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Results (displaying both matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 27.27.27485917061841905258715957728464424188465393850574441.1 | x27 - 9x26 - 45x25 + 558x24 + 564x23 - 14325x22 + 3278x21 + 200187x20 - 152250x19 - 1689790x18 + 1662003x17 + 9058716x16 - 9244050x15 - 31587348x14 + 28970679x13 + 71864499x12 - 50585529x11 - 103930188x10 + 44676536x9 + 88142967x8 - 15697422x7 - 37059379x6 + 2104236x5 + 7157724x4 - 134797x3 - 528300x2 + 16716x + 7064 | \( 3^{36}\cdot 7^{18}\cdot 13^{18} \) | $C_3^3$ (as 27T4) | Trivial (GRH) |
| 27.27.25450405558360134867067668541820239712260815470994619689.1 | x27 - 9x26 - 63x25 + 774x24 + 834x23 - 26013x22 + 24482x21 + 438771x20 - 917742x19 - 3954764x18 + 12493773x17 + 17637390x16 - 89943576x15 - 16499340x14 + 367102377x13 - 183437513x12 - 838172511x11 + 827108970x10 + 967374964x9 - 1484013339x8 - 364627638x7 + 1223353523x6 - 171844968x5 - 419177382x4 + 123185675x3 + 52146132x2 - 17057376x - 1145024 | \( 3^{36}\cdot 7^{18}\cdot 19^{18} \) | $C_3^3$ (as 27T4) | $[2, 2]$ (GRH) |