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Label Polynomial Discriminant Galois group Class group
21.5.16253945603436050603615041.1 x21 - x20 - 6x19 + 8x18 + 15x17 - 28x16 - 39x15 + 74x14 + 112x13 - 127x12 - 227x11 + 89x10 + 306x9 + x8 - 244x7 - 55x6 + 122x5 + 40x4 - 41x3 - 6x2 + 8x - 1 \( 13^{8}\cdot 109^{8} \) $\PSL(2,7)$ (as 21T14) Trivial (GRH)
21.5.26730926988131422081122304.1 x21 - 5x20 + 11x19 - 16x18 + 25x17 - 38x16 + 36x15 - 25x14 + 18x13 - 4x12 - 3x11 - 17x10 - 23x9 - 12x8 + 55x7 + 18x6 - 46x5 - 17x4 + 19x3 + 9x2 - 2x - 1 \( 2^{18}\cdot 317^{8} \) $\PSL(2,7)$ (as 21T14) Trivial (GRH)
21.21.50434533500374375555123632117121024.1 x21 - 3x20 - 35x19 + 103x18 + 465x17 - 1353x16 - 2985x15 + 8673x14 + 9901x13 - 29145x12 - 17071x11 + 52175x10 + 14997x9 - 49437x8 - 6223x7 + 23447x6 + 1118x5 - 4872x4 - 114x3 + 334x2 - 6x - 2 \( 2^{38}\cdot 809^{8} \) $\PSL(2,7)$ (as 21T14) Trivial (GRH)
21.21.354339010128398236785800917962194944.1 x21 - 2x20 - 43x19 + 68x18 + 733x17 - 988x16 - 6395x15 + 8040x14 + 30708x13 - 39018x12 - 79894x11 + 110250x10 + 98768x9 - 165588x8 - 29458x7 + 106634x6 - 26074x5 - 14068x4 + 6574x3 - 756x2 - 8x + 4 \( 2^{22}\cdot 4129^{8} \) $\PSL(2,7)$ (as 21T14) Trivial (GRH)



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