| 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 $p$ |
| 5.1.4435959609.1 |
$x^{5} - 2 x^{4} - 58 x^{3} + 53 x^{2} + 1092 x - 588$ |
$5$ |
(1, 2) |
$3^{2}\cdot 149^{4}$ |
$2$ |
$84.9958099206$ |
$94.86579314817202$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$9935.54574356$ |
$1$ |
$149$ |
| 5.1.7886150416.1 |
$x^{5} - x^{4} - 89 x^{3} + 137 x^{2} + 2117 x - 4507$ |
$5$ |
(1, 2) |
$2^{4}\cdot 149^{4}$ |
$2$ |
$95.3614862818$ |
$109.54158242196894$ |
|
|
? |
$A_5$ (as 5T4) |
$[6]$ |
$[6]$ |
$2$ |
$2$ |
$495.920250813$ |
$1$ |
$149$ |
| 5.3.31544601664.1 |
$x^{5} - x^{4} - 89 x^{3} + 137 x^{2} + 2266 x - 782$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 149^{4}$ |
$2$ |
$125.830235532$ |
$219.08316484393788$ |
|
|
|
$S_5$ (as 5T5) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$8418.11576506$ |
$3$ |
$149$ |
| 5.1.31544601664.1 |
$x^{5} - x^{4} + 60 x^{3} - 12 x^{2} - 2204 x - 5252$ |
$5$ |
(1, 2) |
$2^{6}\cdot 149^{4}$ |
$2$ |
$125.830235532$ |
$154.9151915049587$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$13739.0442418$ |
$1$ |
$149$ |
| 5.1.31544601664.2 |
$x^{5} + 596 x - 2384$ |
$5$ |
(1, 2) |
$2^{6}\cdot 149^{4}$ |
$2$ |
$125.830235532$ |
$154.9151915049587$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$2219.45259716$ |
$1$ |
$149$ |
| 5.1.31544601664.3 |
$x^{5} - x^{4} + 60 x^{3} + 286 x^{2} - 714 x + 1602$ |
$5$ |
(1, 2) |
$2^{6}\cdot 149^{4}$ |
$2$ |
$125.830235532$ |
$154.9151915049587$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$3709.45741426$ |
$1$ |
$149$ |
| 5.1.39923636481.1 |
$x^{5} - 149 x^{2} - 894 x - 1341$ |
$5$ |
(1, 2) |
$3^{4}\cdot 149^{4}$ |
$2$ |
$131.900371427$ |
$197.3288016885008$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$2218.4184938$ |
$1$ |
$149$ |
| 5.1.39923636481.2 |
$x^{5} - 2 x^{4} + 91 x^{3} + 53 x^{2} + 2135 x + 6713$ |
$5$ |
(1, 2) |
$3^{4}\cdot 149^{4}$ |
$2$ |
$131.900371427$ |
$197.3288016885008$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$4192.525894401111$ |
$1$ |
$149$ |
| 5.1.49288440100.1 |
$x^{5} - x^{4} - 89 x^{3} + 584 x^{2} - 1906 x + 15906$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{2}\cdot 149^{4}$ |
$3$ |
$137.578007286$ |
$194.41093128720757$ |
|
|
? |
$A_5$ (as 5T4) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$8289.99411488$ |
$1$ |
$149$ |
| 5.1.59639012521.1 |
$x^{5} - x^{4} + 60 x^{3} - 459 x^{2} - 2651 x - 6146$ |
$5$ |
(1, 2) |
$11^{2}\cdot 149^{4}$ |
$2$ |
$142.924304918$ |
$181.65416391773076$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$9022.42946204$ |
$1$ |
$149$ |
| 5.1.59639012521.2 |
$x^{5} - x^{4} + 60 x^{3} - 12 x^{2} + 776 x + 112$ |
$5$ |
(1, 2) |
$11^{2}\cdot 149^{4}$ |
$2$ |
$142.924304918$ |
$181.65416391773076$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$6942.25056382$ |
$1$ |
$149$ |
| 5.1.61610550125.1 |
$x^{5} - x^{4} + 60 x^{3} - 310 x^{2} + 925 x - 1080$ |
$5$ |
(1, 2) |
$5^{3}\cdot 149^{4}$ |
$2$ |
$143.857005985$ |
$183.13717809116847$ |
|
|
? |
$F_5$ (as 5T3) |
$[25]$ |
$[25]$ |
$2$ |
$2$ |
$289.92315517$ |
$1$ |
$149$ |
| 5.1.61610550125.2 |
$x^{5} - 149$ |
$5$ |
(1, 2) |
$5^{3}\cdot 149^{4}$ |
$2$ |
$143.857005985$ |
$183.13717809116847$ |
|
|
? |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$1756.38859134$ |
$1$ |
$149$ |
| 5.3.62596318927.1 |
$x^{5} - 2 x^{4} + 91 x^{3} + 202 x^{2} - 1739 x + 1796$ |
$5$ |
(3, 1) |
$-\,127\cdot 149^{4}$ |
$2$ |
$144.314430183$ |
$617.2354699581119$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$15300.303167223356$ |
$3$ |
$149$ |
| 5.1.110898990225.1 |
$x^{5} - 2 x^{4} - 58 x^{3} + 53 x^{2} + 1092 x - 141$ |
$5$ |
(1, 2) |
$3^{2}\cdot 5^{2}\cdot 149^{4}$ |
$3$ |
$161.80260833$ |
$212.1263622187464$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$14351.4125113$ |
$1$ |
$149$ |
| 5.1.142443591889.1 |
$x^{5} - x^{4} + 60 x^{3} + 435 x^{2} + 925 x + 559$ |
$5$ |
(1, 2) |
$17^{2}\cdot 149^{4}$ |
$2$ |
$170.10950596$ |
$225.8257573615404$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$1587.4181434707302$ |
$1$ |
$149$ |
| 5.5.159694545924.1 |
$x^{5} - x^{4} - 89 x^{3} - 12 x^{2} + 1968 x + 2496$ |
$5$ |
(5, 0) |
$2^{2}\cdot 3^{4}\cdot 149^{4}$ |
$3$ |
$174.043583531$ |
$376.18142865077266$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$4$ |
$26122.0809575$ |
$5$ |
$149$ |
| 5.1.260735848129.1 |
$x^{5} - 2 x^{4} - 207 x^{3} + 351 x^{2} + 10777 x - 14445$ |
$5$ |
(1, 2) |
$23^{2}\cdot 149^{4}$ |
$2$ |
$191.972998846$ |
$262.6714870464186$ |
|
|
? |
$A_5$ (as 5T4) |
$[6]$ |
$[6]$ |
$2$ |
$2$ |
$1577.0623660969798$ |
$1$ |
$149$ |
| 5.1.260735848129.2 |
$x^{5} - 2 x^{4} + 91 x^{3} + 1841 x^{2} + 5413 x - 4015$ |
$5$ |
(1, 2) |
$23^{2}\cdot 149^{4}$ |
$2$ |
$191.972998846$ |
$262.6714870464186$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$4937.0377050340685$ |
$1$ |
$149$ |
| 5.3.504713626624.1 |
$x^{5} - x^{4} + 60 x^{3} - 1204 x^{2} + 4948 x - 5252$ |
$5$ |
(3, 1) |
$-\,2^{10}\cdot 149^{4}$ |
$2$ |
$219.083164844$ |
$368.452495919412$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$35848.39738150833$ |
$3$ |
$149$ |
| 5.3.504713626624.2 |
$x^{5} - x^{4} + 60 x^{3} - 608 x^{2} - 2502 x + 6966$ |
$5$ |
(3, 1) |
$-\,2^{10}\cdot 149^{4}$ |
$2$ |
$219.083164844$ |
$368.452495919412$ |
|
|
? |
$S_5$ (as 5T5) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$30654.913152164056$ |
$3$ |
$149$ |
| 5.1.630892033280.1 |
$x^{5} - 2 x^{4} - 58 x^{3} + 1096 x^{2} - 2335 x + 133810$ |
$5$ |
(1, 2) |
$2^{8}\cdot 5\cdot 149^{4}$ |
$3$ |
$229.082022468$ |
$489.88484931683723$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$59070.073515$ |
$1$ |
$149$ |
| 5.5.638778183696.1 |
$x^{5} - x^{4} - 89 x^{3} + 137 x^{2} + 925 x - 1825$ |
$5$ |
(5, 0) |
$2^{4}\cdot 3^{4}\cdot 149^{4}$ |
$3$ |
$229.651885289$ |
$394.6576033770016$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$4$ |
$129903.144444$ |
$5$ |
$149$ |
| 5.1.674758744969.1 |
$x^{5} - 149 x^{3} - 149 x^{2} + 8195 x - 11622$ |
$5$ |
(1, 2) |
$37^{2}\cdot 149^{4}$ |
$2$ |
$232.182618286$ |
$333.1577165329634$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$19618.991894646984$ |
$1$ |
$149$ |
| 5.1.911343257449.1 |
$x^{5} - 2 x^{4} + 91 x^{3} + 3182 x^{2} + 23889 x + 45304$ |
$5$ |
(1, 2) |
$43^{2}\cdot 149^{4}$ |
$2$ |
$246.567820875$ |
$359.156096293411$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$53514.54919640726$ |
$1$ |
$149$ |
| 5.1.1715730599881.1 |
$x^{5} + 149 x^{3} - 149 x^{2} - 894 x - 29651$ |
$5$ |
(1, 2) |
$59^{2}\cdot 149^{4}$ |
$2$ |
$279.827130748$ |
$420.7024300176527$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$28402.18882454483$ |
$1$ |
$149$ |
| 5.1.1715730599881.2 |
$x^{5} - x^{4} + 209 x^{3} + 3713 x^{2} + 17166 x + 22760$ |
$5$ |
(1, 2) |
$59^{2}\cdot 149^{4}$ |
$2$ |
$279.827130748$ |
$420.7024300176527$ |
|
|
? |
$A_5$ (as 5T4) |
$[6]$ |
$[6]$ |
$2$ |
$2$ |
$28157.280578084086$ |
$1$ |
$149$ |
| 5.1.1834022856121.1 |
$x^{5} + 298 x^{3} - 447 x^{2} + 3874 x + 188485$ |
$5$ |
(1, 2) |
$61^{2}\cdot 149^{4}$ |
$2$ |
$283.58349376$ |
$427.7735543047425$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$7275.709648327731$ |
$1$ |
$149$ |
| 5.1.2484630265441.1 |
$x^{5} - 149 x^{3} - 894 x^{2} + 17284 x - 32333$ |
$5$ |
(1, 2) |
$71^{2}\cdot 149^{4}$ |
$2$ |
$301.336926408$ |
$461.5068899391265$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$11441.534491021333$ |
$1$ |
$149$ |
| 5.1.2626580972929.1 |
$x^{5} - 2 x^{4} - 207 x^{3} + 649 x^{2} + 12863 x - 63168$ |
$5$ |
(1, 2) |
$73^{2}\cdot 149^{4}$ |
$2$ |
$304.704002329$ |
$467.96184524065586$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$25253.259742511862$ |
$1$ |
$149$ |
| 5.1.2626580972929.2 |
$x^{5} - 2 x^{4} + 91 x^{3} + 53 x^{2} + 49 x + 8$ |
$5$ |
(1, 2) |
$73^{2}\cdot 149^{4}$ |
$2$ |
$304.704002329$ |
$467.96184524065586$ |
|
|
? |
$A_5$ (as 5T4) |
$[15]$ |
$[15]$ |
$2$ |
$2$ |
$2913.044609121584$ |
$1$ |
$149$ |
| 5.1.2626580972929.3 |
$x^{5} + 149 x^{3} - 745 x^{2} + 3427 x + 46339$ |
$5$ |
(1, 2) |
$73^{2}\cdot 149^{4}$ |
$2$ |
$304.704002329$ |
$467.96184524065586$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$2636.5063882338177$ |
$1$ |
$149$ |
| 5.1.3395480638489.1 |
$x^{5} - 2 x^{4} - 207 x^{3} - 2331 x^{2} - 10530 x - 54675$ |
$5$ |
(1, 2) |
$83^{2}\cdot 149^{4}$ |
$2$ |
$320.760034622$ |
$498.98565540485436$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$389616.2820598425$ |
$1$ |
$149$ |
| 5.1.3730642031169.1 |
$x^{5} - x^{4} + 60 x^{3} + 137 x^{2} + 31 x - 633$ |
$5$ |
(1, 2) |
$3^{2}\cdot 29^{2}\cdot 149^{4}$ |
$3$ |
$326.856191303$ |
$510.8679306624376$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$69814.2936312$ |
$1$ |
$149$ |
| 5.1.5027913774601.1 |
$x^{5} - x^{4} + 209 x^{3} - 12 x^{2} - 2800 x + 84744$ |
$5$ |
(1, 2) |
$101^{2}\cdot 149^{4}$ |
$2$ |
$346.958526105$ |
$550.4396393407752$ |
|
|
|
$A_5$ (as 5T4) |
$[6]$ |
$[6]$ |
$2$ |
$2$ |
$22361.35340208706$ |
$1$ |
$149$ |
| 5.5.6293640916369.1 |
$x^{5} - 447 x^{3} - 2086 x^{2} + 37846 x + 234973$ |
$5$ |
(5, 0) |
$113^{2}\cdot 149^{4}$ |
$2$ |
$362.894505018$ |
$582.2214968516104$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[6]$ |
$2$ |
$4$ |
$10839.064176367061$ |
$4$ |
$149$ |
| 5.1.7949732503729.1 |
$x^{5} - x^{4} - 238 x^{3} + 1031 x^{2} + 4799 x + 6072$ |
$5$ |
(1, 2) |
$127^{2}\cdot 149^{4}$ |
$2$ |
$380.251121055$ |
$617.2354699581119$ |
|
|
|
$A_5$ (as 5T4) |
$[6]$ |
$[6]$ |
$2$ |
$2$ |
$44667.06222132552$ |
$1$ |
$149$ |
| 5.5.9250947322369.1 |
$x^{5} - 2 x^{4} - 654 x^{3} - 6205 x^{2} + 4668 x + 105053$ |
$5$ |
(5, 0) |
$137^{2}\cdot 149^{4}$ |
$2$ |
$391.955931994$ |
$641.0756749972531$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
$[2, 2]$ |
$2$ |
$4$ |
$218941.0163162078$ |
$3$ |
$149$ |
| 5.1.9523019511721.1 |
$x^{5} - x^{4} + 60 x^{3} - 3439 x^{2} + 11951 x - 22536$ |
$5$ |
(1, 2) |
$139^{2}\cdot 149^{4}$ |
$2$ |
$394.234779155$ |
$645.7381049720841$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$77672.66998215573$ |
$1$ |
$149$ |
| 5.1.12020957655989.1 |
$x^{5} - x^{4} - 89 x^{3} - 4035 x^{2} + 5395 x - 86904$ |
$5$ |
(1, 2) |
$29^{3}\cdot 149^{4}$ |
$2$ |
$413.035911823$ |
$684.4591177592877$ |
|
|
? |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$16766.59037243801$ |
$1$ |
$149$ |
| 5.1.12020957655989.2 |
$x^{5} - x^{4} + 60 x^{3} + 3713 x^{2} + 29086 x + 2943$ |
$5$ |
(1, 2) |
$29^{3}\cdot 149^{4}$ |
$2$ |
$413.035911823$ |
$684.4591177592877$ |
|
|
? |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$15730.179208671809$ |
$1$ |
$149$ |
| 5.3.14683519190191.1 |
$x^{5} - x^{4} - 89 x^{3} + 1776 x^{2} + 4203 x - 73494$ |
$5$ |
(3, 1) |
$-\,31^{3}\cdot 149^{4}$ |
$2$ |
$429.898600224$ |
$957.96672973889$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$957464.8254568137$ |
$3$ |
$149$ |
| 5.1.24644220050000.1 |
$x^{5} - 2384$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{5}\cdot 149^{4}$ |
$3$ |
$476.807431409$ |
$606.9997556485819$ |
|
|
? |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$23670.4588155$ |
$1$ |
$149$ |
| 5.1.24644220050000.2 |
$x^{5} - 1192$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{5}\cdot 149^{4}$ |
$3$ |
$476.807431409$ |
$606.9997556485819$ |
|
|
? |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$23865.4410681$ |
$1$ |
$149$ |
| 5.1.24644220050000.3 |
$x^{5} - 596$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{5}\cdot 149^{4}$ |
$3$ |
$476.807431409$ |
$606.9997556485819$ |
|
|
? |
$F_5$ (as 5T3) |
$[40]$ |
$[40]$ |
$2$ |
$2$ |
$3183.92247117$ |
$1$ |
$149$ |
| 5.1.24644220050000.4 |
$x^{5} - 298$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{5}\cdot 149^{4}$ |
$3$ |
$476.807431409$ |
$606.9997556485819$ |
|
|
✓ |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$36570.8467577$ |
$1$ |
$149$ |
| 5.1.24966073563853.1 |
$x^{5} - x^{4} - 238 x^{3} + 2819 x^{2} - 12932 x + 33935$ |
$5$ |
(1, 2) |
$37^{3}\cdot 149^{4}$ |
$2$ |
$478.046396861$ |
$821.6754432892258$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$86966.13816305232$ |
$1$ |
$149$ |
| 5.1.38506593828125.1 |
$x^{5} - 745 x^{3} + 111005 x - 749321$ |
$5$ |
(1, 2) |
$5^{7}\cdot 149^{4}$ |
$2$ |
$521.323162077$ |
$663.6705117189965$ |
|
|
? |
$F_5$ (as 5T3) |
$[20]$ |
$[20]$ |
$2$ |
$2$ |
$7731.4913552926955$ |
$1$ |
$149$ |
| 5.1.38506593828125.2 |
$x^{5} - 745 x^{3} + 111005 x - 577226$ |
$5$ |
(1, 2) |
$5^{7}\cdot 149^{4}$ |
$2$ |
$521.323162077$ |
$663.6705117189965$ |
|
|
? |
$F_5$ (as 5T3) |
$[20]$ |
$[20]$ |
$2$ |
$2$ |
$9066.28118873275$ |
$1$ |
$149$ |
| 5.1.38506593828125.3 |
$x^{5} + 745 x^{3} + 111005 x - 341657$ |
$5$ |
(1, 2) |
$5^{7}\cdot 149^{4}$ |
$2$ |
$521.323162077$ |
$663.6705117189965$ |
|
|
? |
$F_5$ (as 5T3) |
$[5, 5]$ |
$[5, 5]$ |
$2$ |
$2$ |
$5925.011011602649$ |
$1$ |
$149$ |
