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Label Polynomial Discriminant Galois group Class group
6.2.246955328.1 x6 - 3x5 + 9x4 - 10x3 - 5x2 + 9x - 5 $2^{6}\cdot 17\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.355906208.1 x6 - 2x5 + 2x4 - 8x3 - 8x2 + 88x - 64 $2^{5}\cdot 7^{2}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.726339200.1 x6 - 2x5 - 14x4 + 28x3 + 28x2 - 128x + 88 $2^{7}\cdot 5^{2}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.0.1743214080.1 x6 - 3x5 + 3x4 + 8x3 + 16x2 + 12x + 12 $-\,2^{9}\cdot 3\cdot 5\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.0.2179017600.1 x6 - 2x4 - 26x3 + 62x2 + 148x + 108 $-\,2^{7}\cdot 3\cdot 5^{2}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.2353339008.1 x6 + 19x4 - 16x3 + 75x2 - 152x - 119 $2^{7}\cdot 3^{4}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.0.3814869667.1 x6 - x5 + 106x4 - 106x3 + 3256x2 - 3256x + 26881 $-\,7^{5}\cdot 61^{3}$ $C_6$ (as 6T1) $[38]$
6.0.3951285248.1 x6 + 4x4 - 44x3 + 126x2 - 88x + 240 $-\,2^{10}\cdot 17\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.5535839609.2 x6 - x5 + 9x4 - 23x3 - 3x2 - 71x + 15 $29^{3}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.0.5694499328.2 x6 - 2x5 - 3x4 + 14x3 - 6x2 - 20x + 513 $-\,2^{9}\cdot 7^{2}\cdot 61^{3}$ $S_3\times C_3$ (as 6T5) $[2, 2, 10]$
6.2.6043142144.1 x6 - 2x5 - 10x4 + 16x3 - 112x2 + 64x - 192 $2^{11}\cdot 13\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.6177514896.1 x6 - 3x5 - 3x4 - 41x3 + 186x2 - 252x + 108 $2^{4}\cdot 3^{5}\cdot 7\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.0.9413356032.2 x6 - 10x4 - 50x3 + 147x2 + 982x + 1723 $-\,2^{9}\cdot 3^{4}\cdot 61^{3}$ $S_3\times C_3$ (as 6T5) $[10]$
6.0.9731810375.1 x6 - x5 - 5x4 - 11x3 + 28x2 + 31x + 436 $-\,5^{3}\cdot 7^{3}\cdot 61^{3}$ $\PGL(2,5)$ (as 6T14) $[2, 2]$
6.2.10982248704.1 x6 - x5 - 5x4 + 22x3 - 19x2 + 13x - 321 $2^{8}\cdot 3^{3}\cdot 7\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.0.11621427200.1 x6 - 2x5 + 13x4 - 37x2 - 50x + 97 $-\,2^{11}\cdot 5^{2}\cdot 61^{3}$ $S_6$ (as 6T16) $[2, 2]$
6.2.11621427200.4 x6 + 8x4 - 48x3 + 138x2 - 192x + 88 $2^{11}\cdot 5^{2}\cdot 61^{3}$ $\PGL(2,5)$ (as 6T14) $[2]$
6.2.14497049489.1 x6 - 2x5 + x4 + 33x3 - 33x2 + 13 $13\cdot 17^{3}\cdot 61^{3}$ $C_3^2:D_4$ (as 6T13) $[2]$
6.4.16734855168.1 x6 - 2x5 + 11x4 - 108x3 + x2 + 730x - 649 $-\,2^{13}\cdot 3^{2}\cdot 61^{3}$ $C_3^2:D_4$ (as 6T13) $[2]$
6.2.19640211968.1 x6 - 2x5 - 10x4 + 42x3 - 77x2 + 104x - 80 $2^{9}\cdot 13^{2}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.22777997312.7 x6 - 2x5 - 7x4 - 20x3 - 17x2 - 10x + 13 $2^{11}\cdot 7^{2}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.4.24471048591.1 x6 - 2x5 - 28x4 + 16x3 + 269x2 + 97x - 461 $-\,3^{4}\cdot 11^{3}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.25316779797.1 x6 - 3x5 + 48x4 + 46x3 - 1533x2 + 5673x - 62911 $3^{8}\cdot 17\cdot 61^{3}$ $A_4\times C_2$ (as 6T6) $[6]$
6.0.28240068096.1 x6 - 2x5 + 5x4 + 38x3 + 84x2 + 84x + 75 $-\,2^{9}\cdot 3^{5}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.0.33633136656.1 x6 - x5 + 2x4 + 10x3 + 2x2 + 20x + 36 $-\,2^{4}\cdot 3^{3}\cdot 7^{3}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.33792250337.1 x6 - x5 - 19x4 + 58x3 + 220x2 - 112x - 741 $53^{3}\cdot 61^{3}$ $\PGL(2,5)$ (as 6T14) $[2, 2]$
6.0.37653424128.3 x6 - 20x4 - 20x3 + 222x2 + 688x + 588 $-\,2^{11}\cdot 3^{4}\cdot 61^{3}$ $S_3^2$ (as 6T9) $[10]$
6.4.40907423744.1 x6 - 2x5 - 19x4 + 48x3 + 72x2 - 280x - 292 $-\,2^{14}\cdot 11\cdot 61^{3}$ $C_3^2:D_4$ (as 6T13) $[2]$
6.0.41953352192.1 x6 - 2x5 - 35x4 + 50x3 + 432x2 - 252x + 49 $-\,2^{9}\cdot 19^{2}\cdot 61^{3}$ $S_3\times C_3$ (as 6T5) $[10]$
6.4.45989074372.1 x6 - 2x5 - 5x4 + 51x3 - 36x2 - 135x - 58 $-\,2^{2}\cdot 37^{3}\cdot 61^{3}$ $C_3^2:D_4$ (as 6T13) $[2]$
6.4.49593305671.1 x6 - 3x5 - 103x4 + 211x3 - 5043x2 + 4937x + 321511 $-\,7^{5}\cdot 13\cdot 61^{3}$ $A_4\times C_2$ (as 6T6) $[2]$
6.0.50204565504.3 x6 - 2x5 + 17x4 + 12x3 + 219x2 + 102x + 867 $-\,2^{13}\cdot 3^{3}\cdot 61^{3}$ $\PGL(2,5)$ (as 6T14) $[2]$
6.6.54642724997.1 x6 - 2x5 - 45x4 + 61x3 + 514x2 - 345x - 203 $7^{2}\cdot 17^{3}\cdot 61^{3}$ $S_3\times C_3$ (as 6T5) $[2]$
6.4.59792242944.1 x6 - 2x5 - 11x4 + 46x3 + 2x2 - 204x - 138 $-\,2^{8}\cdot 3\cdot 7^{3}\cdot 61^{3}$ $C_3^2:D_4$ (as 6T13) $[6]$
6.0.61037914672.1 x6 - 2x5 + 25x4 + 62x3 + 485x2 + 1032x + 1849 $-\,2^{4}\cdot 7^{5}\cdot 61^{3}$ $S_3\times C_3$ (as 6T5) $[6]$
6.2.73413145773.1 x6 + 9x4 - 91x3 - 483x2 - 684x - 324 $3^{5}\cdot 11^{3}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.4.84720204288.1 x6 - 2x5 - 19x4 - 12x3 - 356x2 + 1784x - 232 $-\,2^{9}\cdot 3^{6}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.90327769893.1 x6 - 36x4 - 141x3 - 225x2 - 207x - 108 $3^{4}\cdot 17^{3}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.2.90792400000.1 x6 - 2x5 + 10x4 + 110x3 + 130x2 + 2518x + 4379 $2^{7}\cdot 5^{5}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.4.98055792000.1 x6 - 2x5 - 25x4 + 195x2 - 150x - 75 $-\,2^{7}\cdot 3^{3}\cdot 5^{3}\cdot 61^{3}$ $S_6$ (as 6T16) $[2]$
6.6.103001481009.1 x6 - x5 - 321x4 + 321x3 + 29303x2 - 29303x - 652049 $3^{3}\cdot 7^{5}\cdot 61^{3}$ $C_6$ (as 6T1) $[2]$
6.2.112960272384.2 x6 - 2x5 - 35x4 + 56x3 - 184x2 + 128x - 144 $2^{11}\cdot 3^{5}\cdot 61^{3}$ $S_6$ (as 6T16) $[2, 2]$
6.2.125094676644.1 x6 + 21x4 - 54x3 - 27x2 - 18x - 3 $2^{2}\cdot 3^{9}\cdot 7\cdot 61^{3}$ $S_6$ (as 6T16) $[6]$
6.2.130512259152.4 x6 - x5 + 25x4 - 119x3 + 175x2 - 1309x + 2740 $2^{4}\cdot 3^{3}\cdot 11^{3}\cdot 61^{3}$ $\PGL(2,5)$ (as 6T14) $[2]$
6.2.134532546624.10 x6 - x5 + 7x4 - 86x3 + 67x2 - 337x + 781 $2^{6}\cdot 3^{3}\cdot 7^{3}\cdot 61^{3}$ $\PGL(2,5)$ (as 6T14) $[2]$
6.0.135322213523.1 x6 - 2x5 + 6x4 - 68x3 + 420x2 - 859x + 1343 $-\,7^{2}\cdot 23^{3}\cdot 61^{3}$ $S_3\times C_3$ (as 6T5) $[14]$
6.4.157655328075.1 x6 - 9x4 - 41x3 - 300x2 + 825x + 100 $-\,3^{4}\cdot 5^{2}\cdot 7^{3}\cdot 61^{3}$ $C_3^2:D_4$ (as 6T13) $[2]$
6.0.167813408768.4 x6 + 122x4 + 14884x2 + 453962 $-\,2^{11}\cdot 19^{2}\cdot 61^{3}$ $D_{6}$ (as 6T3) $[10]$
6.2.167813408768.1 x6 - 122x4 + 14884x2 - 453962 $2^{11}\cdot 19^{2}\cdot 61^{3}$ $D_{6}$ (as 6T3) $[2]$
6.2.167813408768.3 x6 - 2x5 + 19x4 + 24x3 + 39x2 + 378x - 47 $2^{11}\cdot 19^{2}\cdot 61^{3}$ $S_3^2$ (as 6T9) $[2]$
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