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Label Polynomial Discriminant Galois group Class group
4.4.725.1 x4 - x3 - 3x2 + x + 1 \( 5^{2}\cdot 29 \) $D_{4}$ (as 4T3) trivial
4.0.1421.1 x4 - 2x3 + 2x2 - x + 2 \( 7^{2}\cdot 29 \) $D_{4}$ (as 4T3) trivial
4.2.1856.1 x4 - 2x3 + x2 - 2x - 1 \( -\,2^{6}\cdot 29 \) $S_4$ (as 4T5) trivial
4.0.1856.1 x4 - 2x3 - 4x + 10 \( 2^{6}\cdot 29 \) $D_{4}$ (as 4T3) trivial
4.0.2320.1 x4 - 2x3 - 3x2 + 4x + 8 \( 2^{4}\cdot 5\cdot 29 \) $D_{4}$ (as 4T3) trivial
4.0.2320.2 x4 + x2 - 6x + 9 \( 2^{4}\cdot 5\cdot 29 \) $D_{4}$ (as 4T3) trivial
4.0.2349.1 x4 - x3 + 3x2 - 3x + 3 \( 3^{4}\cdot 29 \) $S_4$ (as 4T5) trivial
4.0.4901.1 x4 - 2x3 + 6x2 - 5x + 3 \( 13^{2}\cdot 29 \) $D_{4}$ (as 4T3) trivial
4.0.7540.1 x4 - x3 + 5x2 - x + 6 \( 2^{2}\cdot 5\cdot 13\cdot 29 \) $S_4$ (as 4T5) trivial
4.2.7975.2 x4 - 2x3 + x2 - 20 \( -\,5^{2}\cdot 11\cdot 29 \) $D_{4}$ (as 4T3) $[2]$
4.2.8236.1 x4 + 6x2 - 2x - 1 \( -\,2^{2}\cdot 29\cdot 71 \) $S_4$ (as 4T5) trivial
4.2.9019.1 x4 - x3 + x2 - x - 3 \( -\,29\cdot 311 \) $S_4$ (as 4T5) trivial
4.0.11020.1 x4 - x3 + 5x2 + 2 \( 2^{2}\cdot 5\cdot 19\cdot 29 \) $S_4$ (as 4T5) trivial
4.2.11252.1 x4 - x3 - 4x2 - x + 3 \( -\,2^{2}\cdot 29\cdot 97 \) $S_4$ (as 4T5) trivial
4.0.11368.2 x4 - x3 + 6x2 + 5x + 11 \( 2^{3}\cdot 7^{2}\cdot 29 \) $D_{4}$ (as 4T3) $[2]$
4.2.11600.1 x4 - 3x2 - 29 \( -\,2^{4}\cdot 5^{2}\cdot 29 \) $D_{4}$ (as 4T3) $[2]$
4.2.11600.2 x4 + 3x2 - 29 \( -\,2^{4}\cdot 5^{2}\cdot 29 \) $D_{4}$ (as 4T3) $[2]$
4.0.11600.1 x4 + 11x2 + 29 \( 2^{4}\cdot 5^{2}\cdot 29 \) $D_{4}$ (as 4T3) $[2]$
4.2.11948.1 x4 - x3 + 8x - 16 \( -\,2^{2}\cdot 29\cdot 103 \) $S_4$ (as 4T5) trivial
4.2.12267.1 x4 + 2x2 - 3x - 2 \( -\,3^{2}\cdot 29\cdot 47 \) $S_4$ (as 4T5) trivial
4.2.13775.2 x4 - x3 + 5x2 + 12x - 36 \( -\,5^{2}\cdot 19\cdot 29 \) $D_{4}$ (as 4T3) $[2]$
4.0.14036.1 x4 - 2x2 - 2x + 7 \( 2^{2}\cdot 11^{2}\cdot 29 \) $S_4$ (as 4T5) trivial
4.0.14384.1 x4 - 8x + 11 \( 2^{4}\cdot 29\cdot 31 \) $S_4$ (as 4T5) trivial
4.2.14703.1 x4 + 5x2 - x - 1 \( -\,3\cdot 13^{2}\cdot 29 \) $S_4$ (as 4T5) trivial
4.2.14703.3 x4 - x3 + 3x2 + 10x - 4 \( -\,3\cdot 13^{2}\cdot 29 \) $D_{4}$ (as 4T3) trivial
4.0.14848.1 x4 - 14x2 + 58 \( 2^{9}\cdot 29 \) $D_{4}$ (as 4T3) trivial
4.0.14993.1 x4 - x3 - 4x2 + x + 8 \( 11\cdot 29\cdot 47 \) $S_4$ (as 4T5) trivial
4.0.15341.1 x4 - x3 - 2x2 + 4x + 16 \( 23^{2}\cdot 29 \) $D_{4}$ (as 4T3) $[3]$
4.2.15544.1 x4 - x3 + 4x2 - 2x - 4 \( -\,2^{3}\cdot 29\cdot 67 \) $S_4$ (as 4T5) trivial
4.2.15544.2 x4 - x3 + 7x + 1 \( -\,2^{3}\cdot 29\cdot 67 \) $S_4$ (as 4T5) trivial
4.0.15689.1 x4 - x3 + 4x2 + x + 7 \( 29\cdot 541 \) $S_4$ (as 4T5) trivial
4.0.17168.2 x4 - 3x2 - 16x + 68 \( 2^{4}\cdot 29\cdot 37 \) $D_{4}$ (as 4T3) trivial
4.0.17893.1 x4 - x3 + 6x2 - 3x + 13 \( 29\cdot 617 \) $S_4$ (as 4T5) trivial
4.0.19604.1 x4 - x3 + 4x2 + 4x + 2 \( 2^{2}\cdot 13^{2}\cdot 29 \) $S_4$ (as 4T5) trivial
4.2.20039.1 x4 - 2x3 + x2 - 9x + 5 \( -\,29\cdot 691 \) $S_4$ (as 4T5) trivial
4.0.20532.1 x4 - x3 + 2x2 - 4x + 10 \( 2^{2}\cdot 3\cdot 29\cdot 59 \) $S_4$ (as 4T5) trivial
4.2.20619.1 x4 - 4x2 - 3x + 4 \( -\,3^{2}\cdot 29\cdot 79 \) $S_4$ (as 4T5) trivial
4.2.22475.2 x4 - 2x3 + 6x2 - 5x - 55 \( -\,5^{2}\cdot 29\cdot 31 \) $D_{4}$ (as 4T3) $[2]$
4.2.22504.1 x4 - 2x3 + 2x2 + 2x - 19 \( -\,2^{3}\cdot 29\cdot 97 \) $S_4$ (as 4T5) trivial
4.2.22736.1 x4 - x2 - 14x + 9 \( -\,2^{4}\cdot 7^{2}\cdot 29 \) $S_4$ (as 4T5) trivial
4.0.22736.1 x4 + 2x2 - 6x + 9 \( 2^{4}\cdot 7^{2}\cdot 29 \) $S_4$ (as 4T5) trivial
4.0.22736.2 x4 - 2x2 + 29 \( 2^{4}\cdot 7^{2}\cdot 29 \) $D_{4}$ (as 4T3) $[2]$
4.2.23200.1 x4 + x2 - 6x + 2 \( -\,2^{5}\cdot 5^{2}\cdot 29 \) $S_4$ (as 4T5) trivial
4.2.24012.1 x4 - x3 - 8x2 + 12 \( -\,2^{2}\cdot 3^{2}\cdot 23\cdot 29 \) $S_4$ (as 4T5) trivial
4.0.24621.1 x4 - x3 + 8x2 - 3x + 3 \( 3\cdot 29\cdot 283 \) $S_4$ (as 4T5) trivial
4.2.25056.1 x4 - 2x3 - 2x - 17 \( -\,2^{5}\cdot 3^{3}\cdot 29 \) $S_4$ (as 4T5) trivial
4.0.25172.1 x4 - x3 + 7x2 + x + 4 \( 2^{2}\cdot 7\cdot 29\cdot 31 \) $S_4$ (as 4T5) $[3]$
4.2.25288.1 x4 - x3 - 5x2 - 2x - 2 \( -\,2^{3}\cdot 29\cdot 109 \) $S_4$ (as 4T5) trivial
4.0.26680.1 x4 - x3 - 6x2 + x + 15 \( 2^{3}\cdot 5\cdot 23\cdot 29 \) $S_4$ (as 4T5) $[5]$
4.4.26825.1 x4 - 2x3 - 5x2 + 5x + 5 \( 5^{2}\cdot 29\cdot 37 \) $S_4$ (as 4T5) trivial
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