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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
4.4.1125.1 x4 - x3 - 4x2 + 4x + 1 \( 3^{2}\cdot 5^{3} \) $C_4$ (as 4T1) Trivial
4.4.1600.1 x4 - 6x2 + 4 \( 2^{6}\cdot 5^{2} \) $C_2^2$ (as 4T2) Trivial
4.4.1957.1 x4 - 4x2 - x + 1 \( 19\cdot 103 \) $S_4$ (as 4T5) Trivial
4.4.2000.1 x4 - 5x2 + 5 \( 2^{4}\cdot 5^{3} \) $C_4$ (as 4T1) Trivial
4.4.2048.1 x4 - 4x2 + 2 \( 2^{11} \) $C_4$ (as 4T1) Trivial
4.4.2225.1 x4 - x3 - 5x2 + 2x + 4 \( 5^{2}\cdot 89 \) $D_{4}$ (as 4T3) Trivial
4.4.2304.1 x4 - 4x2 + 1 \( 2^{8}\cdot 3^{2} \) $C_2^2$ (as 4T2) Trivial
4.4.2525.1 x4 - 2x3 - 4x2 + 5x + 5 \( 5^{2}\cdot 101 \) $D_{4}$ (as 4T3) Trivial
4.4.2624.1 x4 - 2x3 - 3x2 + 2x + 1 \( 2^{6}\cdot 41 \) $D_{4}$ (as 4T3) Trivial
4.4.2777.1 x4 - x3 - 4x2 + x + 2 \( 2777 \) $S_4$ (as 4T5) Trivial
4.4.3600.1 x4 - 2x3 - 7x2 + 8x + 1 \( 2^{4}\cdot 3^{2}\cdot 5^{2} \) $C_2^2$ (as 4T2) Trivial
4.4.3981.1 x4 - x3 - 4x2 + 2x + 1 \( 3\cdot 1327 \) $S_4$ (as 4T5) Trivial
4.4.4205.1 x4 - x3 - 5x2 - x + 1 \( 5\cdot 29^{2} \) $D_{4}$ (as 4T3) Trivial
4.4.4225.1 x4 - 9x2 + 4 \( 5^{2}\cdot 13^{2} \) $C_2^2$ (as 4T2) Trivial
4.4.4352.1 x4 - 6x2 - 4x + 2 \( 2^{8}\cdot 17 \) $D_{4}$ (as 4T3) Trivial
4.4.4400.1 x4 - 7x2 + 11 \( 2^{4}\cdot 5^{2}\cdot 11 \) $D_{4}$ (as 4T3) Trivial
4.4.4525.1 x4 - x3 - 7x2 + 3x + 9 \( 5^{2}\cdot 181 \) $D_{4}$ (as 4T3) Trivial
4.4.4752.1 x4 - 2x3 - 3x2 + 4x + 1 \( 2^{4}\cdot 3^{3}\cdot 11 \) $D_{4}$ (as 4T3) Trivial
4.4.4913.1 x4 - x3 - 6x2 + x + 1 \( 17^{3} \) $C_4$ (as 4T1) Trivial
4.4.5125.1 x4 - 2x3 - 6x2 + 7x + 11 \( 5^{3}\cdot 41 \) $D_{4}$ (as 4T3) Trivial
4.4.5225.1 x4 - x3 - 8x2 + x + 11 \( 5^{2}\cdot 11\cdot 19 \) $D_{4}$ (as 4T3) Trivial
4.4.5725.1 x4 - x3 - 8x2 + 6x + 11 \( 5^{2}\cdot 229 \) $D_{4}$ (as 4T3) Trivial
4.4.5744.1 x4 - 5x2 - 2x + 1 \( 2^{4}\cdot 359 \) $S_4$ (as 4T5) Trivial
4.4.6125.1 x4 - x3 - 9x2 + 9x + 11 \( 5^{3}\cdot 7^{2} \) $C_4$ (as 4T1) Trivial
4.4.6224.1 x4 - 6x2 - 2x + 5 \( 2^{4}\cdot 389 \) $S_4$ (as 4T5) Trivial
4.4.6809.1 x4 - 5x2 - x + 1 \( 11\cdot 619 \) $S_4$ (as 4T5) Trivial
4.4.7053.1 x4 - 2x3 - 4x2 + 3x + 3 \( 3\cdot 2351 \) $S_4$ (as 4T5) Trivial
4.4.7056.1 x4 - 5x2 + 1 \( 2^{4}\cdot 3^{2}\cdot 7^{2} \) $C_2^2$ (as 4T2) Trivial
4.4.7168.1 x4 - 6x2 + 7 \( 2^{10}\cdot 7 \) $D_{4}$ (as 4T3) Trivial
4.4.7225.1 x4 - 11x2 + 9 \( 5^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) Trivial
4.4.7232.1 x4 - 2x3 - 5x2 + 4x + 4 \( 2^{6}\cdot 113 \) $D_{4}$ (as 4T3) Trivial
4.4.7488.1 x4 - 2x3 - 4x2 + 2x + 1 \( 2^{6}\cdot 3^{2}\cdot 13 \) $D_{4}$ (as 4T3) Trivial
4.4.7537.1 x4 - x3 - 5x2 + 4x + 3 \( 7537 \) $S_4$ (as 4T5) Trivial
4.4.7600.1 x4 - 9x2 + 19 \( 2^{4}\cdot 5^{2}\cdot 19 \) $D_{4}$ (as 4T3) Trivial
4.4.7625.1 x4 - x3 - 9x2 + 4x + 16 \( 5^{3}\cdot 61 \) $D_{4}$ (as 4T3) Trivial
4.4.8000.1 x4 - 10x2 + 20 \( 2^{6}\cdot 5^{3} \) $C_4$ (as 4T1) Trivial
4.4.8069.1 x4 - x3 - 5x2 + 5x + 1 \( 8069 \) $S_4$ (as 4T5) Trivial
4.4.8112.1 x4 - 5x2 + 3 \( 2^{4}\cdot 3\cdot 13^{2} \) $D_{4}$ (as 4T3) Trivial
4.4.8468.1 x4 - x3 - 5x2 + 3x + 4 \( 2^{2}\cdot 29\cdot 73 \) $S_4$ (as 4T5) Trivial
4.4.8525.1 x4 - 2x3 - 8x2 + 9x + 19 \( 5^{2}\cdot 11\cdot 31 \) $D_{4}$ (as 4T3) Trivial
4.4.8725.1 x4 - x3 - 10x2 + 2x + 19 \( 5^{2}\cdot 349 \) $D_{4}$ (as 4T3) Trivial
4.4.8768.1 x4 - 2x3 - 5x2 + 6x + 7 \( 2^{6}\cdot 137 \) $D_{4}$ (as 4T3) Trivial
4.4.8789.1 x4 - x3 - 6x2 - 2x + 1 \( 11\cdot 17\cdot 47 \) $S_4$ (as 4T5) Trivial
4.4.8957.1 x4 - x3 - 5x2 + x + 1 \( 13^{2}\cdot 53 \) $D_{4}$ (as 4T3) Trivial
4.4.9225.1 x4 - x3 - 10x2 + 7x + 19 \( 3^{2}\cdot 5^{2}\cdot 41 \) $D_{4}$ (as 4T3) Trivial
4.4.9248.1 x4 - 5x2 + 2 \( 2^{5}\cdot 17^{2} \) $D_{4}$ (as 4T3) Trivial
4.4.9301.1 x4 - x3 - 5x2 + x + 3 \( 71\cdot 131 \) $S_4$ (as 4T5) Trivial
4.4.9792.1 x4 - 2x3 - 7x2 + 2x + 7 \( 2^{6}\cdot 3^{2}\cdot 17 \) $D_{4}$ (as 4T3) Trivial
4.4.9909.1 x4 - 6x2 - 3x + 3 \( 3^{3}\cdot 367 \) $S_4$ (as 4T5) Trivial

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