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Label Polynomial Discriminant Galois group Class group
21.3.214...807.1 x21 - x20 - x19 + x18 - x17 + 6x16 - 7x15 + 2x14 - 4x13 + 5x12 + 9x11 - 17x10 + 11x9 - 4x8 - 3x7 + 9x6 - 6x5 - x4 + 3x3 - x2 - x + 1 \( -\,184607^{5} \) 21T38 trivial (GRH)
21.3.270...407.1 x21 - 4x18 - x17 + x16 + 7x15 + x14 - 6x13 - 11x12 + 2x11 + 10x10 + 14x9 - 2x8 - 5x7 - 6x6 + 2x5 - 2x4 - 3x3 + 2x2 - 1 \( -\,193327^{5} \) 21T38 trivial (GRH)
21.5.123...001.1 x21 - 2x19 - x18 - 8x17 + 16x15 + 16x14 + 21x13 - 27x12 - 29x11 - 63x10 - 3x9 + 86x8 + 60x7 + 11x6 - 69x5 - 49x4 + 30x3 + 16x2 - 6x - 1 \( 7^{9}\cdot 12503^{5} \) 21T38 trivial (GRH)
21.5.348...177.1 x21 - 2x20 - 5x18 + 12x17 - 5x16 + 4x15 - 27x14 + 16x13 - 8x12 + 8x11 - 22x10 - 8x9 - 2x8 + 9x7 + 15x6 + 12x5 + 13x4 + 2x3 - x2 - 2x - 1 \( 3^{8}\cdot 37^{5}\cdot 2381^{5} \) 21T38 trivial (GRH)
21.11.391...159.1 x21 - 2x20 - 9x19 + 12x18 + 25x17 + 8x16 - 79x15 + 7x14 + 170x13 - 132x12 - 294x11 - 136x10 + 534x9 + 158x8 - 345x7 + 242x6 + 243x5 - 58x4 - 53x3 - 6x2 + 2x + 1 \( -\,7^{5}\cdot 17^{8}\cdot 2017^{5} \) 21T38 trivial (GRH)
21.11.344...967.1 x21 - 6x20 - x19 + 71x18 - 93x17 - 305x16 + 665x15 + 567x14 - 2100x13 - 214x12 + 3718x11 - 982x10 - 3941x9 + 1934x8 + 2506x7 - 1669x6 - 928x5 + 820x4 + 128x3 - 214x2 + 45x - 1 \( -\,3^{9}\cdot 280909^{5} \) 21T38 trivial (GRH)
21.21.539...056.1 x21 - 3x20 - 30x19 + 86x18 + 349x17 - 953x16 - 2026x15 + 5248x14 + 6380x13 - 15522x12 - 11326x11 + 25300x10 + 11568x9 - 22602x8 - 6770x7 + 10604x6 + 2191x5 - 2351x4 - 352x3 + 194x2 + 23x - 1 \( 2^{18}\cdot 728809^{5} \) 21T38 trivial (GRH)
21.21.330...193.1 x21 - 6x20 - 13x19 + 122x18 - 9x17 - 857x16 + 633x15 + 2723x14 - 2843x13 - 4388x12 + 5538x11 + 3675x10 - 5631x9 - 1441x8 + 3112x7 + 105x6 - 903x5 + 87x4 + 121x3 - 21x2 - 5x + 1 \( 71^{5}\cdot 283583^{5} \) 21T38 trivial (GRH)
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