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Label Polynomial Discriminant Galois group Class group
4.0.117.1 x4 - x3 - x2 + x + 1 \( 3^{2}\cdot 13 \) $D_{4}$ (as 4T3) Trivial
4.0.125.1 x4 - x3 + x2 - x + 1 \( 5^{3} \) $C_4$ (as 4T1) Trivial
4.0.144.1 x4 - x2 + 1 \( 2^{4}\cdot 3^{2} \) $C_2^2$ (as 4T2) Trivial
4.0.189.1 x4 - x3 + 2x + 1 \( 3^{3}\cdot 7 \) $D_{4}$ (as 4T3) Trivial
4.0.225.1 x4 - x3 + 2x2 + x + 1 \( 3^{2}\cdot 5^{2} \) $C_2^2$ (as 4T2) Trivial
4.0.229.1 x4 - x + 1 \( 229 \) $S_4$ (as 4T5) Trivial
4.0.256.1 x4 + 1 \( 2^{8} \) $C_2^2$ (as 4T2) Trivial
4.0.257.1 x4 + x2 - x + 1 \( 257 \) $S_4$ (as 4T5) Trivial
4.0.272.1 x4 + x2 - 2x + 1 \( 2^{4}\cdot 17 \) $D_{4}$ (as 4T3) Trivial
4.2.275.1 x4 - x3 + 2x - 1 \( -\,5^{2}\cdot 11 \) $D_{4}$ (as 4T3) Trivial
4.2.283.1 x4 - x - 1 \( -\,283 \) $S_4$ (as 4T5) Trivial
4.0.320.1 x4 - 2x3 + 2 \( 2^{6}\cdot 5 \) $D_{4}$ (as 4T3) Trivial
4.2.331.1 x4 - x3 + x2 + x - 1 \( -\,331 \) $S_4$ (as 4T5) Trivial
4.0.333.1 x4 - x3 - 2x2 + 3 \( 3^{2}\cdot 37 \) $D_{4}$ (as 4T3) Trivial
4.0.392.1 x4 - x3 + x + 1 \( 2^{3}\cdot 7^{2} \) $D_{4}$ (as 4T3) Trivial
4.2.400.1 x4 - x2 - 1 \( -\,2^{4}\cdot 5^{2} \) $D_{4}$ (as 4T3) Trivial
4.0.400.1 x4 + 3x2 + 1 \( 2^{4}\cdot 5^{2} \) $C_2^2$ (as 4T2) Trivial
4.0.432.1 x4 - 3x2 + 3 \( 2^{4}\cdot 3^{3} \) $D_{4}$ (as 4T3) Trivial
4.0.441.1 x4 - x3 - x2 - 2x + 4 \( 3^{2}\cdot 7^{2} \) $C_2^2$ (as 4T2) Trivial
4.2.448.1 x4 - 2x3 + x2 - 2x + 1 \( -\,2^{6}\cdot 7 \) $D_{4}$ (as 4T3) Trivial
4.2.475.1 x4 - 2x3 + 2x2 - x - 1 \( -\,5^{2}\cdot 19 \) $D_{4}$ (as 4T3) Trivial
4.2.491.1 x4 - x3 - x2 + 3x - 1 \( -\,491 \) $S_4$ (as 4T5) Trivial
4.2.507.1 x4 - x3 - x2 - x + 1 \( -\,3\cdot 13^{2} \) $D_{4}$ (as 4T3) Trivial
4.0.512.1 x4 - 2x2 + 2 \( 2^{9} \) $D_{4}$ (as 4T3) Trivial
4.0.513.1 x4 - x3 - 3x2 + 2x + 4 \( 3^{3}\cdot 19 \) $D_{4}$ (as 4T3) Trivial
4.0.549.1 x4 - 2x3 - 2x2 + 3x + 3 \( 3^{2}\cdot 61 \) $D_{4}$ (as 4T3) Trivial
4.2.563.1 x4 - x3 + x2 - x - 1 \( -\,563 \) $S_4$ (as 4T5) Trivial
4.0.576.1 x4 - 2x2 + 4 \( 2^{6}\cdot 3^{2} \) $C_2^2$ (as 4T2) Trivial
4.0.576.2 x4 + 2x2 + 4 \( 2^{6}\cdot 3^{2} \) $C_2^2$ (as 4T2) Trivial
4.0.592.1 x4 + 2x2 - 2x + 1 \( 2^{4}\cdot 37 \) $S_4$ (as 4T5) Trivial
4.0.605.1 x4 - x3 + x2 + x + 1 \( 5\cdot 11^{2} \) $D_{4}$ (as 4T3) Trivial
4.2.643.1 x4 - x3 - 2x + 1 \( -\,643 \) $S_4$ (as 4T5) Trivial
4.0.656.1 x4 - 2x3 - x2 + 2x + 2 \( 2^{4}\cdot 41 \) $D_{4}$ (as 4T3) Trivial
4.0.657.1 x4 - x3 + 5x2 - 2x + 4 \( 3^{2}\cdot 73 \) $D_{4}$ (as 4T3) Trivial
4.2.688.1 x4 - 2x - 1 \( -\,2^{4}\cdot 43 \) $S_4$ (as 4T5) Trivial
4.0.697.1 x4 - x3 + 2x2 - x + 2 \( 17\cdot 41 \) $S_4$ (as 4T5) Trivial
4.4.725.1 x4 - x3 - 3x2 + x + 1 \( 5^{2}\cdot 29 \) $D_{4}$ (as 4T3) Trivial
4.2.731.1 x4 - x3 + 2x2 - 1 \( -\,17\cdot 43 \) $S_4$ (as 4T5) Trivial
4.2.751.1 x4 - 2x3 + x2 - x - 1 \( -\,751 \) $S_4$ (as 4T5) Trivial
4.0.761.1 x4 - x3 + x2 + 2x + 1 \( 761 \) $S_4$ (as 4T5) Trivial
4.2.775.1 x4 - x3 - 3x - 1 \( -\,5^{2}\cdot 31 \) $D_{4}$ (as 4T3) Trivial
4.0.784.1 x4 - 3x2 + 4 \( 2^{4}\cdot 7^{2} \) $C_2^2$ (as 4T2) Trivial
4.0.788.1 x4 - x3 + 2x2 - 2x + 2 \( 2^{2}\cdot 197 \) $S_4$ (as 4T5) Trivial
4.0.832.1 x4 - 2x3 - 2x + 5 \( 2^{6}\cdot 13 \) $D_{4}$ (as 4T3) Trivial
4.0.837.1 x4 - x3 - 3x2 - x + 7 \( 3^{3}\cdot 31 \) $D_{4}$ (as 4T3) Trivial
4.2.848.1 x4 - x2 - 2x + 1 \( -\,2^{4}\cdot 53 \) $S_4$ (as 4T5) Trivial
4.0.873.1 x4 - x3 - 4x2 + x + 7 \( 3^{2}\cdot 97 \) $D_{4}$ (as 4T3) Trivial
4.0.892.1 x4 - x3 - x2 + 2 \( 2^{2}\cdot 223 \) $S_4$ (as 4T5) Trivial
4.2.976.1 x4 - 2x3 + 3x2 - 1 \( -\,2^{4}\cdot 61 \) $S_4$ (as 4T5) Trivial
4.0.981.1 x4 - x3 - 4x2 + 4x + 7 \( 3^{2}\cdot 109 \) $D_{4}$ (as 4T3) Trivial

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