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Label Polynomial Discriminant Galois group Class group
5.1.1609.1 x5 - x3 - x2 + x + 1 \( 1609 \) $S_5$ (as 5T5) Trivial
5.1.1649.1 x5 - x4 + x2 - x + 1 \( 17\cdot 97 \) $S_5$ (as 5T5) Trivial
5.1.1777.1 x5 - x4 + x3 - 2x2 + x - 1 \( 1777 \) $S_5$ (as 5T5) Trivial
5.1.2209.1 x5 - 2x4 + 2x3 - x2 + 1 \( 47^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.2297.1 x5 - x4 + x3 - x2 - 1 \( 2297 \) $S_5$ (as 5T5) Trivial
5.1.2617.1 x5 + x3 - 2x2 - 1 \( 2617 \) $S_5$ (as 5T5) Trivial
5.1.2665.1 x5 - x4 + x3 - x2 + 2x - 1 \( 5\cdot 13\cdot 41 \) $S_5$ (as 5T5) Trivial
5.1.2869.1 x5 - x - 1 \( 19\cdot 151 \) $S_5$ (as 5T5) Trivial
5.1.3017.1 x5 - x2 + 1 \( 7\cdot 431 \) $S_5$ (as 5T5) Trivial
5.1.3089.1 x5 - x3 + 2x - 1 \( 3089 \) $S_5$ (as 5T5) Trivial
5.1.3233.1 x5 - x2 - 1 \( 53\cdot 61 \) $S_5$ (as 5T5) Trivial
5.1.3369.1 x5 + x3 - x2 - x - 1 \( 3\cdot 1123 \) $S_5$ (as 5T5) Trivial
5.1.3857.1 x5 - x4 + x3 - x2 + 1 \( 7\cdot 19\cdot 29 \) $S_5$ (as 5T5) Trivial
5.1.3889.1 x5 - x4 + x3 + x - 1 \( 3889 \) $S_5$ (as 5T5) Trivial
5.1.4169.1 x5 + 2x3 - x2 + 2x - 1 \( 11\cdot 379 \) $S_5$ (as 5T5) Trivial
5.1.4261.1 x5 - 2x2 - 2x - 1 \( 4261 \) $S_5$ (as 5T5) Trivial
5.1.4409.1 x5 - x4 + x2 + x - 1 \( 4409 \) $S_5$ (as 5T5) Trivial
5.1.4417.1 x5 - 2x4 + 2x3 - x2 - 1 \( 7\cdot 631 \) $S_5$ (as 5T5) Trivial
5.1.4429.1 x5 - x4 + 2x3 - x2 + 1 \( 43\cdot 103 \) $S_5$ (as 5T5) Trivial
5.1.4432.1 x5 - x4 + 2x2 - x + 1 \( 2^{4}\cdot 277 \) $S_5$ (as 5T5) Trivial
5.1.4477.1 x5 + x3 + x - 1 \( 11^{2}\cdot 37 \) $S_5$ (as 5T5) Trivial
5.3.4511.1 x5 - x3 - 2x2 + 1 \( -\,13\cdot 347 \) $S_5$ (as 5T5) Trivial
5.1.4549.1 x5 - x4 + 2x3 - 2x2 - 1 \( 4549 \) $S_5$ (as 5T5) Trivial
5.1.4597.1 x5 + x3 - 2x2 - x - 1 \( 4597 \) $S_5$ (as 5T5) Trivial
5.1.4757.1 x5 - x4 + 2x3 - x2 + 2x - 1 \( 67\cdot 71 \) $S_5$ (as 5T5) Trivial
5.1.4817.1 x5 - 2x4 + 2x3 - x2 + 2x - 1 \( 4817 \) $S_5$ (as 5T5) Trivial
5.1.4897.1 x5 - x4 - x3 + x2 + 1 \( 59\cdot 83 \) $S_5$ (as 5T5) Trivial
5.3.4903.1 x5 - x4 - x3 + 2x2 - x - 1 \( -\,4903 \) $S_5$ (as 5T5) Trivial
5.1.5025.1 x5 - x4 - x2 + x + 1 \( 3\cdot 5^{2}\cdot 67 \) $S_5$ (as 5T5) Trivial
5.1.5164.1 x5 - x4 - x3 + 2x + 1 \( 2^{2}\cdot 1291 \) $S_5$ (as 5T5) Trivial
5.1.5437.1 x5 - 2x4 + 2x3 - 2x2 - 1 \( 5437 \) $S_5$ (as 5T5) Trivial
5.1.5501.1 x5 - 2x4 + 2x2 - x + 1 \( 5501 \) $S_5$ (as 5T5) Trivial
5.3.5519.1 x5 - x4 - x3 + 3x2 - 1 \( -\,5519 \) $S_5$ (as 5T5) Trivial
5.1.5584.1 x5 - x4 + x + 1 \( 2^{4}\cdot 349 \) $S_5$ (as 5T5) Trivial
5.1.5653.1 x5 - x4 + 2x - 1 \( 5653 \) $S_5$ (as 5T5) Trivial
5.1.5753.1 x5 - x4 - x3 + 2x2 - x + 1 \( 11\cdot 523 \) $S_5$ (as 5T5) Trivial
5.3.5783.1 x5 - 2x4 + x3 + 2x2 - 2x - 1 \( -\,5783 \) $S_5$ (as 5T5) Trivial
5.1.5864.1 x5 - x4 + x3 + 2x2 - 2x + 1 \( 2^{3}\cdot 733 \) $S_5$ (as 5T5) Trivial
5.1.5913.1 x5 - x4 + 2x3 - x2 + x + 1 \( 3^{4}\cdot 73 \) $S_5$ (as 5T5) Trivial
5.1.6241.1 x5 - x4 + x3 - 2x2 + 3x - 1 \( 79^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.6449.1 x5 - x4 + x3 - 3x2 - 1 \( 6449 \) $S_5$ (as 5T5) Trivial
5.1.6581.1 x5 - 2x2 - 1 \( 6581 \) $S_5$ (as 5T5) Trivial
5.1.6757.1 x5 - x4 + 3x2 - 2x + 1 \( 29\cdot 233 \) $S_5$ (as 5T5) Trivial
5.1.6793.1 x5 - x4 + x3 + x + 1 \( 6793 \) $S_5$ (as 5T5) Trivial
5.3.7031.1 x5 - x3 - x2 - x + 1 \( -\,79\cdot 89 \) $S_5$ (as 5T5) Trivial
5.1.7096.1 x5 - x2 + x + 1 \( 2^{3}\cdot 887 \) $S_5$ (as 5T5) Trivial
5.1.7177.1 x5 - x4 + 3x3 - x2 + 2x - 1 \( 7177 \) $S_5$ (as 5T5) Trivial
5.1.7265.1 x5 - x4 + x3 + 2x2 - x + 1 \( 5\cdot 1453 \) $S_5$ (as 5T5) Trivial
5.1.7333.1 x5 - 2x4 + 2x3 - 2x2 + 3x - 1 \( 7333 \) $S_5$ (as 5T5) Trivial
5.3.7367.1 x5 - 2x4 + 3x2 - 2x - 1 \( -\,53\cdot 139 \) $S_5$ (as 5T5) Trivial

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