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 |
7.1.357911.1 |
$x^{7} - x^{6} - x^{5} + x^{4} - x^{3} - x^{2} + 2 x + 1$ |
$7$ |
[1,3] |
$-\,71^{3}$ |
$1$ |
$6.21436038191$ |
$8.426149773176359$ |
|
|
✓ |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$0.604934372036$ |
7.1.3442951.1 |
$x^{7} - x^{6} + x^{5} + 3 x^{3} - x^{2} + 3 x + 1$ |
$7$ |
[1,3] |
$-\,151^{3}$ |
$1$ |
$8.58711468458$ |
$12.288205727444508$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$3.17307455114$ |
7.1.9938375.1 |
$x^{7} - x^{6} + x^{5} + 4 x^{4} - 6 x^{3} + x^{2} + 4 x + 1$ |
$7$ |
[1,3] |
$-\,5^{3}\cdot 43^{3}$ |
$2$ |
$9.99117308862$ |
$14.66287829861518$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$6.00354045392$ |
7.1.11089567.1 |
$x^{7} + x^{5} - 4 x^{4} - x^{3} + 5 x + 1$ |
$7$ |
[1,3] |
$-\,223^{3}$ |
$1$ |
$10.1488391615$ |
$14.933184523068078$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$6.80400936116$ |
7.1.15813251.1 |
$x^{7} + 4 x^{5} - 2 x^{4} + 2 x^{3} - 3 x + 2$ |
$7$ |
[1,3] |
$-\,251^{3}$ |
$1$ |
$10.6765661429$ |
$15.84297951775486$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$13.8070516826$ |
7.1.23639903.1 |
$x^{7} - 2 x^{5} - x^{4} - 2 x^{3} + 6 x + 5$ |
$7$ |
[1,3] |
$-\,7^{3}\cdot 41^{3}$ |
$2$ |
$11.3077957607$ |
$16.941074346097416$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$8.83728427982$ |
7.1.40353607.1 |
$x^{7} + 7 x^{3} - 7 x^{2} + 7 x + 1$ |
$7$ |
[1,3] |
$-\,7^{9}$ |
$1$ |
$12.2054732399$ |
$14.025513436926797$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$15.0397285204$ |
7.1.59776471.1 |
$x^{7} - 2 x^{6} + 6 x^{5} - 8 x^{4} + 14 x^{3} - 10 x^{2} + 9 x - 1$ |
$7$ |
[1,3] |
$-\,17^{3}\cdot 23^{3}$ |
$2$ |
$12.9101977937$ |
$19.77371993328519$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$15.4605552836$ |
7.1.65939264.1 |
$x^{7} - x^{6} - 3 x^{5} + 5 x^{4} - 6 x^{2} + 8 x - 8$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 101^{3}$ |
$2$ |
$13.0924397815$ |
$20.09975124224178$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$91.142994955$ |
7.1.80062991.1 |
$x^{7} - x^{6} - x^{5} - x^{4} + 2 x^{3} - 5 x^{2} + 9 x + 7$ |
$7$ |
[1,3] |
$-\,431^{3}$ |
$1$ |
$13.4605153371$ |
$20.760539492026695$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$14.6806253032$ |
7.1.89314623.1 |
$x^{7} - x^{6} - 3 x^{5} + 6 x^{4} - 15 x^{2} + 20 x - 17$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 149^{3}$ |
$2$ |
$13.6724417361$ |
$21.142374511865974$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$44.0299175572$ |
7.1.99252847.1 |
$x^{7} - 3 x^{6} + 7 x^{5} - 7 x^{4} + 8 x^{3} - 9 x^{2} + 11 x + 1$ |
$7$ |
[1,3] |
$-\,463^{3}$ |
$1$ |
$13.880076294$ |
$21.517434791350013$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$25.5539719224$ |
7.1.101847563.1 |
$x^{7} - 2 x^{6} + x^{5} - x^{4} - 5 x^{2} - 6 x - 4$ |
$7$ |
[1,3] |
$-\,467^{3}$ |
$1$ |
$13.931341839$ |
$21.61018278497431$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$45.6795196525$ |
7.1.115501303.1 |
$x^{7} - 2 x^{6} + 3 x^{5} - 2 x^{4} + 2 x^{3} - 7 x^{2} + 9 x + 5$ |
$7$ |
[1,3] |
$-\,487^{3}$ |
$1$ |
$14.183980523$ |
$22.06807649071391$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$27.8998177498$ |
7.1.127263527.1 |
$x^{7} - x^{6} + 5 x^{5} - x^{4} + 10 x^{3} + 8 x + 1$ |
$7$ |
[1,3] |
$-\,503^{3}$ |
$1$ |
$14.381853176$ |
$22.427661492005804$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$15.5426991436$ |
7.1.133432831.1 |
$x^{7} - x^{5} - 3 x^{4} - 3 x^{3} + 2 x^{2} + 14 x - 7$ |
$7$ |
[1,3] |
$-\,7^{3}\cdot 73^{3}$ |
$2$ |
$14.4794416245$ |
$22.60530911091463$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$31.4514133189$ |
7.1.153130375.1 |
$x^{7} - 2 x^{6} + 4 x^{5} - 7 x^{4} + 5 x^{3} - 11 x^{2} + 20 x - 15$ |
$7$ |
[1,3] |
$-\,5^{3}\cdot 107^{3}$ |
$2$ |
$14.7670749116$ |
$23.130067012440755$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$42.027290106$ |
7.1.153990656.1 |
$x^{7} - 2 x^{6} + 2 x^{5} - x^{3} - 6 x^{2} - 6 x - 4$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 67^{3}$ |
$2$ |
$14.7788980328$ |
$23.15167380558045$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$157.793579751$ |
7.7.192100033.1 |
$x^{7} - 2 x^{6} - 7 x^{5} + 10 x^{4} + 13 x^{3} - 10 x^{2} - x + 1$ |
$7$ |
[7,0] |
$577^{3}$ |
$1$ |
$15.2532034424$ |
$24.020824298928627$ |
|
|
✓ |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$6$ |
$59.674307501$ |
7.1.202262003.1 |
$x^{7} - 3 x^{6} + 9 x^{5} - 11 x^{4} + 7 x^{3} + 3 x^{2} - 6 x - 4$ |
$7$ |
[1,3] |
$-\,587^{3}$ |
$1$ |
$15.3659418823$ |
$24.228082879171435$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$68.8040926063$ |
7.1.211708736.1 |
$x^{7} - 2 x^{6} - 2 x^{4} + x^{3} - 4 x^{2} - 6 x - 4$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 149^{3}$ |
$2$ |
$15.4664718039$ |
$24.413111231467404$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$192.409314715$ |
7.1.331373888.1 |
$x^{7} - x^{6} + 3 x^{5} + 3 x^{4} - 4 x^{3} + 14 x^{2} + 8 x + 8$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 173^{3}$ |
$2$ |
$16.4887725085$ |
$26.30589287593181$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$261.847283422$ |
7.1.347428927.1 |
$x^{7} - 3 x^{6} + 8 x^{5} - 6 x^{4} + 10 x^{2} - 4 x - 5$ |
$7$ |
[1,3] |
$-\,19^{3}\cdot 37^{3}$ |
$2$ |
$16.6005971552$ |
$26.514147167125703$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$46.0711244297$ |
7.1.410172407.1 |
$x^{7} - 2 x^{6} + 5 x^{5} - 12 x^{4} + 10 x^{3} - 11 x^{2} + 13 x + 1$ |
$7$ |
[1,3] |
$-\,743^{3}$ |
$1$ |
$16.9990157911$ |
$27.258026340878022$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$31.3408969598$ |
7.1.525557943.1 |
$x^{7} - 3 x^{6} + 6 x^{5} - 11 x^{4} + 12 x^{3} - 21 x^{2} + 18 x - 27$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 269^{3}$ |
$2$ |
$17.6117674969$ |
$28.407745422683583$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$130.69302626$ |
7.1.533411731.1 |
$x^{7} - x^{6} - 3 x^{5} + 11 x^{4} - 9 x^{3} - 19 x^{2} + 38 x - 36$ |
$7$ |
[1,3] |
$-\,811^{3}$ |
$1$ |
$17.6491267972$ |
$28.478061731796284$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$154.442857538$ |
7.1.565609283.1 |
$x^{7} - 2 x^{6} + 3 x^{5} + x^{4} - 2 x^{3} - 7 x^{2} - 6 x - 4$ |
$7$ |
[1,3] |
$-\,827^{3}$ |
$1$ |
$17.797520592$ |
$28.75760768909681$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$128.022421377$ |
7.1.573856191.1 |
$x^{7} - 2 x^{6} + 8 x^{5} + 4 x^{4} + 11 x^{3} + 28 x^{2} + 22 x + 9$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 277^{3}$ |
$2$ |
$17.8343621627$ |
$28.827070610799147$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$115.4553786$ |
7.1.633839779.1 |
$x^{7} - 3 x^{6} - 2 x^{5} + 13 x^{4} - 11 x^{3} - 6 x^{2} + 28 x - 32$ |
$7$ |
[1,3] |
$-\,859^{3}$ |
$1$ |
$18.089461624$ |
$29.30870177950569$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$171.436557094$ |
7.1.642735647.1 |
$x^{7} - x^{6} - 4 x^{5} + 6 x^{4} + 10 x^{3} - 24 x^{2} + 16 x + 1$ |
$7$ |
[1,3] |
$-\,863^{3}$ |
$1$ |
$18.1255144157$ |
$29.376861643136763$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$40.4319760493$ |
7.1.726572699.1 |
$x^{7} - 2 x^{6} - x^{5} - 3 x^{4} + 2 x^{3} - 3 x^{2} - 6 x - 4$ |
$7$ |
[1,3] |
$-\,29^{3}\cdot 31^{3}$ |
$2$ |
$18.4457794128$ |
$29.9833287011299$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$113.393869738$ |
7.1.817400375.1 |
$x^{7} - x^{6} + 6 x^{5} + 6 x^{3} - 2 x^{2} - 10 x - 5$ |
$7$ |
[1,3] |
$-\,5^{3}\cdot 11^{3}\cdot 17^{3}$ |
$3$ |
$18.7587966726$ |
$30.577769702841312$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$88.689067401$ |
7.7.1027243729.1 |
$x^{7} - x^{6} - 9 x^{5} + 2 x^{4} + 21 x^{3} + x^{2} - 13 x - 1$ |
$7$ |
[7,0] |
$1009^{3}$ |
$1$ |
$19.3812564622$ |
$31.76476034853718$ |
|
|
✓ |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$6$ |
$116.613482444$ |
7.1.1095912791.1 |
$x^{7} - x^{6} + 4 x^{5} - 9 x^{4} + 26 x^{3} - 30 x^{2} + 21 x + 1$ |
$7$ |
[1,3] |
$-\,1031^{3}$ |
$1$ |
$19.5612485262$ |
$32.109188716004645$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$51.2467662148$ |
7.1.1312932375.1 |
$x^{7} - 3 x^{6} + 3 x^{5} + 14 x^{4} - 12 x^{3} - 3 x^{2} + 36 x + 45$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 5^{3}\cdot 73^{3}$ |
$3$ |
$20.0727118899$ |
$33.090784215548595$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$282.926523128$ |
7.1.1375036928.1 |
$x^{7} - 3 x^{6} + 7 x^{5} - 5 x^{4} + 6 x^{3} + 18 x^{2} - 16 x + 32$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 139^{3}$ |
$2$ |
$20.2056804429$ |
$33.34666400106613$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$615.876875074$ |
7.1.1573037747.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + 14 x^{4} - 12 x^{3} - 26 x^{2} + 37 x - 14$ |
$7$ |
[1,3] |
$-\,1163^{3}$ |
$1$ |
$20.5977545075$ |
$34.10278580995987$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$229.372778632$ |
7.1.1605723211.1 |
$x^{7} - 3 x^{6} + 3 x^{5} + 13 x^{4} + 7 x^{3} + 13 x^{2} + 26 x + 12$ |
$7$ |
[1,3] |
$-\,1171^{3}$ |
$1$ |
$20.6583586133$ |
$34.219877264537345$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$306.396393431$ |
7.1.1655595487.1 |
$x^{7} - 3 x^{6} + 2 x^{5} + 6 x^{4} + 3 x^{3} - 16 x^{2} - 7 x - 7$ |
$7$ |
[1,3] |
$-\,7^{3}\cdot 13^{6}$ |
$2$ |
$20.7488228124$ |
$23.84281931849507$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$149.983509716$ |
7.1.1775956931.1 |
$x^{7} - x^{6} + 5 x^{5} + 5 x^{4} + x^{3} + 7 x^{2} + 14 x - 4$ |
$7$ |
[1,3] |
$-\,7^{3}\cdot 173^{3}$ |
$2$ |
$20.9578867831$ |
$34.79942528261063$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$267.072508425$ |
7.1.1829276567.1 |
$x^{7} - 2 x^{6} + 8 x^{5} - 4 x^{4} + 5 x^{3} + 5 x^{2} - 9 x - 5$ |
$7$ |
[1,3] |
$-\,1223^{3}$ |
$1$ |
$21.0466397445$ |
$34.97141690009142$ |
|
|
? |
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$83.5500136252$ |
7.1.2253243231.1 |
$x^{7} - x^{6} + x^{5} + x^{4} - 22 x^{3} - 8 x^{2} + 72 x - 21$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 19^{3}\cdot 23^{3}$ |
$3$ |
$21.6828037624$ |
$36.207733980463345$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$258.682642584$ |
7.1.2379270375.1 |
$x^{7} - 6 x^{5} - 22 x^{4} - 15 x^{3} + 6 x^{2} - 18 x - 27$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 5^{3}\cdot 89^{3}$ |
$3$ |
$21.8520392049$ |
$36.53765181289022$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$408.16364386$ |
7.1.2471326208.1 |
$x^{7} - 2 x^{6} - 2 x^{5} - 4 x^{4} + 3 x^{3} - 2 x^{2} - 6 x - 4$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 13^{6}$ |
$2$ |
$21.9708648976$ |
$25.489046007018146$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$885.346568835$ |
7.1.2537716544.1 |
$x^{7} - 2 x^{6} + 4 x^{5} + 2 x^{4} - 3 x^{3} - 8 x^{2} - 6 x - 4$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 11^{3}\cdot 31^{3}$ |
$3$ |
$22.0542286566$ |
$36.932370625238775$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$785.630721777$ |
7.1.2720547136.1 |
$x^{7} - 2 x^{6} - 4 x^{5} + 6 x^{4} - 11 x^{3} + 12 x^{2} + 66 x + 4$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 349^{3}$ |
$2$ |
$22.2745037073$ |
$37.36308338453881$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$1167.68256098$ |
7.1.2761677827.1 |
$x^{7} - 2 x^{6} + 6 x^{4} + 12 x^{3} - 4 x^{2} - 7 x - 10$ |
$7$ |
[1,3] |
$-\,23^{3}\cdot 61^{3}$ |
$2$ |
$22.3223031529$ |
$37.456641600656084$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$271.968397539$ |
7.1.3080271375.1 |
$x^{7} - x^{6} - 5 x^{5} - 6 x^{4} + 12 x^{3} + 45 x^{2} - 18 x + 27$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 5^{3}\cdot 97^{3}$ |
$3$ |
$22.6731943865$ |
$38.144462245521304$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$476.82120616$ |
7.1.3235225239.1 |
$x^{7} - x^{6} + 2 x^{5} + 16 x^{4} - 36 x^{3} + 78 x^{2} - 72 x + 63$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 17^{3}\cdot 29^{3}$ |
$3$ |
$22.8327272532$ |
$38.45776904605882$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$320.374632693$ |
7.1.3261545587.1 |
$x^{7} - x^{5} - x^{4} + 4 x^{3} - 31 x^{2} + 48 x - 36$ |
$7$ |
[1,3] |
$-\,1483^{3}$ |
$1$ |
$22.8591718881$ |
$38.50973902793941$ |
|
|
|
$D_{7}$ (as 7T2) |
trivial |
$2$ |
$3$ |
$494.383132237$ |