Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
10.2.4165509529.1 |
x10 - x9 - x8 + 3x7 - 2x6 - x5 + 3x4 - x2 - x + 1 |
$10$ |
[2,4] |
$1609^{3}$ |
$$ |
$9.16150479476$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$4.78851392314$ |
10.2.4483962449.1 |
x10 - x7 - x5 + x4 - 2x3 + x2 - x + 1 |
$10$ |
[2,4] |
$17^{3}\cdot 97^{3}$ |
$$ |
$9.22924546222$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$5.90538181209$ |
10.2.5441006848.2 |
x10 - x8 - 4x7 + 2x6 - 2x5 + 4x4 - 4x3 + x2 - 2x + 1 |
$10$ |
[2,4] |
$2^{8}\cdot 277^{3}$ |
$$ |
$9.40952991361$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$6.62426511052$ |
10.2.5611284433.1 |
x10 - x9 + x8 - 2x7 + x6 + x5 - 4x4 + 3x3 - 2x + 1 |
$10$ |
[2,4] |
$1777^{3}$ |
$$ |
$9.43857059288$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$5.80208478511$ |
10.2.10882188544.1 |
x10 - x8 - 2x7 - 2x6 - 4x5 + 2x3 + x2 + 1 |
$10$ |
[2,4] |
$2^{8}\cdot 349^{3}$ |
$$ |
$10.0849006602$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$9.09322598856$ |
10.2.12119452073.2 |
x10 - x9 + x8 - x6 - x5 + x3 - x2 - x + 1 |
$10$ |
[2,4] |
$2297^{3}$ |
$$ |
$10.1940861283$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$10.5649221834$ |
10.2.17923019113.1 |
x10 - x9 - 4x7 + 2x6 + 2x5 + x4 - x3 - 2x + 1 |
$10$ |
[2,4] |
$2617^{3}$ |
$$ |
$10.6008604331$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$9.83053678535$ |
10.2.18927429625.1 |
x10 - x9 - x8 + 2x7 - 3x6 - x5 + 4x4 - x3 + x2 - x + 1 |
$10$ |
[2,4] |
$5^{3}\cdot 13^{3}\cdot 41^{3}$ |
$$ |
$10.6588208799$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$11.5338423415$ |
10.2.23615200909.3 |
x10 + x8 - x6 - 2x5 - x4 - x3 + 1 |
$10$ |
[2,4] |
$19^{3}\cdot 151^{3}$ |
$$ |
$10.8973064585$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$22.3279296286$ |
10.2.25080878336.1 |
x10 - x9 - x8 + 2x7 + 3x6 + 3x5 - 5x4 - 12x3 - 11x2 - 5x - 1 |
$10$ |
[2,4] |
$2^{8}\cdot 461^{3}$ |
$$ |
$10.9631226838$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$18.76633546$ |
10.2.27461605913.1 |
x10 - x7 - x6 - 2x5 + x + 1 |
$10$ |
[2,4] |
$7^{3}\cdot 431^{3}$ |
$$ |
$11.0629918653$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$17.7848312304$ |
10.2.29474993969.1 |
x10 - x9 - 2x8 + 4x7 - 4x6 - 2x5 + 7x4 - x3 - 2x2 + 1 |
$10$ |
[2,4] |
$3089^{3}$ |
$$ |
$11.1415438144$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$14.0762389296$ |
10.2.33608047921.1 |
x10 - 3x8 + 2x6 - 2x5 + 5x4 + 4x3 - 3x2 - 4x - 1 |
$10$ |
[2,4] |
$7^{4}\cdot 241^{3}$ |
$$ |
$11.2887103211$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$18.676897024$ |
10.2.33792250337.1 |
x10 - x7 + x6 - 2x5 - x + 1 |
$10$ |
[2,4] |
$53^{3}\cdot 61^{3}$ |
$$ |
$11.2948823451$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$18.5117480209$ |
10.2.38238692409.1 |
x10 - x9 + x8 - 3x7 - x5 + 3x4 - 2x3 - x2 - x + 1 |
$10$ |
[2,4] |
$3^{3}\cdot 1123^{3}$ |
$$ |
$11.4353721644$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$20.6325121629$ |
10.2.54470700288.2 |
x10 - 2x6 - 4x3 + 4x2 - 4x + 4 |
$10$ |
[2,4] |
$2^{8}\cdot 3^{3}\cdot 199^{3}$ |
$$ |
$11.8472157061$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$33.313495222$ |
10.2.56409309184.1 |
x10 - x9 + 2x8 - 7x7 + 3x6 + 2x5 - 7x4 + 5x3 - 3x + 1 |
$10$ |
[2,4] |
$2^{14}\cdot 151^{3}$ |
$$ |
$11.8887194342$ |
|
|
|
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$45.5221642912$ |
10.2.57378463793.1 |
x10 - x9 + x8 - 2x7 + x6 - 3x5 + x3 + x2 + x + 1 |
$10$ |
[2,4] |
$7^{3}\cdot 19^{3}\cdot 29^{3}$ |
$$ |
$11.9089889327$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$24.9742948243$ |
10.2.58818484369.1 |
x10 - x9 - x8 + 2x7 - 3x6 - x5 + 2x4 - x3 + 1 |
$10$ |
[2,4] |
$3889^{3}$ |
$$ |
$11.9385445106$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$19.5377117302$ |
10.2.58968677632.1 |
x10 - 2x9 + 2x8 - 2x7 + 4x5 - 8x4 + 4x3 + 4x2 - 8x + 4 |
$10$ |
[2,4] |
$2^{8}\cdot 613^{3}$ |
$$ |
$11.9415895259$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$27.5601543374$ |
10.2.59501707264.1 |
x10 - 4x9 + 5x8 - 6x6 + 4x5 + 5x2 - 1 |
$10$ |
[2,4] |
$2^{18}\cdot 61^{3}$ |
$$ |
$11.9523401094$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$61.2859856522$ |
10.2.59897527569.1 |
x10 - x9 - x8 - x7 + 6x6 + 5x5 - 3x4 - 4x3 + x2 + 5x - 1 |
$10$ |
[2,4] |
$3^{8}\cdot 11^{3}\cdot 19^{3}$ |
$$ |
$11.9602674047$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$26.7498676466$ |
10.2.66331758592.2 |
x10 - x9 - 2x8 + x7 - 5x6 - 2x5 + 5x4 - 3x3 + x + 1 |
$10$ |
[2,4] |
$2^{12}\cdot 11^{3}\cdot 23^{3}$ |
$$ |
$12.0829269856$ |
|
|
|
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$36.4949128117$ |
10.2.72459558809.1 |
x10 - 2x9 - 2x8 + 7x7 - 3x6 - 6x5 + 4x4 - 2x3 + 4x2 - x + 1 |
$10$ |
[2,4] |
$11^{3}\cdot 379^{3}$ |
$$ |
$12.1901645645$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$25.8765661644$ |
10.4.72758649087.1 |
x10 - x9 + 3x8 - 6x7 - 3x6 - 3x5 - 6x4 + 3x3 + 2x + 1 |
$10$ |
[4,3] |
$-\,3^{8}\cdot 223^{3}$ |
$$ |
$12.1951869594$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$6$ |
$30.6901611785$ |
10.4.74515853627.1 |
x10 - 2x9 + 2x8 - x7 - 5x6 + 3x5 - 3x4 + x3 + 7x2 + 4x + 1 |
$10$ |
[4,3] |
$-\,19^{4}\cdot 83^{3}$ |
$$ |
$12.2243244486$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$6$ |
$55.1347630923$ |
10.2.75049519552.1 |
x10 - x9 - 2x8 - 3x7 - 2x6 + 4x4 + x3 + 3x2 - 2x - 1 |
$10$ |
[2,4] |
$2^{6}\cdot 7^{3}\cdot 43^{4}$ |
$$ |
$12.2330511495$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$46.5119692301$ |
10.2.77363231581.1 |
x10 + 2x8 - 4x7 - 2x6 - 2x5 + 4x4 - 2x3 - 2x + 1 |
$10$ |
[2,4] |
$4261^{3}$ |
$$ |
$12.2702513821$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$30.0397475333$ |
10.2.79433915648.1 |
x10 + x8 - 4x7 + 4x6 - 2x5 - 6x4 + 4x3 - x2 - 2x + 1 |
$10$ |
[2,4] |
$2^{8}\cdot 677^{3}$ |
$$ |
$12.3027046238$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$34.3199517734$ |
10.2.85707789929.1 |
x10 - 2x8 - x7 - 2x6 + x5 + 3x4 - 2x3 - x2 + x + 1 |
$10$ |
[2,4] |
$4409^{3}$ |
$$ |
$12.3965840598$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$24.4605225553$ |
10.2.86175179713.1 |
x10 - 2x9 + 2x8 + x7 - 3x6 - 2x5 - 2x4 - 2x2 - x + 1 |
$10$ |
[2,4] |
$7^{3}\cdot 631^{3}$ |
$$ |
$12.4033277492$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$27.5240171192$ |
10.2.86879445589.1 |
x10 - 2x9 + x8 - 2x7 + 4x6 - 5x5 + x4 - 2x3 + x2 + x + 1 |
$10$ |
[2,4] |
$43^{3}\cdot 103^{3}$ |
$$ |
$12.4134272708$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$33.1655845358$ |
10.2.89734879333.1 |
x10 - x9 - x8 + 2x7 - x6 - 3x5 + 2x4 + x2 + 1 |
$10$ |
[2,4] |
$11^{6}\cdot 37^{3}$ |
$$ |
$12.4536348668$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$35.9216147033$ |
10.4.91794884831.1 |
x10 - x9 + 4x7 - 2x6 - 2x5 - x4 + x3 - 2x + 1 |
$10$ |
[4,3] |
$-\,13^{3}\cdot 347^{3}$ |
$$ |
$12.4819330306$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$6$ |
$36.1853120565$ |
10.2.94134281149.2 |
x10 - 2x9 + 2x8 - 3x7 - 3x6 + 4x5 + x4 - x2 - 2x + 1 |
$10$ |
[2,4] |
$4549^{3}$ |
$$ |
$12.51338426$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$44.7397967292$ |
10.2.97145684173.2 |
x10 - x9 + x8 - 6x7 + x6 + x5 + 6x4 - 2x3 - x2 - 2x + 1 |
$10$ |
[2,4] |
$4597^{3}$ |
$$ |
$12.5528503428$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$38.1005761988$ |
10.2.107365139712.2 |
x10 - x9 + x8 + 4x7 - 15x6 + x5 + 27x4 - 14x3 - 13x2 + 11x - 1 |
$10$ |
[2,4] |
$2^{8}\cdot 3^{4}\cdot 173^{3}$ |
$$ |
$12.6790387562$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$40.8746207381$ |
10.2.107646386093.1 |
x10 - 2x9 - x8 + 6x7 - 6x6 - 3x5 + 7x4 - 4x3 + 3x2 - x + 1 |
$10$ |
[2,4] |
$67^{3}\cdot 71^{3}$ |
$$ |
$12.6823561619$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$48.7653737163$ |
10.2.111771206513.1 |
x10 - 2x9 + x7 - 3x6 - 2x5 + 8x4 - 6x3 + 2x2 - x + 1 |
$10$ |
[2,4] |
$4817^{3}$ |
$$ |
$12.7301345494$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$30.362674495$ |
10.2.117433042273.2 |
x10 - x9 - x8 + 2x7 - 3x6 + 5x5 - 2x4 + 3x3 + x2 + x + 1 |
$10$ |
[2,4] |
$59^{3}\cdot 83^{3}$ |
$$ |
$12.7931953401$ |
|
|
✓ |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$29.6416155266$ |
10.4.117865222327.1 |
x10 - x9 - x8 + 3x6 - 3x5 - 8x4 + 7x3 - 2x + 1 |
$10$ |
[4,3] |
$-\,4903^{3}$ |
$$ |
$12.7978957451$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$6$ |
$57.8296423144$ |
10.2.118940458033.1 |
x10 - x8 - 6x7 - 3x6 + x5 - x4 - 6x3 - 8x2 - 3x - 1 |
$10$ |
[2,4] |
$19^{4}\cdot 97^{3}$ |
$$ |
$12.8095230837$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$35.0449643191$ |
10.4.126237434624.1 |
x10 - 3x9 + x8 + 2x7 - x6 - 3x5 + 11x4 - 4x3 + x2 + 3x - 1 |
$10$ |
[4,3] |
$-\,2^{8}\cdot 7^{4}\cdot 59^{3}$ |
$$ |
$12.886020444$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$6$ |
$55.7962913178$ |
10.2.126884390625.1 |
x10 - 3x7 - 2x6 - 3x5 + 3x4 + 4x3 + x2 + x + 1 |
$10$ |
[2,4] |
$3^{3}\cdot 5^{6}\cdot 67^{3}$ |
$$ |
$12.8926092378$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$53.1753805254$ |
10.2.129602962688.1 |
x10 - 2x9 - 2x7 + 8x6 - 4x5 - 8x3 + 4x2 + 4 |
$10$ |
[2,4] |
$2^{8}\cdot 797^{3}$ |
$$ |
$12.9199696346$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$51.4432096337$ |
10.2.132031254528.2 |
x10 - 2x9 + 2x8 - 2x7 + 3x6 - 8x5 + 9x4 + 4x3 - 20x2 + 16x - 4 |
$10$ |
[2,4] |
$2^{12}\cdot 3^{8}\cdot 17^{3}$ |
$$ |
$12.9439752835$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$64.7115102512$ |
10.4.133541229312.1 |
x10 - 2x9 - x8 + 10x7 - 6x6 - 2x5 + 6x4 - 14x3 + x2 + 4x - 1 |
$10$ |
[4,3] |
$-\,2^{8}\cdot 3^{8}\cdot 43^{3}$ |
$$ |
$12.9587030173$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$6$ |
$59.4906287429$ |
10.2.137707850944.1 |
x10 - x9 - 2x8 + 7x7 - 8x6 + 2x5 + 8x4 - 5x3 - x2 + 1 |
$10$ |
[2,4] |
$2^{6}\cdot 1291^{3}$ |
$$ |
$12.9985787634$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$66.5085583303$ |
10.2.150288260544.1 |
x10 - 3x9 + 8x8 - 6x7 + x6 + 9x5 - 5x4 + 3x3 + 5x2 - 3x - 2 |
$10$ |
[2,4] |
$2^{6}\cdot 3^{8}\cdot 71^{3}$ |
$$ |
$13.1127114888$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$68.5106452112$ |
10.2.160722988453.1 |
x10 - 2x9 + 4x8 - 2x7 - 2x6 - 2x5 - 2x4 + 4x3 - 2x2 - 2x + 1 |
$10$ |
[2,4] |
$5437^{3}$ |
$$ |
$13.2010294494$ |
|
|
not computed |
$S_5$ (as 10T13) |
trivial |
$2$ |
$5$ |
$44.5320791146$ |