Further refine search
Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 17.1.133249137678121328919445504.1 | x17 - 3x16 - 4x14 + 12x13 + 24x12 + 12x11 - 28x10 - 90x9 - 74x8 + 116x6 + 132x5 + 72x4 + 28x3 + 12x2 + 5x + 1 | \( 2^{30}\cdot 137^{8} \) | $\PSL(2,16)$ (as 17T6) | $[15]$ |
| 17.1.861526607800060221948166144.1 | x17 - x16 - 4x15 + 2x14 + 54x13 - 6x12 - 36x11 + 16x10 + 714x9 + 1238x8 + 484x7 - 764x6 - 1084x5 + 520x4 + 668x3 - 776x2 + 382x - 74 | \( 2^{30}\cdot 173^{8} \) | $\PSL(2,16)$ (as 17T6) | $[15]$ (GRH) |
| 17.1.2640732930336770744777703424.1 | x17 - 2x16 - 14x15 + 16x14 + 116x13 - 92x12 - 520x11 - 12x10 + 612x9 - 1488x8 - 1540x7 - 180x6 + 1580x5 - 1192x4 + 1608x3 - 844x2 + 122x - 40 | \( 2^{30}\cdot 199^{8} \) | $\PSL(2,16)$ (as 17T6) | $[15]$ (GRH) |
| 17.1.39726964294200827244451673677113820402444926976.1 | x17 + 221x15 - 850x14 + 19601x13 - 97036x12 + 2452233x11 - 5536254x10 + 159332007x9 - 1851117488x8 + 12939379031x7 - 45700927246x6 + 12487240571x5 + 217180838276x4 - 328446625597x3 + 138506493022x2 + 2281813189964x + 1767616042808 | \( 2^{24}\cdot 17^{32} \) | $D_{17}$ (as 17T2) | $[17]$ (GRH) |
| 17.17.8972555039016074378226050552414591426720707963201.1 | x17 - 4x16 - 476x15 + 3026x14 + 82996x13 - 736812x12 - 6121180x11 + 80531352x10 + 108448584x9 - 4267795762x8 + 9723361580x7 + 95353221324x6 - 524744382701x5 - 7660737412x4 + 6800548404356x3 - 21491689501032x2 + 27480501953536x - 12878683864992 | \( 17^{12}\cdot 137^{16} \) | $C_{17}:C_{4}$ (as 17T3) | $[17]$ (GRH) |
| 17.17.54471546860208560987402602575661525149433755592659973376605441.1 | x17 - 3502x15 - 21012x14 + 3586048x13 + 27140500x12 - 1455974010x11 - 13391942168x10 + 247158969538x9 + 2699830692822x8 - 15367054046543x7 - 210262575924428x6 + 207808365630713x5 + 5600534069106679x4 + 891648638079425x3 - 50160692092741008x2 - 11309428987726617x + 145001801906376687 | \( 17^{24}\cdot 103^{16} \) | $D_{17}$ (as 17T2) | $[17]$ (GRH) |