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

Label Polynomial Discriminant Galois group Class group
4.4.39605.1 x4 - 2x3 - 8x2 + 9x - 2 $$5\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.0.71289.1 x4 - x3 + 23x2 + 22x + 484 $$3^{2}\cdot 89^{2}$$ $C_2^2$ (as 4T2) trivial
4.0.134657.1 x4 - x3 - 6x2 - 8x + 64 $$17\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[7]$
4.2.158420.1 x4 - 3x2 - 20 $$-\,2^{2}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.2.158420.2 x4 + 3x2 - 20 $$-\,2^{2}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.2.285156.1 x4 - x3 - 7x2 + 37x + 34 $$-\,2^{2}\cdot 3^{2}\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.2.316840.1 x4 - 7x2 - 10 $$-\,2^{3}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.2.316840.2 x4 + 14x2 - 40 $$-\,2^{3}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.0.316840.1 x4 - x3 - 4x2 - 9x + 81 $$2^{3}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.0.316840.2 x4 - x3 - 3x2 + 35x + 68 $$2^{3}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[8]$
4.2.372287.1 x4 - x3 - 9x2 + 38x + 20 $$-\,47\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.0.388129.1 x4 - 41x2 + 576 $$7^{2}\cdot 89^{2}$$ $C_2^2$ (as 4T2) $[11]$
4.0.419813.1 x4 - 2x3 + 22x2 - 21x + 88 $$53\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[5]$
4.2.435655.1 x4 - 2x3 + 5x2 - 4x - 85 $$-\,5\cdot 11\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.2.435655.2 x4 - 2x3 - 17x2 + 18x - 8 $$-\,5\cdot 11\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.2.538628.1 x4 - x3 - 5x2 + 36x + 50 $$-\,2^{2}\cdot 17\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.2.538628.2 x4 - x3 - 10x2 + 83x - 53 $$-\,2^{2}\cdot 17\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.2.562391.1 x4 - x3 - 19x2 - 46x - 20 $$-\,71\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.2.570312.1 x4 - 27x2 - 18 $$-\,2^{3}\cdot 3^{2}\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.4.570312.1 x4 - x3 - 19x2 + 43x - 20 $$2^{3}\cdot 3^{2}\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.2.625759.1 x4 - x3 - 3x2 - 54x + 68 $$-\,79\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.0.633680.1 x4 + 13x2 + 20 $$2^{4}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2, 2]$
4.0.641601.1 x4 - x3 - 11x + 32 $$3^{4}\cdot 89^{2}$$ $A_4$ (as 4T4) $[2]$
4.2.784179.1 x4 - 2x3 - 12x2 + 13x - 158 $$-\,3^{2}\cdot 11\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.2.847547.1 x4 - 2x3 - 10x2 + 11x - 170 $$-\,89^{2}\cdot 107$$ $D_{4}$ (as 4T3) trivial
4.0.863389.1 x4 - x3 + 5x2 - 58x + 160 $$89^{2}\cdot 109$$ $D_{4}$ (as 4T3) $[11]$
4.2.1037651.1 x4 - 2x3 - 6x2 + 7x - 10 $$-\,89^{2}\cdot 131$$ $D_{4}$ (as 4T3) trivial
4.2.1077256.1 x4 - x3 - 21x2 - 45x - 22 $$-\,2^{3}\cdot 17\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.2.1077256.2 x4 - x3 - 9x2 - 51x + 20 $$-\,2^{3}\cdot 17\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[3]$
4.4.1077256.1 x4 - 15x2 + 34 $$2^{3}\cdot 17\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.4.1077256.2 x4 - 30x2 + 136 $$2^{3}\cdot 17\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.0.1140624.1 x4 + 43x2 + 529 $$2^{4}\cdot 3^{2}\cdot 89^{2}$$ $C_2^2$ (as 4T2) $[12]$
4.4.1140624.1 x4 - 2x3 - 49x2 + 50x + 358 $$2^{4}\cdot 3^{2}\cdot 89^{2}$$ $C_2^2$ (as 4T2) trivial
4.0.1140624.3 x4 - 89x2 + 7921 $$2^{4}\cdot 3^{2}\cdot 89^{2}$$ $C_2^2$ (as 4T2) $[12]$
4.0.1243597.1 x4 - x3 + 2x2 - 12x + 144 $$89^{2}\cdot 157$$ $D_{4}$ (as 4T3) $[9]$
4.2.1267360.1 x4 - 14x2 - 40 $$-\,2^{5}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.2.1267360.2 x4 + 7x2 - 10 $$-\,2^{5}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.4.1267360.1 x4 - 29x2 + 10 $$2^{5}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.4.1267360.2 x4 - 27x2 + 160 $$2^{5}\cdot 5\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[2]$
4.4.1338649.1 x4 - 51x2 + 361 $$13^{2}\cdot 89^{2}$$ $C_2^2$ (as 4T2) trivial
4.4.1370333.1 x4 - 2x3 - 10x2 + 11x + 8 $$89^{2}\cdot 173$$ $D_{4}$ (as 4T3) trivial
4.2.1481227.1 x4 - x3 - 20x2 + 88x - 88 $$-\,11\cdot 17\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.2.1481227.2 x4 - 2x3 + 8x2 - 7x - 10 $$-\,11\cdot 17\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.0.1489148.1 x4 + 29x2 + 188 $$2^{2}\cdot 47\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[10]$
4.4.1489148.1 x4 - x3 - 18x2 - 2x + 4 $$2^{2}\cdot 47\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.0.1497069.1 x4 - x3 + 201x2 - 67x + 10363 $$3^{3}\cdot 7\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[14]$
4.2.1552516.1 x4 - x3 - 2x2 + 79x + 11 $$-\,2^{2}\cdot 7^{2}\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial
4.2.1576279.1 x4 - 2x3 + 19x2 - 18x - 8 $$-\,89^{2}\cdot 199$$ $D_{4}$ (as 4T3) trivial
4.2.1679252.1 x4 - 12x2 - 53 $$-\,2^{2}\cdot 53\cdot 89^{2}$$ $D_{4}$ (as 4T3) $[3]$
4.2.1679252.2 x4 + 12x2 - 53 $$-\,2^{2}\cdot 53\cdot 89^{2}$$ $D_{4}$ (as 4T3) trivial