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Label Polynomial Discriminant Galois group Class group
5.5.14641.1 x5 - x4 - 4x3 + 3x2 + 3x - 1 \( 11^{4} \) $C_5$ Trivial
5.5.24217.1 x5 - 5x3 - x2 + 3x + 1 \( 61\cdot 397 \) $S_5$ Trivial
5.5.36497.1 x5 - 2x4 - 3x3 + 5x2 + x - 1 \( 36497 \) $S_5$ Trivial
5.5.38569.1 x5 - 5x3 + 4x - 1 \( 38569 \) $S_5$ Trivial
5.5.65657.1 x5 - x4 - 5x3 + 2x2 + 5x + 1 \( 65657 \) $S_5$ Trivial
5.5.70601.1 x5 - x4 - 5x3 + 2x2 + 3x - 1 \( 17\cdot 4153 \) $S_5$ Trivial
5.5.81509.1 x5 - x4 - 5x3 + 3x2 + 5x - 2 \( 81509 \) $S_5$ Trivial
5.5.81589.1 x5 - 6x3 + 8x - 1 \( 83\cdot 983 \) $S_5$ Trivial
5.5.89417.1 x5 - 6x3 - x2 + 8x + 3 \( 89417 \) $S_5$ Trivial
5.5.101833.1 x5 - x4 - 5x3 + 5x2 + 2x - 1 \( 101833 \) $S_5$ Trivial
5.5.106069.1 x5 - 2x4 - 4x3 + 7x2 + 3x - 4 \( 73\cdot 1453 \) $S_5$ Trivial
5.5.117688.1 x5 - x4 - 5x3 + 4x2 + 4x - 1 \( 2^{3}\cdot 47\cdot 313 \) $S_5$ Trivial
5.5.122821.1 x5 - 2x4 - 4x3 + 4x2 + 3x - 1 \( 263\cdot 467 \) $S_5$ Trivial
5.5.124817.1 x5 - 7x3 - 6x2 + 2x + 1 \( 7\cdot 11\cdot 1621 \) $S_5$ Trivial
5.5.126032.1 x5 - 6x3 + 6x - 2 \( 2^{4}\cdot 7877 \) $S_5$ Trivial
5.5.135076.1 x5 - x4 - 5x3 + 4x2 + 4x - 2 \( 2^{2}\cdot 33769 \) $S_5$ Trivial
5.5.138136.1 x5 - x4 - 6x3 + 3x2 + 4x - 2 \( 2^{3}\cdot 31\cdot 557 \) $S_5$ Trivial
5.5.138917.1 x5 - 6x3 - 2x2 + 3x + 1 \( 138917 \) $S_5$ Trivial
5.5.144209.1 x5 - 6x3 - x2 + 6x - 1 \( 13\cdot 11093 \) $S_5$ Trivial
5.5.147109.1 x5 - 2x4 - 4x3 + 5x2 + 3x - 2 \( 157\cdot 937 \) $S_5$ Trivial
5.5.149169.1 x5 - 6x3 - 3x2 + 4x + 1 \( 3\cdot 19\cdot 2617 \) $S_5$ Trivial
5.5.153424.1 x5 - 2x4 - 4x3 + 8x2 - 2 \( 2^{4}\cdot 43\cdot 223 \) $S_5$ Trivial
5.5.157457.1 x5 - 2x4 - 4x3 + 5x2 + 4x - 1 \( 157457 \) $S_5$ Trivial
5.5.160801.1 x5 - x4 - 5x3 + 4x2 + 3x - 1 \( 401^{2} \) $D_5$ Trivial
5.5.161121.1 x5 - x4 - 6x3 + 3x2 + 5x + 1 \( 3\cdot 43\cdot 1249 \) $S_5$ Trivial
5.5.170701.1 x5 - x4 - 6x3 + 4x + 1 \( 170701 \) $S_5$ Trivial
5.5.173513.1 x5 - 2x4 - 5x3 + 3x2 + 3x - 1 \( 167\cdot 1039 \) $S_5$ Trivial
5.5.176281.1 x5 - x4 - 5x3 + 3x2 + 4x - 1 \( 7\cdot 25183 \) $S_5$ Trivial
5.5.176684.1 x5 - 6x3 - x2 + 5x - 1 \( 2^{2}\cdot 44171 \) $S_5$ Trivial
5.5.179024.1 x5 - 8x3 + 6x - 2 \( 2^{4}\cdot 67\cdot 167 \) $S_5$ Trivial
5.5.180769.1 x5 - 2x4 - 4x3 + 7x2 - 1 \( 41\cdot 4409 \) $S_5$ Trivial
5.5.181057.1 x5 - 2x4 - 4x3 + 7x2 + 2x - 3 \( 331\cdot 547 \) $S_5$ Trivial
5.5.186037.1 x5 - x4 - 6x3 + 2x2 + 5x - 2 \( 186037 \) $S_5$ Trivial
5.5.195829.1 x5 - 2x4 - 5x3 + 6x2 + 7x + 1 \( 113\cdot 1733 \) $S_5$ Trivial
5.5.202817.1 x5 - 2x4 - 4x3 + 5x2 + 2x - 1 \( 202817 \) $S_5$ Trivial
5.5.205225.1 x5 - x4 - 6x3 + 3x2 + 7x - 3 \( 5^{2}\cdot 8209 \) $S_5$ Trivial
5.5.207184.1 x5 - x4 - 6x3 + 2x2 + 7x - 1 \( 2^{4}\cdot 23\cdot 563 \) $S_5$ Trivial
5.5.210557.1 x5 - x4 - 6x3 + 4x2 + 8x - 1 \( 210557 \) $S_5$ Trivial
5.5.216637.1 x5 - 2x4 - 4x3 + 7x2 + x - 2 \( 23\cdot 9419 \) $S_5$ Trivial
5.5.218524.1 x5 - 2x4 - 4x3 + 5x2 + 3x - 1 \( 2^{2}\cdot 54631 \) $S_5$ Trivial
5.5.220036.1 x5 - 2x4 - 5x3 + 11x2 - 2x - 1 \( 2^{2}\cdot 55009 \) $S_5$ Trivial
5.5.220669.1 x5 - 7x3 - 2x2 + 11x + 5 \( 149\cdot 1481 \) $S_5$ Trivial
5.5.223824.1 x5 - 2x4 - 4x3 + 6x2 + 2x - 2 \( 2^{4}\cdot 3\cdot 4663 \) $S_5$ Trivial
5.5.223952.1 x5 - 6x3 - 2x2 + 6x + 2 \( 2^{4}\cdot 13997 \) $S_5$ Trivial
5.5.224773.1 x5 - x4 - 6x3 + 2x2 + 7x + 2 \( 53\cdot 4241 \) $S_5$ Trivial
5.5.230224.1 x5 - 2x4 - 4x3 + 6x2 + 3x - 2 \( 2^{4}\cdot 14389 \) $S_5$ Trivial
5.5.233489.1 x5 - x4 - 6x3 + x2 + 5x - 1 \( 233489 \) $S_5$ Trivial
5.5.236549.1 x5 - x4 - 6x3 + 7x2 + 2x - 1 \( 236549 \) $S_5$ Trivial
5.5.240133.1 x5 - 2x4 - 4x3 + 6x2 + 2x - 1 \( 439\cdot 547 \) $S_5$ Trivial
5.5.240881.1 x5 - 2x4 - 5x3 + 9x2 + 5x - 7 \( 240881 \) $S_5$ Trivial

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