| 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 |
| 7.1.184607.1 |
$x^{7} - x^{6} - x^{5} + x^{4} - x^{2} + x + 1$ |
$7$ |
[1,3] |
$-\,184607$ |
$1$ |
$5.65354907534$ |
$429.65916724771506$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.38044710632$ |
| 7.1.193327.1 |
$x^{7} - x^{6} + 2 x^{4} - 2 x^{3} + 2 x - 1$ |
$7$ |
[1,3] |
$-\,193327$ |
$1$ |
$5.69094835632$ |
$439.68966328536766$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.393017719366$ |
| 7.1.193607.1 |
$x^{7} - x^{4} - x^{3} + x^{2} + 1$ |
$7$ |
[1,3] |
$-\,193607$ |
$1$ |
$5.69212510227$ |
$440.0079544735527$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.393408738575$ |
| 7.1.196127.1 |
$x^{7} - 2 x^{6} + 2 x^{5} - x^{4} + 2 x^{2} - 2 x + 1$ |
$7$ |
[1,3] |
$-\,29\cdot 6763$ |
$2$ |
$5.70265067941$ |
$442.86228107618285$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.396915724261$ |
| 7.1.199559.1 |
$x^{7} - x^{6} + x^{3} - x + 1$ |
$7$ |
[1,3] |
$-\,199559$ |
$1$ |
$5.71680061491$ |
$446.7202704153909$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.401633777334$ |
| 7.1.201671.1 |
$x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 1$ |
$7$ |
[1,3] |
$-\,17\cdot 11863$ |
$2$ |
$5.72540492691$ |
$449.07794423685516$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.404575486366$ |
| 7.1.202471.1 |
$x^{7} - x^{6} - x^{5} + 2 x^{4} - x^{2} + 1$ |
$7$ |
[1,3] |
$-\,202471$ |
$1$ |
$5.72864397615$ |
$449.96777662406004$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.406196645226$ |
| 7.1.207911.1 |
$x^{7} - x^{5} - x^{4} - x^{3} + x^{2} + x + 1$ |
$7$ |
[1,3] |
$-\,11\cdot 41\cdot 461$ |
$3$ |
$5.75038312609$ |
$455.9725868953089$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.413665504587$ |
| 7.1.211831.1 |
$x^{7} - x^{6} + 2 x^{5} - x^{4} + x^{2} - 2 x + 1$ |
$7$ |
[1,3] |
$-\,19\cdot 11149$ |
$2$ |
$5.76574784303$ |
$460.2510184670969$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.418943361216$ |
| 7.1.214607.1 |
$x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} - 1$ |
$7$ |
[1,3] |
$-\,214607$ |
$1$ |
$5.77648183449$ |
$463.2569481400144$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.422976590532$ |
| 7.1.224647.1 |
$x^{7} - 2 x^{5} - x^{4} + 2 x^{3} + 2 x^{2} - 1$ |
$7$ |
[1,3] |
$-\,277\cdot 811$ |
$2$ |
$5.81433551514$ |
$473.96940829551437$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.437537324447$ |
| 7.1.227287.1 |
$x^{7} - 2 x^{6} + 3 x^{5} - 3 x^{4} + 3 x^{3} - 2 x^{2} + 2 x - 1$ |
$7$ |
[1,3] |
$-\,167\cdot 1361$ |
$2$ |
$5.82404795569$ |
$476.7462637504357$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.440973429986$ |
| 7.1.237751.1 |
$x^{7} - x^{6} + x^{5} - x^{4} + x^{3} + x^{2} - 2 x + 1$ |
$7$ |
[1,3] |
$-\,23\cdot 10337$ |
$2$ |
$5.86161755087$ |
$487.597169803107$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.455031505787$ |
| 7.1.242147.1 |
$x^{7} - 2 x^{6} + 2 x^{5} - x^{4} - x^{3} + 2 x^{2} - x + 1$ |
$7$ |
[1,3] |
$-\,242147$ |
$1$ |
$5.87697923351$ |
$492.0843423641927$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.462048944553$ |
| 7.1.242971.1 |
$x^{7} - x^{6} - x^{5} + 2 x^{4} - 2 x^{2} + x + 1$ |
$7$ |
[1,3] |
$-\,242971$ |
$1$ |
$5.87983203622$ |
$492.92088614705705$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.463179955519$ |
| 7.1.250367.1 |
$x^{7} - 2 x^{6} + 4 x^{5} - 4 x^{4} + 3 x^{3} - x^{2} - x + 1$ |
$7$ |
[1,3] |
$-\,13\cdot 19259$ |
$2$ |
$5.90507336826$ |
$500.3668654097711$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.47044808157$ |
| 7.1.252071.1 |
$x^{7} - x^{6} + 2 x^{4} - x^{3} - 2 x^{2} + x + 1$ |
$7$ |
[1,3] |
$-\,83\cdot 3037$ |
$2$ |
$5.91079811742$ |
$502.06672863275855$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.477737923503$ |
| 7.1.261871.1 |
$x^{7} - x^{6} - x^{5} + 2 x^{4} - x^{3} - x^{2} + x - 1$ |
$7$ |
[1,3] |
$-\,307\cdot 853$ |
$2$ |
$5.94309245715$ |
$511.7333289907938$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.486346206108$ |
| 7.1.267347.1 |
$x^{7} - x^{4} - 2 x^{3} + x^{2} + x - 1$ |
$7$ |
[1,3] |
$-\,101\cdot 2647$ |
$2$ |
$5.96068914485$ |
$517.0560898007101$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.494190197375$ |
| 7.1.270607.1 |
$x^{7} - x^{6} + x^{5} - 3 x^{4} + 2 x^{3} - 2 x^{2} + 2 x - 1$ |
$7$ |
[1,3] |
$-\,461\cdot 587$ |
$2$ |
$5.97101871474$ |
$520.199000383507$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.501506225408$ |
| 7.1.272671.1 |
$x^{7} - 2 x^{6} + 3 x^{5} - 4 x^{4} + 4 x^{3} - 3 x^{2} + x - 1$ |
$7$ |
[1,3] |
$-\,7\cdot 38953$ |
$2$ |
$5.97750365205$ |
$522.1790880531314$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.503526635102$ |
| 7.1.283223.1 |
$x^{7} + x^{3} - 2 x - 1$ |
$7$ |
[1,3] |
$-\,61\cdot 4643$ |
$2$ |
$6.01001426292$ |
$532.1869972105669$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.51649446517$ |
| 7.1.286711.1 |
$x^{7} - x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - x - 1$ |
$7$ |
[1,3] |
$-\,286711$ |
$1$ |
$6.02053253858$ |
$535.4540129646989$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.522130800433$ |
| 7.1.289831.1 |
$x^{7} + x^{5} - x^{4} + x^{3} - x^{2} + x - 1$ |
$7$ |
[1,3] |
$-\,109\cdot 2659$ |
$2$ |
$6.02984856129$ |
$538.3595452854904$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.525879627826$ |
| 7.1.289987.1 |
$x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} - x^{2} + x - 1$ |
$7$ |
[1,3] |
$-\,289987$ |
$1$ |
$6.0303121021$ |
$538.5044103811964$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.522561592791$ |
| 7.1.300527.1 |
$x^{7} - 2 x^{6} + 2 x^{5} - 2 x^{3} + 4 x^{2} - 3 x + 1$ |
$7$ |
[1,3] |
$-\,29\cdot 43\cdot 241$ |
$3$ |
$6.06114655535$ |
$548.2034293945999$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.554319459602$ |
| 7.1.311071.1 |
$x^{7} - x^{6} + 3 x^{5} - 3 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ |
$7$ |
[1,3] |
$-\,277\cdot 1123$ |
$2$ |
$6.09107879886$ |
$557.7373934030244$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.551167883255$ |
| 7.1.315631.1 |
$x^{7} - x^{5} - 2 x^{4} + x^{2} + x + 1$ |
$7$ |
[1,3] |
$-\,315631$ |
$1$ |
$6.10375499982$ |
$561.810466260642$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.572829060133$ |
| 7.1.317159.1 |
$x^{7} - 3 x^{6} + 4 x^{5} - 4 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ |
$7$ |
[1,3] |
$-\,317159$ |
$1$ |
$6.10796753424$ |
$563.1687136196399$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.574674996244$ |
| 7.1.319831.1 |
$x^{7} - x^{6} + 2 x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$ |
$7$ |
[1,3] |
$-\,319831$ |
$1$ |
$6.11529232696$ |
$565.5360289141621$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.556553782424$ |
| 7.1.320975.1 |
$x^{7} - x^{6} + x^{5} - x^{4} + 2 x^{2} - 2 x + 1$ |
$7$ |
[1,3] |
$-\,5^{2}\cdot 37\cdot 347$ |
$3$ |
$6.11841236479$ |
$331.31843579389084$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.579234073903$ |
| 7.1.330487.1 |
$x^{7} + x^{5} - x^{3} - x - 1$ |
$7$ |
[1,3] |
$-\,23\cdot 14369$ |
$2$ |
$6.14399177779$ |
$574.879987475647$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.576186901918$ |
| 7.1.332447.1 |
$x^{7} - x^{5} - x^{4} + x^{3} + x^{2} - x - 1$ |
$7$ |
[1,3] |
$-\,332447$ |
$1$ |
$6.14918399759$ |
$576.5821710736467$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.593670022855$ |
| 7.1.334727.1 |
$x^{7} - x^{5} - 2 x^{4} - x^{3} + 2 x^{2} + x + 1$ |
$7$ |
[1,3] |
$-\,334727$ |
$1$ |
$6.15519101525$ |
$578.5559609925388$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.574923274999$ |
| 7.1.338191.1 |
$x^{7} - x^{4} - 2 x^{3} + 2 x + 1$ |
$7$ |
[1,3] |
$-\,7\cdot 48313$ |
$2$ |
$6.16425068742$ |
$581.5419159441561$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.58504050247$ |
| 7.1.349847.1 |
$x^{7} - x^{6} + x^{5} - x^{4} + x^{2} - x + 1$ |
$7$ |
[1,3] |
$-\,19\cdot 18413$ |
$2$ |
$6.1941624833$ |
$591.4786555743157$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.59590218239$ |
| 7.1.351587.1 |
$x^{7} - 2 x^{5} - 2 x^{4} + 2 x^{3} + 3 x^{2} - 1$ |
$7$ |
[1,3] |
$-\,351587$ |
$1$ |
$6.19855417442$ |
$592.9477211356833$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.638803050262$ |
| 7.1.351655.1 |
$x^{7} - x^{6} - 2 x^{4} + x^{3} + x + 1$ |
$7$ |
[1,3] |
$-\,5\cdot 53\cdot 1327$ |
$3$ |
$6.19872542517$ |
$593.0050590003427$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.616197560931$ |
| 7.1.364871.1 |
$x^{7} - x^{6} + 2 x^{4} + 2 x + 1$ |
$7$ |
[1,3] |
$-\,13^{2}\cdot 17\cdot 127$ |
$3$ |
$6.23148186231$ |
$167.5320864789787$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.631311355925$ |
| 7.1.371131.1 |
$x^{7} - x^{4} - 2 x^{2} - x - 1$ |
$7$ |
[1,3] |
$-\,371131$ |
$1$ |
$6.24664387708$ |
$609.2052199382405$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.662365609841$ |
| 7.1.373607.1 |
$x^{7} - x^{6} + x^{5} - 2 x^{3} + 3 x^{2} - 2 x + 1$ |
$7$ |
[1,3] |
$-\,13\cdot 29\cdot 991$ |
$3$ |
$6.25258042141$ |
$611.2339977455442$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.641053178539$ |
| 7.1.376163.1 |
$x^{7} - x^{6} - x^{4} - x^{3} + x^{2} + x + 1$ |
$7$ |
[1,3] |
$-\,389\cdot 967$ |
$2$ |
$6.25867350642$ |
$613.3212861135671$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.668307729133$ |
| 7.1.380831.1 |
$x^{7} - x^{5} - x^{4} - x^{3} + 2 x + 1$ |
$7$ |
[1,3] |
$-\,11\cdot 89\cdot 389$ |
$3$ |
$6.26971024638$ |
$617.1150622047724$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.63105320574$ |
| 7.1.382631.1 |
$x^{7} - x^{5} + x^{3} - x - 1$ |
$7$ |
[1,3] |
$-\,382631$ |
$1$ |
$6.2739350993$ |
$618.5717419992608$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.633168351139$ |
| 7.1.383687.1 |
$x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + x^{3} - x + 1$ |
$7$ |
[1,3] |
$-\,31\cdot 12377$ |
$2$ |
$6.27640575735$ |
$619.4247331193678$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.652352405095$ |
| 7.1.396259.1 |
$x^{7} - x^{4} - x^{3} + x + 1$ |
$7$ |
[1,3] |
$-\,396259$ |
$1$ |
$6.30538059113$ |
$629.491064273354$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.644452230084$ |
| 7.1.397703.1 |
$x^{7} + x^{5} + x^{3} - 2 x^{2} + x - 1$ |
$7$ |
[1,3] |
$-\,499\cdot 797$ |
$2$ |
$6.30865795045$ |
$630.6369795690703$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.658575476914$ |
| 7.1.397991.1 |
$x^{7} - 2 x^{5} + 3 x^{3} - x^{2} - x + 1$ |
$7$ |
[1,3] |
$-\,11\cdot 97\cdot 373$ |
$3$ |
$6.3093103863$ |
$630.8652788036444$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.649296920624$ |
| 7.1.402011.1 |
$x^{7} - x^{6} + 2 x^{5} - 4 x^{4} + 3 x^{3} - 3 x^{2} + 2 x - 1$ |
$7$ |
[1,3] |
$-\,73\cdot 5507$ |
$2$ |
$6.31837531276$ |
$634.0433739106497$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.698068206909$ |
| 7.1.409091.1 |
$x^{7} - x^{5} + 2 x^{3} - 2 x - 1$ |
$7$ |
[1,3] |
$-\,313\cdot 1307$ |
$2$ |
$6.33415316462$ |
$639.6022201337328$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$0.709061461966$ |
