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Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 21.3.4297390112987454978404646912.1 | x21 - x20 + 9x19 - 7x18 + 35x17 - 27x16 + 83x15 - 61x14 + 123x13 - 111x12 + 163x11 - 225x10 + 213x9 - 253x8 + 177x7 - 167x6 + 192x5 - 180x4 + 136x3 - 76x2 - 12x + 4 | \( -\,2^{38}\cdot 3^{18}\cdot 7^{9} \) | $SO(3,7)$ (as 21T20) | Trivial (GRH) |
| 21.3.7146646609494406531041460224.1 | x21 - 3x20 - 4x19 + 16x18 - 9x17 - 33x16 + 52x15 + 12x14 - 136x13 + 96x12 + 180x11 - 260x10 - 144x9 + 312x8 + 44x7 - 220x6 + 15x5 + 59x4 - 16x3 + 36x2 - 31x + 1 | \( -\,2^{64}\cdot 3^{18} \) | $SO(3,7)$ (as 21T20) | Trivial (GRH) |
| 21.5.27984468103350046268523020288.1 | x21 - 2x19 - 7x18 - 5x17 + 11x16 + 17x15 + 34x14 - 32x13 - 19x12 - 120x11 - 65x10 - 276x9 + 43x8 + 539x7 + 983x6 + 606x5 + 280x4 + 121x3 + 40x2 - 13x - 5 | \( 2^{27}\cdot 181^{9} \) | $SO(3,7)$ (as 21T20) | Trivial (GRH) |
| 21.5.124359384669552020013669011789.1 | x21 - 7x20 + 22x19 - 36x18 + 16x17 + 90x16 - 359x15 + 819x14 - 1304x13 + 1479x12 - 987x11 - 415x10 + 2526x9 - 4472x8 + 5201x7 - 4365x6 + 2658x5 - 1122x4 + 291x3 - 23x2 - 4x - 1 | \( 1709^{9} \) | $SO(3,7)$ (as 21T20) | Trivial (GRH) |
| 21.21.1918683763390753406969558352246443638814987989.1 | x21 - 7x20 - 74x19 + 589x18 + 2119x17 - 20809x16 - 26782x15 + 399755x14 + 51461x13 - 4495452x12 + 2641366x11 + 29342562x10 - 32803562x9 - 100138483x8 + 164165998x7 + 116217006x6 - 324673546x5 + 109229003x4 + 66372478x3 - 20912877x2 - 4643865x + 27082 | \( 107509^{9} \) | $SO(3,7)$ (as 21T20) | $[2]$ (GRH) |
| 21.21.4873621493405139175690041549663712051200000000.1 | x21 - 3x20 - 114x19 + 378x18 + 4720x17 - 18268x16 - 92372x15 + 440572x14 + 854237x13 - 5819847x12 - 2098218x11 + 43117146x10 - 24499166x9 - 172066922x8 + 212267312x7 + 313874448x6 - 627347440x5 - 93152336x4 + 688442080x3 - 275865888x2 - 111827424x + 53833824 | \( 2^{49}\cdot 3^{8}\cdot 5^{8}\cdot 491^{8} \) | $SO(3,7)$ (as 21T20) | Trivial (GRH) |