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Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 20.0.99150356443299840000000000.1 | x20 - 10x19 + 57x18 - 228x17 + 707x16 - 1780x15 + 3754x14 - 6756x13 + 10523x12 - 14310x11 + 17101x10 - 18004x9 + 16717x8 - 13652x7 + 9760x6 - 6036x5 + 3184x4 - 1392x3 + 484x2 - 120x + 20 | \( 2^{28}\cdot 3^{8}\cdot 5^{10}\cdot 7^{8} \) | $D_5\wr C_2$ (as 20T55) | Trivial |
| 20.0.100564814293580902500000000.1 | x20 - 6x19 + 14x18 - 24x17 + 80x16 - 266x15 + 553x14 - 784x13 + 1007x12 - 1370x11 + 1591x10 - 1370x9 + 1007x8 - 784x7 + 553x6 - 266x5 + 80x4 - 24x3 + 14x2 - 6x + 1 | \( 2^{8}\cdot 3^{8}\cdot 5^{10}\cdot 19^{10} \) | $D_5\wr C_2$ (as 20T55) | $[4]$ |
| 20.4.1604870732498935699462890625.1 | x20 - 6x19 + 8x18 + 31x17 - 178x16 + 497x15 - 955x14 + 1330x13 - 1375x12 + 1075x11 - 598x10 + 433x9 - 529x8 + 612x7 - 501x6 + 151x5 + 78x4 - 59x3 + 7x2 + 4x - 1 | \( 5^{18}\cdot 29^{10} \) | $D_5\wr C_2$ (as 20T55) | $[2]$ |
| 20.4.1783357279157206502500000000.1 | x20 - 4x19 + 2x18 + 8x17 - 10x16 + 34x15 - 127x14 + 189x13 - 165x12 + 414x11 - 1467x10 + 3021x9 - 3641x8 + 2498x7 - 481x6 - 685x5 + 296x4 + 170x3 + 53x2 - 109x + 19 | \( 2^{8}\cdot 5^{10}\cdot 61^{10} \) | $D_5\wr C_2$ (as 20T55) | Trivial (GRH) |
| 20.20.5120338176785431289672851562500000000.1 | x20 - 40x18 + 680x16 - 12x15 - 6400x14 + 360x13 + 36400x12 - 4320x11 - 128051x10 + 26400x9 + 273020x8 - 86400x7 - 327140x6 + 144522x5 + 180400x4 - 101220x3 - 20400x2 + 10440x + 1636 | \( 2^{8}\cdot 5^{26}\cdot 41^{10} \) | $D_5\wr C_2$ (as 20T55) | Trivial (GRH) |
| 20.20.23846398539764122605523970477353515625.1 | x20 - 8x19 - 33x18 + 439x17 - 416x16 - 6513x15 + 17832x14 + 27381x13 - 162275x12 + 97727x11 + 488062x10 - 917700x9 + 78546x8 + 1375989x7 - 1649718x6 + 712238x5 + 38154x4 - 135903x3 + 38629x2 - 2310x - 121 | \( 5^{10}\cdot 23^{8}\cdot 89^{10} \) | $D_5\wr C_2$ (as 20T55) | $[2]$ (GRH) |