| 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 |
| 7.7.20134393.1 |
$x^{7} - x^{6} - 6 x^{5} + 4 x^{4} + 10 x^{3} - 4 x^{2} - 4 x + 1$ |
$7$ |
[7,0] |
$71\cdot 283583$ |
$2$ |
$11.0514634477$ |
$4487.136391954227$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$14.4469325697$ |
| 7.7.25164057.1 |
$x^{7} - 2 x^{6} - 5 x^{5} + 9 x^{4} + 7 x^{3} - 10 x^{2} - 2 x + 1$ |
$7$ |
[7,0] |
$3\cdot 8388019$ |
$2$ |
$11.4091786362$ |
$5016.378873251102$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$19.80915144$ |
| 7.7.25367689.1 |
$x^{7} - x^{6} - 6 x^{5} + 4 x^{4} + 9 x^{3} - 4 x^{2} - 3 x + 1$ |
$7$ |
[7,0] |
$17\cdot 23\cdot 64879$ |
$3$ |
$11.4223224213$ |
$5036.634689949233$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$16.0058631711$ |
| 7.7.28118369.1 |
$x^{7} - 2 x^{6} - 5 x^{5} + 9 x^{4} + 7 x^{3} - 9 x^{2} - 3 x + 1$ |
$7$ |
[7,0] |
$28118369$ |
$1$ |
$11.5915482299$ |
$5302.675645369986$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$18.1278435397$ |
| 7.7.30653489.1 |
$x^{7} - 7 x^{5} - x^{4} + 11 x^{3} + 3 x^{2} - 3 x - 1$ |
$7$ |
[7,0] |
$1399\cdot 21911$ |
$2$ |
$11.7353792853$ |
$5536.559310618825$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$22.422780934$ |
| 7.7.31056073.1 |
$x^{7} - 3 x^{6} - 3 x^{5} + 11 x^{4} + x^{3} - 9 x^{2} + 1$ |
$7$ |
[7,0] |
$1489\cdot 20857$ |
$2$ |
$11.7572742433$ |
$5572.7975918743$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$19.190933431$ |
| 7.7.32354821.1 |
$x^{7} - 2 x^{6} - 5 x^{5} + 9 x^{4} + 6 x^{3} - 8 x^{2} - x + 1$ |
$7$ |
[7,0] |
$32354821$ |
$1$ |
$11.8262873961$ |
$5688.129833258028$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$21.2315696453$ |
| 7.7.32567681.1 |
$x^{7} - 7 x^{5} - 2 x^{4} + 10 x^{3} + 3 x^{2} - 3 x - 1$ |
$7$ |
[7,0] |
$89\cdot 365929$ |
$2$ |
$11.8373710813$ |
$5706.810054662762$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$19.5076733229$ |
| 7.7.34554953.1 |
$x^{7} - 2 x^{6} - 5 x^{5} + 9 x^{4} + 5 x^{3} - 8 x^{2} + 1$ |
$7$ |
[7,0] |
$34554953$ |
$1$ |
$11.9379579223$ |
$5878.3461109397085$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$20.3078549372$ |
| 7.7.35269513.1 |
$x^{7} - 2 x^{6} - 5 x^{5} + 10 x^{4} + 5 x^{3} - 10 x^{2} - x + 1$ |
$7$ |
[7,0] |
$35269513$ |
$1$ |
$11.9729156611$ |
$5938.8141072102935$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$20.4079688742$ |
| 7.7.39610073.1 |
$x^{7} - x^{6} - 7 x^{5} + 3 x^{4} + 10 x^{3} - 3 x^{2} - 3 x + 1$ |
$7$ |
[7,0] |
$89\cdot 599\cdot 743$ |
$3$ |
$12.1730892485$ |
$6293.653390519691$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$23.8192994162$ |
| 7.7.39829313.1 |
$x^{7} - x^{6} - 7 x^{5} + 5 x^{4} + 13 x^{3} - 5 x^{2} - 6 x - 1$ |
$7$ |
[7,0] |
$373\cdot 106781$ |
$2$ |
$12.1826918525$ |
$6311.046902059911$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$26.2499084846$ |
| 7.7.41153941.1 |
$x^{7} - x^{6} - 7 x^{5} + 5 x^{4} + 13 x^{3} - 6 x^{2} - 7 x + 1$ |
$7$ |
[7,0] |
$41153941$ |
$1$ |
$12.2397644915$ |
$6415.133747631456$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$24.5578304012$ |
| 7.7.41455873.1 |
$x^{7} - 8 x^{5} - x^{4} + 19 x^{3} + 5 x^{2} - 12 x - 5$ |
$7$ |
[7,0] |
$37\cdot 1120429$ |
$2$ |
$12.2525527448$ |
$6438.623533023188$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$24.3431741014$ |
| 7.7.41783473.1 |
$x^{7} - 7 x^{5} - x^{4} + 13 x^{3} + 4 x^{2} - 4 x - 1$ |
$7$ |
[7,0] |
$4639\cdot 9007$ |
$2$ |
$12.2663381715$ |
$6464.013691198372$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$23.5815656478$ |
| 7.7.42855577.1 |
$x^{7} - x^{6} - 7 x^{5} + 3 x^{4} + 14 x^{3} + 2 x^{2} - 4 x - 1$ |
$7$ |
[7,0] |
$197\cdot 211\cdot 1031$ |
$3$ |
$12.310813832$ |
$6546.417111672613$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$23.0470162908$ |
| 7.7.43242544.1 |
$x^{7} - x^{6} - 7 x^{5} + 4 x^{4} + 15 x^{3} - 2 x^{2} - 8 x - 1$ |
$7$ |
[7,0] |
$2^{4}\cdot 101\cdot 26759$ |
$3$ |
$12.3266328958$ |
$4649.867955114424$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$26.0668946854$ |
| 7.7.43723857.1 |
$x^{7} - x^{6} - 7 x^{5} + 7 x^{4} + 12 x^{3} - 10 x^{2} - 6 x + 3$ |
$7$ |
[7,0] |
$3\cdot 31\cdot 470149$ |
$3$ |
$12.3461403397$ |
$6612.401757304225$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$27.8918524098$ |
| 7.7.46643776.1 |
$x^{7} - x^{6} - 7 x^{5} + 3 x^{4} + 13 x^{3} - x^{2} - 5 x - 1$ |
$7$ |
[7,0] |
$2^{6}\cdot 728809$ |
$2$ |
$12.4606861444$ |
$1546.4382179402714$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$37.1660747556$ |
| 7.7.49960857.1 |
$x^{7} - 7 x^{5} + 13 x^{3} - 5 x - 1$ |
$7$ |
[7,0] |
$3\cdot 16653619$ |
$2$ |
$12.5835815647$ |
$7068.299441874262$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$30.5453900289$ |
| 7.7.52011969.1 |
$x^{7} - 3 x^{6} - 3 x^{5} + 13 x^{4} - x^{3} - 13 x^{2} + 4 x + 1$ |
$7$ |
[7,0] |
$3\cdot 251\cdot 69073$ |
$3$ |
$12.6561166996$ |
$7211.932404009344$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$31.2216706257$ |
| 7.7.55073801.1 |
$x^{7} - 2 x^{6} - 6 x^{5} + 8 x^{4} + 8 x^{3} - 6 x^{2} - 3 x + 1$ |
$7$ |
[7,0] |
$47\cdot 1171783$ |
$2$ |
$12.7599594136$ |
$7421.172481488353$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$27.3388336938$ |
| 7.7.55078981.1 |
$x^{7} - x^{6} - 7 x^{5} + 2 x^{4} + 12 x^{3} - 5 x - 1$ |
$7$ |
[7,0] |
$55078981$ |
$1$ |
$12.7601308561$ |
$7421.521474738182$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$25.8498011328$ |
| 7.7.55311169.1 |
$x^{7} - x^{6} - 7 x^{5} + 8 x^{4} + 10 x^{3} - 11 x^{2} - 2 x + 1$ |
$7$ |
[7,0] |
$313\cdot 176713$ |
$2$ |
$12.7678014267$ |
$7437.147907632334$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$27.523108497$ |
| 7.7.57936017.1 |
$x^{7} - x^{6} - 7 x^{5} + 6 x^{4} + 11 x^{3} - 5 x^{2} - 3 x + 1$ |
$7$ |
[7,0] |
$17\cdot 3408001$ |
$2$ |
$12.8526494383$ |
$7611.571256974476$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$33.0010824904$ |
| 7.7.58355513.1 |
$x^{7} - 2 x^{6} - 5 x^{5} + 9 x^{4} + 5 x^{3} - 7 x^{2} - x + 1$ |
$7$ |
[7,0] |
$563\cdot 103651$ |
$2$ |
$12.8659029225$ |
$7639.078020284909$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$28.607795478$ |
| 7.7.61136809.1 |
$x^{7} - 7 x^{5} - 2 x^{4} + 12 x^{3} + 5 x^{2} - 3 x - 1$ |
$7$ |
[7,0] |
$397\cdot 153997$ |
$2$ |
$12.9517653244$ |
$7819.003069445618$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$31.3038798767$ |
| 7.7.63128113.1 |
$x^{7} - 2 x^{6} - 5 x^{5} + 8 x^{4} + 6 x^{3} - 7 x^{2} - x + 1$ |
$7$ |
[7,0] |
$109\cdot 269\cdot 2153$ |
$3$ |
$13.0112057326$ |
$7945.32019493236$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$28.558636017$ |
| 7.7.65698681.1 |
$x^{7} - x^{6} - 8 x^{5} + x^{4} + 12 x^{3} - x^{2} - 4 x + 1$ |
$7$ |
[7,0] |
$3359\cdot 19559$ |
$2$ |
$13.0856050182$ |
$8105.472287288385$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$31.5015984005$ |
| 7.7.65845693.1 |
$x^{7} - 7 x^{5} - 2 x^{4} + 11 x^{3} + 3 x^{2} - 4 x - 1$ |
$7$ |
[7,0] |
$5939\cdot 11087$ |
$2$ |
$13.0897840511$ |
$8114.535907863123$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$31.6897432475$ |
| 7.7.67159593.1 |
$x^{7} - 3 x^{6} - 3 x^{5} + 11 x^{4} + 2 x^{3} - 10 x^{2} + 1$ |
$7$ |
[7,0] |
$3^{2}\cdot 43\cdot 173539$ |
$3$ |
$13.1267826285$ |
$4731.440689684274$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$30.693097893$ |
| 7.7.68249369.1 |
$x^{7} - x^{6} - 7 x^{5} + 2 x^{4} + 12 x^{3} + x^{2} - 4 x - 1$ |
$7$ |
[7,0] |
$109\cdot 293\cdot 2137$ |
$3$ |
$13.1570022402$ |
$8261.31763098357$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$37.8375333914$ |
| 7.7.69012929.1 |
$x^{7} - 2 x^{6} - 6 x^{5} + 8 x^{4} + 11 x^{3} - 6 x^{2} - 6 x - 1$ |
$7$ |
[7,0] |
$619\cdot 111491$ |
$2$ |
$13.1779303721$ |
$8307.402060812996$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$30.3025371273$ |
| 7.7.69678137.1 |
$x^{7} - 3 x^{6} - 3 x^{5} + 13 x^{4} - 2 x^{3} - 9 x^{2} + x + 1$ |
$7$ |
[7,0] |
$191\cdot 601\cdot 607$ |
$3$ |
$13.1960016591$ |
$8347.343110235735$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$31.311727765$ |
| 7.7.69836041.1 |
$x^{7} - 3 x^{6} - 4 x^{5} + 16 x^{4} - 20 x^{2} + 8 x + 1$ |
$7$ |
[7,0] |
$11\cdot 577\cdot 11003$ |
$3$ |
$13.2002696109$ |
$8356.796096591086$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$29.5970336067$ |
| 7.7.70244521.1 |
$x^{7} - 7 x^{5} - x^{4} + 13 x^{3} + 2 x^{2} - 6 x - 1$ |
$7$ |
[7,0] |
$41\cdot 1713281$ |
$2$ |
$13.211272072$ |
$8381.20045100939$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$32.5855580427$ |
| 7.7.75602713.1 |
$x^{7} - 2 x^{6} - 6 x^{5} + 10 x^{4} + 9 x^{3} - 13 x^{2} - x + 1$ |
$7$ |
[7,0] |
$1409\cdot 53657$ |
$2$ |
$13.3507400545$ |
$8694.98205863589$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$35.1504873982$ |
| 7.7.75630121.1 |
$x^{7} - x^{6} - 8 x^{5} + 9 x^{4} + 16 x^{3} - 18 x^{2} - 7 x + 7$ |
$7$ |
[7,0] |
$7\cdot 263\cdot 41081$ |
$3$ |
$13.3514313756$ |
$8696.557997276854$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$35.0401108502$ |
| 7.7.77004029.1 |
$x^{7} - x^{6} - 7 x^{5} + 4 x^{4} + 15 x^{3} - 2 x^{2} - 9 x - 2$ |
$7$ |
[7,0] |
$77004029$ |
$1$ |
$13.3858137645$ |
$8775.193957970389$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$51.589527101$ |
| 7.7.78373945.1 |
$x^{7} - x^{6} - 7 x^{5} + 3 x^{4} + 13 x^{3} + x^{2} - 4 x - 1$ |
$7$ |
[7,0] |
$5\cdot 13\cdot 1205753$ |
$3$ |
$13.4195766538$ |
$8852.906020059176$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$34.6446938558$ |
| 7.7.78534833.1 |
$x^{7} - x^{6} - 7 x^{5} + 5 x^{4} + 14 x^{3} - 4 x^{2} - 8 x - 1$ |
$7$ |
[7,0] |
$13\cdot 211\cdot 28631$ |
$3$ |
$13.4235086307$ |
$8861.9880952301$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$31.869429564$ |
| 7.7.79044293.1 |
$x^{7} - 2 x^{6} - 5 x^{5} + 8 x^{4} + 7 x^{3} - 7 x^{2} - 2 x + 1$ |
$7$ |
[7,0] |
$109^{2}\cdot 6653$ |
$2$ |
$13.435914052$ |
$1861.200213516652$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$34.9501779702$ |
| 7.7.79397476.1 |
$x^{7} - 3 x^{6} - 3 x^{5} + 13 x^{4} - x^{3} - 12 x^{2} + 2 x + 2$ |
$7$ |
[7,0] |
$2^{2}\cdot 29\cdot 47\cdot 14563$ |
$4$ |
$13.4444739444$ |
$7072.289280032421$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$51.3778536518$ |
| 7.7.79438057.1 |
$x^{7} - 8 x^{5} - 4 x^{4} + 10 x^{3} + 4 x^{2} - 3 x - 1$ |
$7$ |
[7,0] |
$613\cdot 129589$ |
$2$ |
$13.4454553911$ |
$8912.802982227307$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$34.3226649757$ |
| 7.7.80750473.1 |
$x^{7} - x^{6} - 7 x^{5} + 6 x^{4} + 9 x^{3} - 5 x^{2} - 3 x + 1$ |
$7$ |
[7,0] |
$80750473$ |
$1$ |
$13.4769666466$ |
$8986.12669619119$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$31.219142469$ |
| 7.7.81323773.1 |
$x^{7} - 3 x^{6} - 3 x^{5} + 12 x^{4} + x^{3} - 12 x^{2} + x + 2$ |
$7$ |
[7,0] |
$81323773$ |
$1$ |
$13.4905940569$ |
$9017.969449937164$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$52.481260067$ |
| 7.7.81437164.1 |
$x^{7} - 7 x^{5} - x^{4} + 12 x^{3} + 2 x^{2} - 4 x - 1$ |
$7$ |
[7,0] |
$2^{2}\cdot 1787\cdot 11393$ |
$3$ |
$13.4932796161$ |
$9024.254207412378$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$52.1624717732$ |
| 7.7.82916101.1 |
$x^{7} - 2 x^{6} - 6 x^{5} + 8 x^{4} + 12 x^{3} - 7 x^{2} - 6 x + 1$ |
$7$ |
[7,0] |
$73\cdot 1135837$ |
$2$ |
$13.5280165081$ |
$9105.827859124067$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$38.9613867782$ |
| 7.7.83266101.1 |
$x^{7} - 8 x^{5} - x^{4} + 18 x^{3} + 5 x^{2} - 10 x - 4$ |
$7$ |
[7,0] |
$3^{2}\cdot 359\cdot 25771$ |
$3$ |
$13.5361594424$ |
$5268.336264894259$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$38.4291482784$ |
| 7.7.83934569.1 |
$x^{7} - 8 x^{5} + 19 x^{3} - x^{2} - 13 x + 1$ |
$7$ |
[7,0] |
$83934569$ |
$1$ |
$13.5516305145$ |
$9161.581140829348$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$6$ |
$35.9249048252$ |
