| 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 |
| 7.5.2306599.1 |
$x^{7} - 3 x^{5} - x^{4} + x^{3} + 3 x^{2} + x - 1$ |
$7$ |
[5,1] |
$-\,107\cdot 21557$ |
$2$ |
$8.10953615179$ |
$1518.7491563783665$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$2.88464598235$ |
| 7.5.2369207.1 |
$x^{7} - 4 x^{5} + 3 x^{3} - x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,23\cdot 239\cdot 431$ |
$3$ |
$8.14062168468$ |
$1539.2228558594106$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$2.93325318954$ |
| 7.5.2616839.1 |
$x^{7} - x^{6} - 3 x^{5} + 4 x^{4} + x^{3} - 5 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,61\cdot 42899$ |
$2$ |
$8.25705706874$ |
$1617.6646747703926$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.13683605225$ |
| 7.5.2790047.1 |
$x^{7} - x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 1$ |
$7$ |
[5,1] |
$-\,13\cdot 157\cdot 1367$ |
$3$ |
$8.33300506139$ |
$1670.3433778717476$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.26802116176$ |
| 7.5.2790551.1 |
$x^{7} - 2 x^{5} - 3 x^{3} - x^{2} + 3 x + 1$ |
$7$ |
[5,1] |
$-\,317\cdot 8803$ |
$2$ |
$8.33322008641$ |
$1670.4942382420838$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.27112614159$ |
| 7.5.2894039.1 |
$x^{7} - x^{6} - x^{5} - 2 x^{3} + 3 x^{2} + 2 x - 1$ |
$7$ |
[5,1] |
$-\,829\cdot 3491$ |
$2$ |
$8.37668248904$ |
$1701.1875264061866$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.34401847196$ |
| 7.5.2932823.1 |
$x^{7} - x^{6} - 4 x^{3} + 2 x^{2} + 2 x - 1$ |
$7$ |
[5,1] |
$-\,17\cdot 172519$ |
$2$ |
$8.39262810562$ |
$1712.5486854393366$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.36845679278$ |
| 7.5.3063719.1 |
$x^{7} - 3 x^{6} + x^{5} + 4 x^{4} - 5 x^{3} + x^{2} + 3 x - 1$ |
$7$ |
[5,1] |
$-\,1423\cdot 2153$ |
$2$ |
$8.44514265371$ |
$1750.348251063199$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.48308968389$ |
| 7.5.3373751.1 |
$x^{7} - 2 x^{5} - 2 x^{4} - x^{3} + 3 x^{2} + x - 1$ |
$7$ |
[5,1] |
$-\,1567\cdot 2153$ |
$2$ |
$8.56224351367$ |
$1836.777340888111$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.78621917316$ |
| 7.5.3394343.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + 6 x^{4} - x^{3} - 5 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,37\cdot 199\cdot 461$ |
$3$ |
$8.5696898354$ |
$1842.3742833637252$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.79947407487$ |
| 7.5.3394511.1 |
$x^{7} - 2 x^{6} + x^{5} - x^{4} - 3 x^{3} + 4 x^{2} + 2 x - 1$ |
$7$ |
[5,1] |
$-\,269\cdot 12619$ |
$2$ |
$8.56975042685$ |
$1842.419876141158$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.71316180418$ |
| 7.5.3404423.1 |
$x^{7} - 2 x^{5} - 3 x^{4} + x^{3} + 5 x^{2} - 1$ |
$7$ |
[5,1] |
$-\,11\cdot 309493$ |
$2$ |
$8.57332078151$ |
$1845.1078559260432$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.72400985616$ |
| 7.5.3444743.1 |
$x^{7} - x^{6} - 4 x^{5} + 4 x^{4} + 3 x^{3} - 4 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,3444743$ |
$1$ |
$8.58775303556$ |
$1856.0018857749042$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.74999504592$ |
| 7.5.3455831.1 |
$x^{7} - x^{6} - 4 x^{5} + 4 x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 1$ |
$7$ |
[5,1] |
$-\,223\cdot 15497$ |
$2$ |
$8.59169651491$ |
$1858.9865518609865$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.75575222976$ |
| 7.5.3685907.1 |
$x^{7} - x^{6} - x^{5} + 4 x^{4} - 2 x^{3} - 4 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,59\cdot 62473$ |
$2$ |
$8.67117133511$ |
$1919.8716102906465$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.97075418981$ |
| 7.5.3689911.1 |
$x^{7} - 2 x^{6} - x^{5} + 4 x^{4} - 5 x^{3} + 4 x^{2} + x - 1$ |
$7$ |
[5,1] |
$-\,3689911$ |
$1$ |
$8.67251635072$ |
$1920.9141053154876$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$3.94479039759$ |
| 7.5.3872527.1 |
$x^{7} - x^{6} - x^{5} - 3 x^{3} + 3 x^{2} + 3 x - 1$ |
$7$ |
[5,1] |
$-\,3872527$ |
$1$ |
$8.73256978493$ |
$1967.8737256236743$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.13078320811$ |
| 7.5.3929623.1 |
$x^{7} - x^{6} - 4 x^{5} + x^{4} + 6 x^{3} + 2 x^{2} - 3 x - 1$ |
$7$ |
[5,1] |
$-\,47\cdot 83609$ |
$2$ |
$8.75084772594$ |
$1982.3276722075996$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.08862031832$ |
| 7.5.3953927.1 |
$x^{7} - 5 x^{5} + 6 x^{3} - x^{2} - x + 1$ |
$7$ |
[5,1] |
$-\,3953927$ |
$1$ |
$8.75855908048$ |
$1988.448390077047$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.08938885647$ |
| 7.5.3998639.1 |
$x^{7} - x^{6} - 2 x^{5} + 5 x^{4} - 6 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,3998639$ |
$1$ |
$8.77264012534$ |
$1999.6597210525595$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.12564280239$ |
| 7.5.4010959.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + 5 x^{4} - 3 x^{3} - 3 x^{2} + 4 x - 1$ |
$7$ |
[5,1] |
$-\,283\cdot 14173$ |
$2$ |
$8.77649631188$ |
$2002.7378760087402$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.11858259416$ |
| 7.5.4071943.1 |
$x^{7} - x^{6} - 3 x^{5} + 2 x^{4} + x^{3} + x^{2} + x - 1$ |
$7$ |
[5,1] |
$-\,23\cdot 31\cdot 5711$ |
$3$ |
$8.79543623246$ |
$2017.9055973954778$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.16042805733$ |
| 7.5.4080391.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + 6 x^{4} - 3 x^{3} - 2 x^{2} + 4 x - 1$ |
$7$ |
[5,1] |
$-\,7\cdot 17^{2}\cdot 2017$ |
$3$ |
$8.79804074066$ |
$489.9214222709597$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.2691081921$ |
| 7.5.4297259.1 |
$x^{7} - 3 x^{5} - 3 x^{4} + 4 x^{3} + 5 x^{2} - 2 x - 1$ |
$7$ |
[5,1] |
$-\,4297259$ |
$1$ |
$8.86336817826$ |
$2072.983116187877$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.37458722995$ |
| 7.5.4375127.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + 5 x^{4} - x^{3} - 3 x^{2} + 2 x + 1$ |
$7$ |
[5,1] |
$-\,4375127$ |
$1$ |
$8.88613592425$ |
$2091.680424921551$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.46312804437$ |
| 7.5.4438087.1 |
$x^{7} - 4 x^{5} + 2 x^{3} - 4 x^{2} - x + 1$ |
$7$ |
[5,1] |
$-\,4438087$ |
$1$ |
$8.9042921678$ |
$2106.676766853425$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.67927459011$ |
| 7.5.4486007.1 |
$x^{7} - 2 x^{6} - x^{5} + 6 x^{4} - 2 x^{3} - 5 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,463\cdot 9689$ |
$2$ |
$8.91796383253$ |
$2118.0195938659303$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.53218253665$ |
| 7.5.4520279.1 |
$x^{7} - x^{6} - x^{5} + 3 x^{4} - 4 x^{3} - 2 x^{2} + 4 x - 1$ |
$7$ |
[5,1] |
$-\,4520279$ |
$1$ |
$8.92766512477$ |
$2126.094776814994$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.4602670592$ |
| 7.5.4582807.1 |
$x^{7} - 3 x^{5} - x^{4} - x^{3} + 4 x + 1$ |
$7$ |
[5,1] |
$-\,4582807$ |
$1$ |
$8.94520347771$ |
$2140.749167931638$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.55694729688$ |
| 7.5.4734119.1 |
$x^{7} - x^{6} - 3 x^{5} + 3 x^{4} - x^{2} + 3 x - 1$ |
$7$ |
[5,1] |
$-\,13\cdot 53\cdot 6871$ |
$3$ |
$8.98681074259$ |
$2175.8030701329567$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.59274157385$ |
| 7.5.4795631.1 |
$x^{7} - 2 x^{5} - 3 x^{4} - 3 x^{3} + 3 x^{2} + 4 x + 1$ |
$7$ |
[5,1] |
$-\,4795631$ |
$1$ |
$9.00339982847$ |
$2189.8929197565803$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.60229628535$ |
| 7.5.4850543.1 |
$x^{7} - x^{6} - 2 x^{5} + 4 x^{4} - x^{3} - 4 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,4850543$ |
$1$ |
$9.01805559668$ |
$2202.394832903492$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.65273282621$ |
| 7.5.4934959.1 |
$x^{7} - x^{6} - 3 x^{5} + 4 x^{3} + 3 x^{2} - 2 x - 1$ |
$7$ |
[5,1] |
$-\,29\cdot 379\cdot 449$ |
$3$ |
$9.04031085476$ |
$2221.476761075839$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$4.89119546322$ |
| 7.5.5025907.1 |
$x^{7} - x^{6} - 4 x^{5} + 3 x^{4} + 3 x^{3} - 3 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,5025907$ |
$1$ |
$9.06392596951$ |
$2241.8534742484844$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.28149516548$ |
| 7.5.5044607.1 |
$x^{7} - 2 x^{6} - 3 x^{5} + 6 x^{4} + x^{3} - 4 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,5044607$ |
$1$ |
$9.06873606817$ |
$2246.0202581455046$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.09809853663$ |
| 7.5.5280527.1 |
$x^{7} - x^{5} - 3 x^{4} - 3 x^{3} + 5 x^{2} + 3 x - 1$ |
$7$ |
[5,1] |
$-\,7\cdot 353\cdot 2137$ |
$3$ |
$9.12814366723$ |
$2297.9397294098035$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.01412562612$ |
| 7.5.5307751.1 |
$x^{7} - x^{6} - x^{5} - 6 x^{3} - 3 x^{2} + 2 x + 1$ |
$7$ |
[5,1] |
$-\,541\cdot 9811$ |
$2$ |
$9.13485179783$ |
$2303.8556812439447$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.1171814326$ |
| 7.5.5334959.1 |
$x^{7} - 3 x^{5} - 3 x^{4} + x^{3} + 4 x^{2} - 1$ |
$7$ |
[5,1] |
$-\,7\cdot 139\cdot 5483$ |
$3$ |
$9.14152658494$ |
$2309.7530170994473$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.0549250517$ |
| 7.5.5560327.1 |
$x^{7} - 2 x^{6} - 3 x^{5} + 7 x^{4} + x^{3} - 7 x^{2} + x + 1$ |
$7$ |
[5,1] |
$-\,5560327$ |
$1$ |
$9.19572048413$ |
$2358.034562935836$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.39761727392$ |
| 7.5.5615543.1 |
$x^{7} - x^{6} - 3 x^{5} + 5 x^{4} + 2 x^{3} - 6 x^{2} + 1$ |
$7$ |
[5,1] |
$-\,1097\cdot 5119$ |
$2$ |
$9.20871055194$ |
$2369.7136957868984$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.47313675543$ |
| 7.5.5663239.1 |
$x^{7} - x^{6} - 3 x^{5} + 3 x^{3} + 3 x^{2} - x - 1$ |
$7$ |
[5,1] |
$-\,5663239$ |
$1$ |
$9.21984363672$ |
$2379.7560799376056$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.25987060542$ |
| 7.5.5671079.1 |
$x^{7} - 2 x^{6} - x^{5} + x^{3} + 6 x^{2} + x - 1$ |
$7$ |
[5,1] |
$-\,41\cdot 138319$ |
$2$ |
$9.22166593374$ |
$2381.4027378837036$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.45551883952$ |
| 7.5.5679431.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + 7 x^{4} - 6 x^{2} + 1$ |
$7$ |
[5,1] |
$-\,5679431$ |
$1$ |
$9.22360486397$ |
$2383.1556810246366$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.46104998427$ |
| 7.5.5839319.1 |
$x^{7} - 2 x^{6} + 5 x^{4} - 6 x^{3} - 2 x^{2} + 4 x - 1$ |
$7$ |
[5,1] |
$-\,5839319$ |
$1$ |
$9.26025980989$ |
$2416.4682907085703$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.56069074167$ |
| 7.5.5983559.1 |
$x^{7} - x^{5} - x^{4} - 3 x^{3} + 2 x^{2} + 2 x - 1$ |
$7$ |
[5,1] |
$-\,89\cdot 67231$ |
$2$ |
$9.29259655896$ |
$2446.131435552881$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.64583137671$ |
| 7.5.6099227.1 |
$x^{7} - 2 x^{6} - 3 x^{5} + 8 x^{4} + x^{3} - 7 x^{2} + 1$ |
$7$ |
[5,1] |
$-\,6099227$ |
$1$ |
$9.31804859488$ |
$2469.661312811941$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.44371797244$ |
| 7.5.6132103.1 |
$x^{7} - x^{6} - 3 x^{5} - x^{4} + 5 x^{3} + 3 x^{2} - 2 x - 1$ |
$7$ |
[5,1] |
$-\,6132103$ |
$1$ |
$9.32520722679$ |
$2476.3083410593276$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.34965889949$ |
| 7.5.6155647.1 |
$x^{7} - 2 x^{5} - 2 x^{3} + 3 x - 1$ |
$7$ |
[5,1] |
$-\,59\cdot 101\cdot 1033$ |
$3$ |
$9.33031366101$ |
$2481.057637379672$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.79769224013$ |
| 7.5.6202855.1 |
$x^{7} - 2 x^{6} + x^{5} + 4 x^{4} - 8 x^{3} + x^{2} + 3 x - 1$ |
$7$ |
[5,1] |
$-\,5\cdot 53\cdot 89\cdot 263$ |
$4$ |
$9.34050232166$ |
$2490.553151410345$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.76848076927$ |
| 7.5.6365719.1 |
$x^{7} - x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{2} + 1$ |
$7$ |
[5,1] |
$-\,193\cdot 32983$ |
$2$ |
$9.3751496558$ |
$2523.0376533060303$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$5$ |
$5.54232803369$ |
