Further refine search
Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 20.0.369768517790072832000000000.1 | x20 - 4x19 + 2x18 + 24x17 - 61x16 + 20x15 + 184x14 - 396x13 + 203x12 + 612x11 - 1410x10 + 968x9 + 849x8 - 2224x7 + 1620x6 - 56x5 - 638x4 + 368x3 - 24x2 - 56x + 20 | \( 2^{42}\cdot 3^{16}\cdot 5^{9} \) | $S_5$ (as 20T35) | Trivial |
| 20.0.407875612060900496297202517.1 | x20 - 8x19 + 40x18 - 131x17 + 333x16 - 674x15 + 1207x14 - 1922x13 + 2822x12 - 3681x11 + 4260x10 - 4222x9 + 3582x8 - 2665x7 + 1813x6 - 1072x5 + 587x4 - 252x3 + 74x2 - 13x + 1 | \( 11^{12}\cdot 37^{9} \) | $S_5$ (as 20T35) | Trivial (GRH) |
| 20.2.1417868996949216476646801408.1 | x20 - 7x19 + 19x18 - 5x17 - 108x16 + 311x15 - 333x14 - 167x13 + 992x12 - 1203x11 + 141x10 + 1555x9 - 2554x8 + 2293x7 - 1387x6 + 609x5 - 208x4 + 77x3 - 33x2 + 9x - 1 | \( -\,2^{16}\cdot 3^{16}\cdot 43^{9} \) | $S_5$ (as 20T35) | $[3]$ |
| 20.2.12962257948142832318230495232.1 | x20 - 5x19 + 5x18 + 3x17 + 42x16 - 153x15 + 131x14 - 151x13 + 700x12 - 963x11 + 273x10 + 105x9 + 106x8 + x7 + 71x6 - 651x5 + 834x4 - 453x3 + 123x2 - 21x + 3 | \( -\,2^{16}\cdot 3^{27}\cdot 11^{10} \) | $S_5$ (as 20T35) | Trivial |
| 20.20.1954417180834054231108741720904630272.1 | x20 - 51x18 + 1051x16 - 11466x14 + 73285x12 - 288141x10 + 708441x8 - 1076170x6 + 965263x4 - 461747x2 + 89557 | \( 2^{16}\cdot 13^{15}\cdot 17^{12} \) | $S_5$ (as 20T35) | Trivial (GRH) |
| 20.20.11920350468069903076814830978072379392.1 | x20 - 6x19 - 42x18 + 266x17 + 601x16 - 4412x15 - 3160x14 + 36624x13 - 1906x12 - 166956x11 + 84220x10 + 427696x9 - 344106x8 - 598132x7 + 620232x6 + 412832x5 - 525839x4 - 109710x3 + 181022x2 + 9590x - 18511 | \( 2^{16}\cdot 11^{12}\cdot 157^{9} \) | $S_5$ (as 20T35) | Trivial (GRH) |