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Label Polynomial Discriminant Galois group Class group
6.2.287296.2 x6 - 2x5 + 3x4 - 4x3 + 2x2 - 2x - 1 \( 2^{6}\cdot 67^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.341056.1 x6 - 2x5 + 4x4 - 4x3 + 3x2 - 2x - 1 \( 2^{6}\cdot 73^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.426409.1 x6 - 2x5 + 2x4 - x3 - 2x2 + x - 2 \( 653^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.678976.1 x6 - 2x5 + 2x4 - 4x3 + x2 - 2x - 1 \( 2^{6}\cdot 103^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.732736.3 x6 - 2x5 - 2x4 + 6x3 + x2 - 6x + 1 \( 2^{6}\cdot 107^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.1000000.1 x6 - 2x5 - 5x2 - 2x - 1 \( 2^{6}\cdot 5^{6} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.1125721.1 x6 - x5 + x4 + 3x3 - 5x2 + 5x - 3 \( 1061^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.1132096.1 x6 - 2x5 + x4 - 4x3 - 2x - 1 \( 2^{6}\cdot 7^{2}\cdot 19^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.1784896.1 x6 - 2x5 - 3x4 + 6x3 + 2x2 - 6x + 1 \( 2^{6}\cdot 167^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.1907161.1 x6 - x5 + x4 - 7x3 - 7x2 - x + 1 \( 1381^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.1993744.1 x6 - x5 - 3x4 + x3 + 4x + 4 \( 2^{4}\cdot 353^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2005056.1 x6 - 2x5 + 2x4 - 2x3 - 5x2 - 3 \( 2^{6}\cdot 3^{2}\cdot 59^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2271049.1 x6 - x5 - 3x4 - x3 - x2 - 3x - 1 \( 11^{2}\cdot 137^{2} \) $\PSL(2,5)$ (as 6T12) $[2]$
6.2.2334784.1 x6 + 2x4 - 2x3 + 5x2 + 6x + 1 \( 2^{6}\cdot 191^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2383936.1 x6 - 2x5 + 5x4 - 4x3 + 4x2 - 2x - 1 \( 2^{6}\cdot 193^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2411809.1 x6 - x5 - 3x4 + 4x2 + 1 \( 1553^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2572816.1 x6 - x5 - x4 + 3x3 - 4x2 + 2x - 2 \( 2^{4}\cdot 401^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2640625.1 x6 - x5 - 5x4 - 5x3 + 3x + 2 \( 5^{6}\cdot 13^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2676496.1 x6 - x5 + x4 + x3 - 4x2 + 2x - 2 \( 2^{4}\cdot 409^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2689600.1 x6 - 2x5 + 2x4 + 4x3 - 11x2 + 10x - 5 \( 2^{6}\cdot 5^{2}\cdot 41^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2849344.1 x6 - 2x5 + 2x4 - 3x2 - 2x - 1 \( 2^{6}\cdot 211^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.2903616.1 x6 + 2x4 - 2x3 - 7x2 - 6x - 3 \( 2^{6}\cdot 3^{2}\cdot 71^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.3003289.1 x6 - 2x5 + 2x4 + x3 - 5x2 + 4x - 3 \( 1733^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.3125824.1 x6 - 2x5 + 4x4 - 4x3 - 3x2 + 2x - 7 \( 2^{6}\cdot 13^{2}\cdot 17^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.3272481.2 x6 - 3x5 + 3x4 + 4x3 - 12x2 + 12x - 3 \( 3^{6}\cdot 67^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.3794704.1 x6 - x5 - x4 - x3 - 2x2 + 2x + 6 \( 2^{4}\cdot 487^{2} \) $\PSL(2,5)$ (as 6T12) $[2]$
6.2.4116841.1 x6 - x5 - x4 + 5x3 - 5x2 + 3x + 1 \( 2029^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.4214809.1 x6 - 2x4 - 3x3 - 7x + 4 \( 2053^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.4338889.1 x6 - 2x5 + x4 - x3 + 2x2 + 4x + 1 \( 2083^{2} \) $\PSL(2,5)$ (as 6T12) $[2]$
6.2.4494400.1 x6 - 2x5 - 2x3 + 5x2 + 2x - 3 \( 2^{6}\cdot 5^{2}\cdot 53^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.4840000.1 x6 - 2x5 - 3x4 + 4x3 + 6x2 - 8x - 3 \( 2^{6}\cdot 5^{4}\cdot 11^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.4950625.2 x6 - x5 - 2x4 + 3x3 + x2 - 9x + 8 \( 5^{4}\cdot 89^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.5058001.1 x6 - 2x5 - 3x3 + 4x2 + 7x + 2 \( 13^{2}\cdot 173^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.5094049.1 x6 - 2x5 + x4 - 5x3 + 2x2 + 4x + 1 \( 37^{2}\cdot 61^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.5257849.1 x6 - 3x5 + 5x4 - x3 - 5x2 + 3x + 1 \( 2293^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.5271616.1 x6 - 2x5 - 2x4 + 8x3 + 7x2 - 4x - 5 \( 2^{6}\cdot 7^{2}\cdot 41^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.5326864.1 x6 - x5 - x4 - x3 - 2x2 - 2 \( 2^{4}\cdot 577^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.5345344.1 x6 - 2x5 + 3x4 - 4x2 + 4x - 3 \( 2^{6}\cdot 17^{4} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.5419584.1 x6 - 2x5 - 4x4 + 6x3 + 9x2 - 18x + 9 \( 2^{6}\cdot 3^{2}\cdot 97^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.5721664.1 x6 - 2x5 + 5x4 - 8x3 - 6x - 17 \( 2^{6}\cdot 13^{2}\cdot 23^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.6031936.3 x6 - 4x4 - 2x3 + 5x2 + 8x + 3 \( 2^{6}\cdot 307^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.6270016.1 x6 - 2x5 - 8x3 + 19x2 - 8x - 3 \( 2^{6}\cdot 313^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.6270016.2 x6 - 2x5 + 4x4 - 2x3 + 5x2 + 4x - 2 \( 2^{6}\cdot 313^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.6661561.1 x6 - 2x5 + 5x4 - 3x3 + x2 + x - 2 \( 29^{2}\cdot 89^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.6806881.1 x6 - 3x5 + x4 + 3x3 + x2 + 3x - 13 \( 2609^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.6974881.1 x6 - x5 - 2x4 - 13x3 - 7x2 - x + 1 \( 19^{2}\cdot 139^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.7011904.3 x6 - 2x5 + x4 + 2x2 + 4x + 1 \( 2^{6}\cdot 331^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.7123561.1 x6 - x5 + 3x4 + 3x3 + 8x2 + 7x - 2 \( 17^{2}\cdot 157^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.7139584.1 x6 - 2x4 - 4x3 - 3x2 - 4x + 8 \( 2^{8}\cdot 167^{2} \) $\PSL(2,5)$ (as 6T12) Trivial
6.2.7327849.1 x6 - x5 + x4 - 5x3 + 3x2 + 3x - 1 \( 2707^{2} \) $\PSL(2,5)$ (as 6T12) $[2]$
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