| 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 |
| 7.1.38014691.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + x^{4} + 6 x^{3} - x - 4$ |
$7$ |
[1,3] |
$-\,11^{3}\cdot 13^{4}$ |
$2$ |
$12.1018066303$ |
$18.336871607339905$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$19.6590265751$ |
| 7.1.52706752.1 |
$x^{7} - 2$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 7^{7}$ |
$2$ |
$12.6801312997$ |
$15.985663254345006$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$26.784023199$ |
| 7.1.102942875.1 |
$x^{7} + 7 x^{5} + 14 x^{3} + 7 x - 1$ |
$7$ |
[1,3] |
$-\,5^{3}\cdot 7^{7}$ |
$2$ |
$13.9526472095$ |
$19.732856230043627$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$37.947512794$ |
| 7.1.110270727.1 |
$x^{7} - 3 x^{6} + 3 x^{5} - 3 x^{4} + 3 x^{3} - 3 x^{2} + 10 x - 9$ |
$7$ |
[1,3] |
$-\,3^{8}\cdot 7^{5}$ |
$2$ |
$14.0903860174$ |
$21.898281770364438$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$26.1576797491$ |
| 7.1.112021056.1 |
$x^{7} - x^{6} + 6 x^{5} - 2 x^{4} + 5 x^{3} + 3 x^{2} + x + 5$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{6}\cdot 7^{4}$ |
$3$ |
$14.1221217643$ |
$18.76678006998222$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$42.1075035385$ |
| 7.1.127353499.1 |
$x^{7} - 2 x^{5} - x^{4} + 4 x^{3} + x^{2} - 4 x - 3$ |
$7$ |
[1,3] |
$-\,7^{3}\cdot 13^{5}$ |
$2$ |
$14.3833052498$ |
$22.430303342683025$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$38.2989261447$ |
| 7.1.144027072.1 |
$x^{7} - 2 x^{6} + 6 x^{5} - 12 x^{4} + 18 x^{3} - 18 x^{2} + 10 x - 2$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{8}\cdot 7^{3}$ |
$3$ |
$14.6383463593$ |
$20.7365452398482$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$49.5693539954$ |
| 7.1.155649627.1 |
$x^{7} - 7 x^{4} + 14 x^{3} - 14 x^{2} + 7 x - 2$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 7^{8}$ |
$2$ |
$14.8015388425$ |
$19.26959054025096$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$47.0827252555$ |
| 7.1.157464000.1 |
$x^{7} - 2 x^{6} + 6 x^{5} - 8 x^{4} + 10 x^{3} - 6 x^{2} + 4 x - 2$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{9}\cdot 5^{3}$ |
$3$ |
$14.8260649063$ |
$21.04711600776041$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$64.6471518624$ |
| 7.1.232339968.1 |
$x^{7} - x^{6} + 4 x^{5} - 2 x^{4} + x^{3} + 3 x^{2} - 5 x + 3$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 3^{3}\cdot 7^{5}$ |
$3$ |
$15.6733041255$ |
$24.794421938893013$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$69.0263105047$ |
| 7.1.307546875.1 |
$x^{7} - 2 x^{6} + 6 x^{5} - 5 x^{4} + 10 x^{3} - 6 x^{2} + 7 x + 4$ |
$7$ |
[1,3] |
$-\,3^{9}\cdot 5^{6}$ |
$2$ |
$16.3139362088$ |
$20.64424614758966$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$94.8332463803$ |
| 7.1.368947264.1 |
$x^{7} - 7 x^{3} - 14 x^{2} - 7 x - 8$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 7^{8}$ |
$2$ |
$16.7437234388$ |
$22.250606571175513$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$79.1865523975$ |
| 7.1.419904000.1 |
$x^{7} - 2 x^{6} + 9 x^{5} - 14 x^{4} + 22 x^{3} - 24 x^{2} + 17 x - 4$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 3^{8}\cdot 5^{3}$ |
$3$ |
$17.0560544229$ |
$27.364761579423373$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$93.6182829609$ |
| 7.1.421654016.1 |
$x^{7} + 7 x^{5} + 14 x^{3} + 7 x - 2$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 7^{7}$ |
$2$ |
$17.0661911589$ |
$24.96030817103255$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$88.6349479999$ |
| 7.1.432081216.1 |
$x^{7} - 3 x^{6} + 3 x^{5} + x^{4} + 6 x^{2} + x + 3$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{9}\cdot 7^{3}$ |
$3$ |
$17.1258524536$ |
$27.49545416973504$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$120.125795622$ |
| 7.1.518616000.1 |
$x^{7} - 2 x^{6} - 6 x^{5} + 16 x^{4} + 12 x^{3} - 44 x^{2} - 6 x + 50$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{3}\cdot 5^{3}\cdot 7^{4}$ |
$4$ |
$17.5783451396$ |
$25.672610595571186$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$93.618971134$ |
| 7.1.562166163.1 |
$x^{7} - 3 x^{6} + 6 x^{5} - 8 x^{4} + 12 x^{3} - 15 x^{2} + 10 x - 9$ |
$7$ |
[1,3] |
$-\,3^{9}\cdot 13^{4}$ |
$2$ |
$17.7820026926$ |
$28.72835664269688$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$131.333066838$ |
| 7.1.600362847.1 |
$x^{7} - 3$ |
$7$ |
[1,3] |
$-\,3^{6}\cdot 7^{7}$ |
$2$ |
$17.9497793981$ |
$22.62903452379226$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$116.792117291$ |
| 7.1.626971072.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + 10 x^{4} - 24 x^{3} + 32 x^{2} - 20 x + 12$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 7^{3}\cdot 13^{4}$ |
$3$ |
$18.0613264898$ |
$26.497422592482533$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$106.530170063$ |
| 7.1.641594304.1 |
$x^{7} - x^{6} - x^{5} + 3 x^{4} + 3 x^{3} - 11 x^{2} + 13 x - 3$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{3}\cdot 13^{5}$ |
$3$ |
$18.1209128371$ |
$26.599438245763572$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$91.5807550827$ |
| 7.1.784147392.1 |
$x^{7} - 18$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{6}\cdot 7^{5}$ |
$3$ |
$18.6478275028$ |
$23.509053955343234$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$125.165226426$ |
| 7.1.851324971.1 |
$x^{7} + 7 x^{5} + 14 x^{3} + 7 x - 12$ |
$7$ |
[1,3] |
$-\,7^{5}\cdot 37^{3}$ |
$2$ |
$18.8680887479$ |
$30.785713876666065$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$126.812274833$ |
| 7.1.959570432.1 |
$x^{7} - 2 x^{6} + 5 x^{5} - 4 x^{4} - x^{3} - 34 x^{2} + 11 x - 16$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 37^{4}$ |
$2$ |
$19.1934849613$ |
$31.406013247262095$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$133.627247779$ |
| 7.1.1008189504.1 |
$x^{7} - x^{6} - 3 x^{5} - 3 x^{4} + 12 x^{3} - 9 x + 9$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{8}\cdot 7^{4}$ |
$3$ |
$19.3294862054$ |
$31.66579252742446$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$130.736402927$ |
| 7.1.1012921875.1 |
$x^{7} - 3 x^{6} + 6 x^{5} - 5 x^{4} + 5 x^{3} - 4 x^{2} + 7 x - 4$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$19.3424218143$ |
$25.181202602331524$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$157.562476431$ |
| 7.1.1042568000.1 |
$x^{7} - 3 x^{6} + 9 x^{5} - 9 x^{4} - 10 x^{3} + 24 x^{2} - 19 x + 9$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 5^{3}\cdot 19^{4}$ |
$3$ |
$19.4222986242$ |
$31.843250878551$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$133.913518813$ |
| 7.1.1051652187.1 |
$x^{7} - x^{6} - x^{5} - 6 x^{4} - 9 x^{3} - 8 x^{2} - 5 x - 2$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 79^{4}$ |
$2$ |
$19.4463848184$ |
$31.889327073571355$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$134.551081908$ |
| 7.1.1075648000.1 |
$x^{7} - 3 x^{6} - 2 x^{5} + 22 x^{4} - 32 x^{3} + 16 x^{2} - 8 x + 8$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 5^{3}\cdot 7^{5}$ |
$3$ |
$19.5091611582$ |
$32.00946108272415$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$164.175146404$ |
| 7.1.1091586375.1 |
$x^{7} - 3 x^{6} + 6 x^{5} + 3 x^{4} - 9 x^{3} + 21 x^{2} + 10 x + 3$ |
$7$ |
[1,3] |
$-\,3^{8}\cdot 5^{3}\cdot 11^{3}$ |
$3$ |
$19.5501979029$ |
$32.08802724398451$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$170.691097603$ |
| 7.1.1183786639.1 |
$x^{7} - 2 x^{6} - 3 x^{5} - 2 x^{4} + 12 x^{3} + 18 x^{2} + 17 x + 6$ |
$7$ |
[1,3] |
$-\,7^{4}\cdot 79^{3}$ |
$2$ |
$19.7779793509$ |
$32.52462058307723$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$163.731649915$ |
| 7.1.1259712000.2 |
$x^{7} - x^{6} - 14 x^{4} - 13 x^{3} - 27 x^{2} - 11 x - 7$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 3^{9}\cdot 5^{3}$ |
$3$ |
$19.9544036134$ |
$32.863353450309965$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$218.445679346$ |
| 7.1.1289671744.1 |
$x^{7} - x^{6} - 5 x^{5} + x^{4} + 8 x^{3} + 8 x^{2} + 5 x - 3$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 67^{4}$ |
$2$ |
$20.0215191287$ |
$32.99234594446782$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$173.236075277$ |
| 7.1.1332542016.1 |
$x^{7} - 2 x^{6} + 6 x^{5} - 4 x^{4} + 11 x^{3} + x + 4$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{6}\cdot 13^{4}$ |
$3$ |
$20.1152689894$ |
$28.354368070580524$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$151.117798536$ |
| 7.1.1347491619.1 |
$x^{7} - 3 x^{6} + 9 x^{5} - 14 x^{4} + 9 x^{3} - 18 x^{2} + 3 x - 18$ |
$7$ |
[1,3] |
$-\,3^{8}\cdot 59^{3}$ |
$2$ |
$20.1473536794$ |
$33.23438746299623$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$284.422605026$ |
| 7.1.1423082304.1 |
$x^{7} - 7 x^{5} + 14 x^{3} - 7 x - 4$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{3}\cdot 7^{7}$ |
$3$ |
$20.3050605229$ |
$30.57000942082569$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$172.621872544$ |
| 7.1.1431687488.1 |
$x^{7} - 3 x^{6} + 11 x^{5} - 17 x^{4} + 32 x^{3} - 24 x^{2} + 25 x + 3$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 7^{5}\cdot 11^{3}$ |
$3$ |
$20.3225555112$ |
$33.57180600871921$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$186.507111844$ |
| 7.1.1805076171.1 |
$x^{7} - 3 x^{5} - 6 x^{4} + 6 x^{3} + 12 x^{2} + 3 x - 15$ |
$7$ |
[1,3] |
$-\,3^{6}\cdot 19^{5}$ |
$2$ |
$21.0066357395$ |
$29.8255922505275$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$146.48580351$ |
| 7.1.1809323971.1 |
$x^{7} + 7 x^{5} + 14 x^{3} + 7 x - 3$ |
$7$ |
[1,3] |
$-\,7^{7}\cdot 13^{3}$ |
$2$ |
$21.0136906159$ |
$31.818274607346105$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$198.544357474$ |
| 7.1.1869629888.1 |
$x^{7} - 2 x^{6} - 4 x^{5} - 2 x^{4} + 24 x^{3} + 12 x^{2} + 8 x - 4$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 7^{4}\cdot 23^{3}$ |
$3$ |
$21.1123472439$ |
$31.789838523457124$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$184.102515549$ |
| 7.1.1977326743.1 |
$x^{7} - 14 x^{4} + 7 x^{3} + 28 x^{2} + 21 x + 8$ |
$7$ |
[1,3] |
$-\,7^{11}$ |
$1$ |
$21.2819395728$ |
$26.829842007890413$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$218.073991803$ |
| 7.1.2058557375.1 |
$x^{7} + 10 x^{5} - 7 x^{4} + 24 x^{3} - 35 x^{2} + 29 x - 14$ |
$7$ |
[1,3] |
$-\,5^{3}\cdot 7^{4}\cdot 19^{3}$ |
$3$ |
$21.4046926687$ |
$35.66650020037905$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$227.04513934$ |
| 7.1.2270799427.1 |
$x^{7} - 2 x^{6} + x^{5} + 17 x^{4} - 22 x^{3} - 21 x^{2} + 55 x - 4$ |
$7$ |
[1,3] |
$-\,13^{4}\cdot 43^{3}$ |
$2$ |
$21.7068581381$ |
$36.25460095540845$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$226.218467209$ |
| 7.1.2502175739.1 |
$x^{7} - x^{6} + 7 x^{3} + 21 x^{2} + 7 x + 42$ |
$7$ |
[1,3] |
$-\,7^{5}\cdot 53^{3}$ |
$2$ |
$22.0098371806$ |
$36.8456567103712$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$234.844592555$ |
| 7.1.2623637527.1 |
$x^{7} - 3 x^{6} + 4 x^{5} - 12 x^{4} + 31 x^{3} - 51 x^{2} + 41 x - 25$ |
$7$ |
[1,3] |
$-\,7^{4}\cdot 103^{3}$ |
$2$ |
$22.159384365$ |
$37.13789685454593$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$302.823117431$ |
| 7.1.2767587264.1 |
$x^{7} - x^{6} + 3 x^{5} + 3 x^{4} - 3 x^{3} - 63 x^{2} + 117 x - 63$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{9}\cdot 13^{3}$ |
$3$ |
$22.3291205113$ |
$33.93745482258096$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$310.895485189$ |
| 7.1.2860806592.1 |
$x^{7} - 2 x^{6} + 2 x^{5} + 20 x^{3} - 16 x^{2} + 20 x - 4$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 7^{3}\cdot 19^{4}$ |
$3$ |
$22.4350441367$ |
$34.12535132661735$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$293.742783452$ |
| 7.1.2941328243.1 |
$x^{7} - x^{6} - 8 x^{5} + 6 x^{4} + 20 x^{3} - 22 x^{2} - x + 54$ |
$7$ |
[1,3] |
$-\,7^{4}\cdot 107^{3}$ |
$2$ |
$22.524184208$ |
$37.852152592640216$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$214.985406053$ |
| 7.1.2951578112.1 |
$x^{7} - 14 x^{4} - 7 x^{3} + 14 x^{2} - 7 x - 24$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 7^{8}$ |
$2$ |
$22.5353806016$ |
$31.46710958398432$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$252.979452152$ |
| 7.1.3112538751.1 |
$x^{7} - 3 x^{6} + 10 x^{5} - 10 x^{4} + 3 x^{3} + 25 x^{2} - 67 x + 61$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 7^{5}\cdot 19^{3}$ |
$3$ |
$22.7069734647$ |
$38.21077044890832$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$299.805813873$ |
| 7.1.3116883375.1 |
$x^{7} - x^{6} + 6 x^{4} + 2 x^{3} - 2 x^{2} + 4 x + 3$ |
$7$ |
[1,3] |
$-\,3^{3}\cdot 5^{3}\cdot 31^{4}$ |
$3$ |
$22.7114986772$ |
$38.21965467350533$ |
|
|
✓ |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$120.497934316$ |
