$5$ |
(3, 1) |
$-\,3^{2}\cdot 19^{4}\cdot 67$ |
$3$ |
$37.9372933876$ |
$149.48613370062387$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$393.904637181$ |
$3$ |
$67$ |
| 5.1.78844205.1 |
$x^{5} - x^{4} + 8 x^{3} - 13 x^{2} - 50 x - 36$ |
$5$ |
(1, 2) |
$5\cdot 11^{2}\cdot 19^{4}$ |
$3$ |
$37.962425767$ |
$116.61372627963524$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$481.210083816$ |
$1$ |
$19$ |
| 5.1.87575712.1 |
$x^{5} - 2 x^{4} + 13 x^{3} - 28 x^{2} + 36 x - 12$ |
$5$ |
(1, 2) |
$2^{5}\cdot 3\cdot 7\cdot 19^{4}$ |
$4$ |
$38.7682980249$ |
$172.18719589548178$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$447.410555015$ |
$1$ |
$19$ |
| 5.3.87966675.1 |
$x^{5} - x^{4} + 8 x^{3} - 13 x^{2} - 164 x - 131$ |
$5$ |
(3, 1) |
$-\,3^{3}\cdot 5^{2}\cdot 19^{4}$ |
$3$ |
$38.80285093$ |
$84.94334257746631$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$539.146051909$ |
$3$ |
$19$ |
| 5.1.91745984.1 |
$x^{5} - 2 x^{4} - 6 x^{3} - 28 x^{2} + 36 x - 88$ |
$5$ |
(1, 2) |
$2^{6}\cdot 11\cdot 19^{4}$ |
$3$ |
$39.1306815857$ |
$139.88115662453046$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$258.505284494$ |
$1$ |
$19$ |
| 5.1.93831120.1 |
$x^{5} - 38 x^{2} + 171 x - 114$ |
$5$ |
(1, 2) |
$2^{4}\cdot 3^{2}\cdot 5\cdot 19^{4}$ |
$4$ |
$39.3069530546$ |
$91.67484237231959$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1070.01906172$ |
$1$ |
$19$ |
| 5.1.93831120.2 |
$x^{5} - x^{4} + 8 x^{3} - 32 x^{2} + 64 x - 112$ |
$5$ |
(1, 2) |
$2^{4}\cdot 3^{2}\cdot 5\cdot 19^{4}$ |
$4$ |
$39.3069530546$ |
$91.67484237231959$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$455.335428038$ |
$1$ |
$19$ |
| 5.3.100086528.1 |
$x^{5} - x^{4} + 8 x^{3} - 32 x^{2} - 126 x + 306$ |
$5$ |
(3, 1) |
$-\,2^{8}\cdot 3\cdot 19^{4}$ |
$3$ |
$39.8176041555$ |
$81.99647174843388$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$1117.60405728$ |
$3$ |
$19$ |
| 5.1.108557393.1 |
$x^{5} - x^{4} - 11 x^{3} + 44 x^{2} - 69 x + 40$ |
$5$ |
(1, 2) |
$7^{2}\cdot 17\cdot 19^{4}$ |
$3$ |
$40.4698766832$ |
$115.0207940551935$ |
|
|
✓ |
$S_5$ (as 5T5) |
$[4]$ |
$[4]$ |
$2$ |
$2$ |
$143.12438391$ |
$1$ |
$19$ |
| 5.1.112597344.1 |
$x^{5} - x^{4} + 27 x^{3} - 51 x^{2} + 216 x - 492$ |
$5$ |
(1, 2) |
$2^{5}\cdot 3^{3}\cdot 19^{4}$ |
$3$ |
$40.7667067431$ |
$85.65094267685365$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$798.775693078$ |
$1$ |
$19$ |
| 5.1.114682480.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 10 x^{2} + 36 x - 164$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5\cdot 11\cdot 19^{4}$ |
$4$ |
$40.9165883858$ |
$197.04143108380097$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$442.174713601$ |
$1$ |
$19$ |
| 5.1.117288900.1 |
$x^{5} - x^{4} - 11 x^{3} - 70 x^{2} + 64 x - 226$ |
$5$ |
(1, 2) |
$2^{2}\cdot 3^{2}\cdot 5^{2}\cdot 19^{4}$ |
$4$ |
$41.1009048057$ |
$84.76765611728662$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$788.70106218$ |
$1$ |
$19$ |
| 5.1.120937888.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 86 x^{2} - 192 x + 216$ |
$5$ |
(1, 2) |
$2^{5}\cdot 19^{4}\cdot 29$ |
$3$ |
$41.353519383$ |
$202.34394133329394$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$758.7389932157073$ |
$1$ |
$29$ |
| 5.5.121459172.1 |
$x^{5} - x^{4} - 11 x^{3} + 6 x^{2} + 26 x + 2$ |
$5$ |
(5, 0) |
$2^{2}\cdot 19^{4}\cdot 233$ |
$3$ |
$41.3891076623$ |
$255.48623424688247$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$4$ |
$773.0052931395184$ |
$4$ |
$233$ |
| 5.3.126150728.1 |
$x^{5} - x^{4} - 11 x^{3} + 82 x^{2} - 164 x + 97$ |
$5$ |
(3, 1) |
$-\,2^{3}\cdot 11^{2}\cdot 19^{4}$ |
$3$ |
$41.7040230758$ |
$147.50599259323232$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$288.500738053$ |
$3$ |
$19$ |
| 5.3.126672012.1 |
$x^{5} - x^{4} - 11 x^{3} - 51 x^{2} - 12 x + 192$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{5}\cdot 19^{4}$ |
$3$ |
$41.7384323826$ |
$125.43301021748725$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$2449.62591509$ |
$2$ |
$19$ |
| 5.1.127193296.1 |
$x^{5} - 2 x^{4} - 6 x^{3} + 10 x^{2} - 2 x + 26$ |
$5$ |
(1, 2) |
$2^{4}\cdot 19^{4}\cdot 61$ |
$3$ |
$41.7727285935$ |
$143.3810626566407$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$374.828119244$ |
$1$ |
$61$ |
| 5.1.129278432.1 |
$x^{5} - 19 x^{3} - 38 x^{2} + 152 x + 228$ |
$5$ |
(1, 2) |
$2^{5}\cdot 19^{4}\cdot 31$ |
$3$ |
$41.9087989962$ |
$209.20499667856197$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1241.9902568819034$ |
$1$ |
$31$ |
| 5.1.131363568.1 |
$x^{5} - 2 x^{4} + 32 x^{3} - 28 x^{2} + 283 x - 354$ |
$5$ |
(1, 2) |
$2^{4}\cdot 3^{2}\cdot 7\cdot 19^{4}$ |
$4$ |
$42.0431248253$ |
$136.6650679499711$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$461.970467885$ |
$1$ |
$19$ |
| 5.1.139834433.1 |
$x^{5} - 19 x^{2} + 38 x - 19$ |
$5$ |
(1, 2) |
$19^{4}\cdot 29\cdot 37$ |
$3$ |
$42.571879593$ |
$345.38441898990857$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$145.90224033147493$ |
$1$ |
$37$ |
| 5.1.141789248.1 |
$x^{5} - 2 x^{4} + 32 x^{3} + 48 x^{2} + 55 x - 50$ |
$5$ |
(1, 2) |
$2^{6}\cdot 17\cdot 19^{4}$ |
$3$ |
$42.6902462386$ |
$122.96240105977687$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$354.225887872$ |
$1$ |
$19$ |
| 5.1.141789248.2 |
$x^{5} - x^{4} + 8 x^{3} - 32 x^{2} + 140 x - 36$ |
$5$ |
(1, 2) |
$2^{6}\cdot 17\cdot 19^{4}$ |
$3$ |
$42.6902462386$ |
$122.96240105977687$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$563.507651277$ |
$1$ |
$19$ |
