## Results (1-50 of at least 1000)

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