| 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 $p$ |
| 5.1.31250000.3 |
$x^{5} - 40$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{9}$ |
$2$ |
$31.547867224$ |
$40.16201601476873$ |
|
|
? |
$F_5$ (as 5T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$72.2762732852$ |
$1$ |
$5$ |
| 5.1.46875000.1 |
$x^{5} - 25 x^{2} - 30$ |
$5$ |
(1, 2) |
$2^{3}\cdot 3\cdot 5^{9}$ |
$3$ |
$34.2127714459$ |
$113.00486200961342$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$736.513388556$ |
$1$ |
$5$ |
| 5.1.80078125.1 |
$x^{5} - 50 x^{2} + 125 x - 85$ |
$5$ |
(1, 2) |
$5^{9}\cdot 41$ |
$2$ |
$38.0805120195$ |
$147.70100038454413$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$220.887906689$ |
$1$ |
$41$ |
| 5.3.109375000.1 |
$x^{5} - 25 x^{2} + 25 x + 5$ |
$5$ |
(3, 1) |
$-\,2^{3}\cdot 5^{9}\cdot 7$ |
$3$ |
$40.5306541549$ |
$172.617778019031$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$502.57708$ |
$2$ |
$7$ |
| 5.3.115234375.1 |
$x^{5} - 50 x^{2} - 25 x + 10$ |
$5$ |
(3, 1) |
$-\,5^{9}\cdot 59$ |
$2$ |
$40.9558939835$ |
$177.1811492313839$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$666.097022493$ |
$3$ |
$59$ |
| 5.3.125000000.1 |
$x^{5} - 100 x - 160$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 5^{9}$ |
$2$ |
$41.6276603701$ |
$92.26808345905883$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$1150.07653913$ |
$3$ |
$5$ |
| 5.1.158203125.2 |
$x^{5} - 405$ |
$5$ |
(1, 2) |
$3^{4}\cdot 5^{9}$ |
$2$ |
$43.6358069365$ |
$55.55056906241114$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
trivial |
$2$ |
$2$ |
$300.202983492$ |
$1$ |
$5$ |
| 5.1.158203125.8 |
$x^{5} - 75 x^{2} + 225 x - 135$ |
$5$ |
(1, 2) |
$3^{4}\cdot 5^{9}$ |
$2$ |
$43.6358069365$ |
$99.80520279143677$ |
|
|
? |
$S_5$ (as 5T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$93.4819459656$ |
$1$ |
$5$ |
| 5.1.158203125.9 |
$x^{5} - 75 x^{2} + 225 x - 180$ |
$5$ |
(1, 2) |
$3^{4}\cdot 5^{9}$ |
$2$ |
$43.6358069365$ |
$83.10611340693556$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$551.107011925$ |
$1$ |
$5$ |
| 5.1.187500000.1 |
$x^{5} - 50 x^{2} - 100 x - 340$ |
$5$ |
(1, 2) |
$2^{5}\cdot 3\cdot 5^{9}$ |
$3$ |
$45.1440225724$ |
$142.3772043863774$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1156.79412448$ |
$1$ |
$5$ |
| 5.1.212890625.1 |
$x^{5} - 25 x^{3} - 125 x^{2} - 250 x - 200$ |
$5$ |
(1, 2) |
$5^{9}\cdot 109$ |
$2$ |
$46.3053645239$ |
$240.82676807557846$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$865.5125732920939$ |
$1$ |
$109$ |
| 5.1.212890625.2 |
$x^{5} - 25 x^{3} - 25 x^{2} + 75 x - 45$ |
$5$ |
(1, 2) |
$5^{9}\cdot 109$ |
$2$ |
$46.3053645239$ |
$240.82676807557846$ |
|
|
? |
$S_5$ (as 5T5) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$34.664194398473455$ |
$1$ |
$109$ |
| 5.3.232421875.1 |
$x^{5} - 25 x^{3} - 200$ |
$5$ |
(3, 1) |
$-\,5^{9}\cdot 7\cdot 17$ |
$3$ |
$47.12543804$ |
$251.63148995601355$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$2205.4140819943173$ |
$2$ |
$17$ |
| 5.1.251953125.1 |
$x^{5} - 25 x^{3} + 375 x - 225$ |
$5$ |
(1, 2) |
$3\cdot 5^{9}\cdot 43$ |
$3$ |
$47.8921076326$ |
$261.9909946033227$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1449.2139703258504$ |
$1$ |
$43$ |
| 5.3.265625000.1 |
$x^{5} - 25 x^{2} + 25 x - 5$ |
$5$ |
(3, 1) |
$-\,2^{3}\cdot 5^{9}\cdot 17$ |
$3$ |
$48.4009392501$ |
$269.0053780396717$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$559.933764959$ |
$3$ |
$17$ |
| 5.1.281250000.3 |
$x^{5} - 50 x^{2} - 150 x - 180$ |
$5$ |
(1, 2) |
$2^{4}\cdot 3^{2}\cdot 5^{9}$ |
$3$ |
$48.957418118$ |
$89.69201841579077$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1677.56460377$ |
$1$ |
$5$ |
| 5.1.382812500.1 |
$x^{5} - 25 x^{3} + 200 x - 560$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{9}\cdot 7^{2}$ |
$3$ |
$52.0711563341$ |
$96.8784523449271$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$2770.59628521$ |
$1$ |
$7$ |
| 5.3.398437500.1 |
$x^{5} - 25 x^{3} - 540$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3\cdot 5^{9}\cdot 17$ |
$4$ |
$52.4894523162$ |
$261.4949223670274$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$2601.79689681$ |
$3$ |
$17$ |
| 5.3.412109375.1 |
$x^{5} - 25 x^{3} - 25 x^{2} + 125 x + 405$ |
$5$ |
(3, 1) |
$-\,5^{9}\cdot 211$ |
$2$ |
$52.8448292378$ |
$335.0678323599991$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$458.278471075$ |
$2$ |
$211$ |
| 5.1.593750000.2 |
$x^{5} - 25 x^{3} + 175 x - 20$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{9}\cdot 19$ |
$3$ |
$56.8487244405$ |
$284.38933285106623$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$446.3920017657771$ |
$1$ |
$19$ |
| 5.3.632812500.1 |
$x^{5} - 25 x^{2} - 225 x - 285$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 5^{9}$ |
$3$ |
$57.5777924456$ |
$166.21222681387113$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$1700.97420901$ |
$2$ |
$5$ |
| 5.1.632812500.4 |
$x^{5} + 25 x^{3} - 150$ |
$5$ |
(1, 2) |
$2^{2}\cdot 3^{4}\cdot 5^{9}$ |
$3$ |
$57.5777924456$ |
$158.4308839030262$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$2598.97362617$ |
$1$ |
$5$ |
| 5.1.666015625.1 |
$x^{5} + 25 x^{3} - 25 x^{2} + 125 x - 95$ |
$5$ |
(1, 2) |
$5^{9}\cdot 11\cdot 31$ |
$3$ |
$58.1697079824$ |
$425.959881898803$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$306.9901244558392$ |
$1$ |
$31$ |
| 5.3.763671875.2 |
$x^{5} - 75 x^{2} - 25 x + 490$ |
$5$ |
(3, 1) |
$-\,5^{9}\cdot 17\cdot 23$ |
$3$ |
$59.7835030625$ |
$456.1208102751033$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$910.5682809106044$ |
$3$ |
$23$ |
| 5.1.798828125.1 |
$x^{5} + 25 x - 35$ |
$5$ |
(1, 2) |
$5^{9}\cdot 409$ |
$2$ |
$60.324074747$ |
$466.5016266792384$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$476.269170573$ |
$1$ |
$409$ |
| 5.3.812500000.2 |
$x^{5} - 25 x^{3} - 150 x^{2} - 500 x - 280$ |
$5$ |
(3, 1) |
$-\,2^{5}\cdot 5^{9}\cdot 13$ |
$3$ |
$60.5291637554$ |
$332.6773060004274$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$3335.9484096641636$ |
$3$ |
$13$ |
| 5.1.812500000.2 |
$x^{5} - 25 x^{3} - 200 x^{2} - 600 x - 910$ |
$5$ |
(1, 2) |
$2^{5}\cdot 5^{9}\cdot 13$ |
$3$ |
$60.5291637554$ |
$296.3817854701622$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$2818.1617106255067$ |
$1$ |
$13$ |
| 5.1.837890625.3 |
$x^{5} - 25 x^{2} + 50 x - 20$ |
$5$ |
(1, 2) |
$3\cdot 5^{9}\cdot 11\cdot 13$ |
$4$ |
$60.9028289591$ |
$477.7714063502392$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$2284.87843008$ |
$1$ |
$13$ |
| 5.1.861328125.3 |
$x^{5} + 25 x^{3} + 125 x - 325$ |
$5$ |
(1, 2) |
$3^{2}\cdot 5^{9}\cdot 7^{2}$ |
$3$ |
$61.2397946431$ |
$105.70636916990999$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
trivial |
$2$ |
$2$ |
$993.883503857$ |
$1$ |
$7$ |
| 5.3.896484375.1 |
$x^{5} - 25 x^{3} - 75 x^{2} - 75 x - 15$ |
$5$ |
(3, 1) |
$-\,3^{3}\cdot 5^{9}\cdot 17$ |
$3$ |
$61.7317437729$ |
$342.6552837113553$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$1358.8239248945379$ |
$3$ |
$17$ |
| 5.1.906250000.2 |
$x^{5} + 25 x^{3} + 100 x - 320$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{9}\cdot 29$ |
$3$ |
$61.8656533697$ |
$248.43941793273643$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1752.0414191923844$ |
$1$ |
$29$ |
| 5.1.945312500.1 |
$x^{5} - 50 x^{2} - 375 x - 540$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{9}\cdot 11^{2}$ |
$3$ |
$62.3900135762$ |
$121.44356703320001$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$6470.68034755$ |
$1$ |
$11$ |
| 5.3.1125000000.1 |
$x^{5} + 25 x^{3} - 175 x - 170$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 3^{2}\cdot 5^{9}$ |
$3$ |
$64.5997004978$ |
$159.81300846809543$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$2155.19085973$ |
$3$ |
$5$ |
| 5.1.1125000000.2 |
$x^{5} - 50 x^{3} + 500 x - 800$ |
$5$ |
(1, 2) |
$2^{6}\cdot 3^{2}\cdot 5^{9}$ |
$3$ |
$64.5997004978$ |
$113.00486200961342$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
trivial |
$2$ |
$2$ |
$1245.97895268$ |
$1$ |
$5$ |
| 5.3.1208984375.1 |
$x^{5} - 50 x^{3} - 125 x^{2} + 200 x + 545$ |
$5$ |
(3, 1) |
$-\,5^{9}\cdot 619$ |
$2$ |
$65.5366348465$ |
$573.9008037328651$ |
|
|
? |
$S_5$ (as 5T5) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$197.997759768$ |
$2$ |
$619$ |
| 5.3.1281250000.2 |
$x^{5} - 50 x^{3} - 100 x^{2} + 100 x + 240$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 5^{9}\cdot 41$ |
$3$ |
$66.3020223783$ |
$417.7615158397921$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$1613.4927868065895$ |
$3$ |
$41$ |
| 5.3.1375000000.2 |
$x^{5} - 50 x^{3} + 625 x - 720$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 5^{9}\cdot 11$ |
$3$ |
$67.2450838773$ |
$216.3878363925365$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$3541.43030646$ |
$3$ |
$11$ |
| 5.1.1423828125.1 |
$x^{5} - 100 x^{2} - 75 x - 15$ |
$5$ |
(1, 2) |
$3^{6}\cdot 5^{9}$ |
$2$ |
$67.7160338586$ |
$172.86768209448363$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1319.53764831$ |
$1$ |
$5$ |
| 5.1.1437500000.2 |
$x^{5} + 25 x^{3} - 100 x^{2} + 400 x - 130$ |
$5$ |
(1, 2) |
$2^{5}\cdot 5^{9}\cdot 23$ |
$3$ |
$67.8455817414$ |
$394.2246278304822$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1525.7228607584416$ |
$1$ |
$23$ |
| 5.3.1476562500.1 |
$x^{5} - 50 x^{3} - 75 x^{2} + 75 x - 795$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 5^{9}\cdot 7$ |
$4$ |
$68.2103639662$ |
$439.75621700776463$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$2810.11142272$ |
$3$ |
$7$ |
| 5.1.1642578125.1 |
$x^{5} - 25 x^{3} + 125 x - 1915$ |
$5$ |
(1, 2) |
$5^{9}\cdot 29^{2}$ |
$2$ |
$69.6795290924$ |
$124.21970896636822$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
trivial |
$2$ |
$2$ |
$1201.60207204$ |
$1$ |
$29$ |
| 5.3.1687500000.2 |
$x^{5} - 25 x^{3} - 100 x^{2} - 450 x - 110$ |
$5$ |
(3, 1) |
$-\,2^{5}\cdot 3^{3}\cdot 5^{9}$ |
$3$ |
$70.0565516177$ |
$187.37893872973692$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$4450.46521517$ |
$3$ |
$5$ |
| 5.3.1818359375.1 |
$x^{5} - 50 x^{3} - 25 x^{2} + 550 x + 985$ |
$5$ |
(3, 1) |
$-\,5^{9}\cdot 7^{2}\cdot 19$ |
$3$ |
$71.1108621387$ |
$266.0218619954763$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$2153.448206240534$ |
$3$ |
$19$ |
| 5.1.1876953125.2 |
$x^{5} + 50 x^{3} - 225 x^{2} + 375 x - 220$ |
$5$ |
(1, 2) |
$5^{9}\cdot 31^{2}$ |
$2$ |
$71.5633537763$ |
$227.63164542423385$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1304.27854353$ |
$1$ |
$31$ |
| 5.1.2126953125.2 |
$x^{5} - 25 x^{2} + 75 x - 60$ |
$5$ |
(1, 2) |
$3^{2}\cdot 5^{9}\cdot 11^{2}$ |
$3$ |
$73.375586182$ |
$197.61227861296126$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$2381.65346003$ |
$1$ |
$11$ |
| 5.1.2156250000.1 |
$x^{5} + 100 x - 320$ |
$5$ |
(1, 2) |
$2^{4}\cdot 3\cdot 5^{9}\cdot 23$ |
$4$ |
$73.5766181991$ |
$383.2181319233673$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1411.57178048$ |
$1$ |
$23$ |
| 5.5.2267578125.1 |
$x^{5} - 50 x^{3} - 25 x^{2} + 600 x + 740$ |
$5$ |
(5, 0) |
$3^{3}\cdot 5^{9}\cdot 43$ |
$3$ |
$74.3211552551$ |
$544.9632296596502$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$4$ |
$12774.397578769567$ |
$4$ |
$43$ |
| 5.5.2296875000.1 |
$x^{5} - 50 x^{3} - 25 x^{2} + 375 x - 345$ |
$5$ |
(5, 0) |
$2^{3}\cdot 3\cdot 5^{9}\cdot 7^{2}$ |
$4$ |
$74.5122147315$ |
$413.5193368121363$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$4$ |
$6359.11322805$ |
$5$ |
$7$ |
| 5.1.2312500000.1 |
$x^{5} + 25 x^{3} - 100 x^{2} - 1280$ |
$5$ |
(1, 2) |
$2^{5}\cdot 5^{9}\cdot 37$ |
$3$ |
$74.6133171587$ |
$561.244840807192$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$2908.99448486$ |
$1$ |
$37$ |
| 5.3.2375000000.1 |
$x^{5} - 500 x - 1200$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 5^{9}\cdot 19$ |
$3$ |
$75.0123416166$ |
$284.38933285106623$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$4423.18698822$ |
$3$ |
$19$ |
