Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
4.0.1921600.2 | $x^{4} - 2 x^{3} + 47 x^{2} + 104 x + 144$ | $2^{6}\cdot 5^{2}\cdot 1201$ | $D_{4}$ (as 4T3) | $[2, 58]$ |
4.0.2228265.3 | $x^{4} - x^{3} - 8 x^{2} - 108 x + 432$ | $3^{2}\cdot 5\cdot 13^{2}\cdot 293$ | $D_{4}$ (as 4T3) | $[104]$ |
4.0.2471625.1 | $x^{4} - x^{3} + 41 x^{2} - 191 x + 406$ | $3^{2}\cdot 5^{3}\cdot 13^{3}$ | $C_4$ (as 4T1) | $[2, 52]$ |
4.0.2712225.1 | $x^{4} - 2 x^{3} + 31 x^{2} - 30 x + 80$ | $3\cdot 5^{2}\cdot 29^{2}\cdot 43$ | $D_{4}$ (as 4T3) | $[104]$ |
4.0.2752576.4 | $x^{4} - 2 x^{3} + 111 x^{2} - 56 x + 2744$ | $2^{6}\cdot 41\cdot 1049$ | $D_{4}$ (as 4T3) | $[104]$ |
4.0.2764864.1 | $x^{4} - 2 x^{3} + 127 x^{2} - 24 x + 2744$ | $2^{6}\cdot 43201$ | $D_{4}$ (as 4T3) | $[105]$ |
4.0.2832200.2 | $x^{4} - x^{3} - x^{2} + 75 x + 270$ | $2^{3}\cdot 5^{2}\cdot 7^{2}\cdot 17^{2}$ | $D_{4}$ (as 4T3) | $[2, 60]$ |
4.0.2859400.2 | $x^{4} - x^{3} - 18 x + 324$ | $2^{3}\cdot 5^{2}\cdot 17\cdot 29^{2}$ | $D_{4}$ (as 4T3) | $[104]$ |
4.0.2892601.1 | $x^{4} - 2 x^{3} + 91 x^{2} - 90 x + 648$ | $17^{2}\cdot 10009$ | $D_{4}$ (as 4T3) | $[113]$ |
4.0.2921536.1 | $x^{4} - 2 x^{3} + 131 x^{2} - 24 x + 2898$ | $2^{6}\cdot 191\cdot 239$ | $D_{4}$ (as 4T3) | $[102]$ |
4.0.2943944.1 | $x^{4} - x^{3} + 31 x^{2} + 29 x + 60$ | $2^{3}\cdot 71^{2}\cdot 73$ | $D_{4}$ (as 4T3) | $[126]$ |
4.0.2958400.4 | $x^{4} + 38 x^{2} + 576$ | $2^{6}\cdot 5^{2}\cdot 43^{2}$ | $C_2^2$ (as 4T2) | $[140]$ |
4.0.3066001.1 | $x^{4} + 43 x^{2} + 900$ | $17^{2}\cdot 103^{2}$ | $C_2^2$ (as 4T2) | $[120]$ |
4.0.3079873.1 | $x^{4} - 2 x^{3} + 73 x^{2} - 72 x + 684$ | $17^{2}\cdot 10657$ | $D_{4}$ (as 4T3) | $[109]$ |
4.0.3100116.2 | $x^{4} - x^{3} + 9 x^{2} + 93 x + 216$ | $2^{2}\cdot 3\cdot 19\cdot 13597$ | $S_4$ (as 4T5) | $[102]$ |
4.0.3114553.1 | $x^{4} - 2 x^{3} + 59 x^{2} - 58 x + 688$ | $13\cdot 17^{2}\cdot 829$ | $D_{4}$ (as 4T3) | $[102]$ |
4.0.3169296.2 | $x^{4} + 73 x^{2} - 12 x + 1432$ | $2^{4}\cdot 3^{2}\cdot 13\cdot 1693$ | $D_{4}$ (as 4T3) | $[104]$ |
4.0.3182656.4 | $x^{4} - 2 x^{3} + 109 x^{2} - 108 x + 3362$ | $2^{6}\cdot 223^{2}$ | $C_2^2$ (as 4T2) | $[112]$ |
4.0.3186225.2 | $x^{4} - x^{3} + 34 x^{2} - 240 x + 480$ | $3^{2}\cdot 5^{2}\cdot 7^{2}\cdot 17^{2}$ | $C_2^2$ (as 4T2) | $[2, 60]$ |
4.0.3194944.1 | $x^{4} - 2 x^{3} + 121 x^{2} - 120 x + 3150$ | $2^{6}\cdot 49921$ | $D_{4}$ (as 4T3) | $[109]$ |
4.0.3246337.1 | $x^{4} - 2 x^{3} + 57 x^{2} - 56 x + 716$ | $17^{2}\cdot 47\cdot 239$ | $D_{4}$ (as 4T3) | $[108]$ |
4.0.3247168.10 | $x^{4} - 2 x^{3} + 139 x^{2} - 24 x + 3218$ | $2^{6}\cdot 113\cdot 449$ | $D_{4}$ (as 4T3) | $[110]$ |
4.0.3265600.7 | $x^{4} + 44 x^{2} - 60 x + 639$ | $2^{6}\cdot 5^{2}\cdot 13\cdot 157$ | $D_{4}$ (as 4T3) | $[116]$ |
4.0.3285641.1 | $x^{4} - x^{3} + 105 x^{2} - 63 x + 2966$ | $17^{2}\cdot 11369$ | $D_{4}$ (as 4T3) | $[103]$ |
4.0.3286800.1 | $x^{4} - 2 x^{3} + 79 x^{2} - 78 x + 1446$ | $2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 11\cdot 83$ | $D_{4}$ (as 4T3) | $[2, 54]$ |
4.0.3342400.4 | $x^{4} - 2 x^{3} + 77 x^{2} - 76 x + 1194$ | $2^{6}\cdot 5^{2}\cdot 2089$ | $D_{4}$ (as 4T3) | $[144]$ |
4.0.3349008.2 | $x^{4} + 97 x^{2} - 108 x + 1528$ | $2^{4}\cdot 3^{2}\cdot 13\cdot 1789$ | $D_{4}$ (as 4T3) | $[104]$ |
4.0.3369024.2 | $x^{4} - 2 x^{3} + 119 x^{2} - 76 x + 3358$ | $2^{6}\cdot 3^{2}\cdot 5849$ | $D_{4}$ (as 4T3) | $[102]$ |
4.0.3376192.4 | $x^{4} - 2 x^{3} + 141 x^{2} - 140 x + 3332$ | $2^{6}\cdot 71\cdot 743$ | $D_{4}$ (as 4T3) | $[110]$ |
4.0.3385057.2 | $x^{4} - x^{3} + 113 x^{2} - 135 x + 3078$ | $13\cdot 17^{3}\cdot 53$ | $D_{4}$ (as 4T3) | $[2, 58]$ |
4.0.3403553.2 | $x^{4} - 2 x^{3} + 65 x^{2} - 64 x + 752$ | $17^{2}\cdot 11777$ | $D_{4}$ (as 4T3) | $[105]$ |
4.0.3438864.1 | $x^{4} - 2 x^{3} + 103 x^{2} - 102 x + 1518$ | $2^{4}\cdot 3^{2}\cdot 11\cdot 13\cdot 167$ | $D_{4}$ (as 4T3) | $[2, 52]$ |
4.0.3441025.4 | $x^{4} + 183 x^{2} + 8836$ | $5^{2}\cdot 7^{2}\cdot 53^{2}$ | $C_2^2$ (as 4T2) | $[112]$ |
4.0.3441232.1 | $x^{4} + 11 x^{2} - 18 x + 90$ | $2^{4}\cdot 215077$ | $S_4$ (as 4T5) | $[106]$ |
4.0.3445776.1 | $x^{4} - 2 x^{3} + 91 x^{2} - 90 x + 1518$ | $2^{4}\cdot 3^{2}\cdot 23929$ | $D_{4}$ (as 4T3) | $[118]$ |
4.0.3462208.1 | $x^{4} - 2 x^{3} + 147 x^{2} - 20 x + 3428$ | $2^{6}\cdot 47\cdot 1151$ | $D_{4}$ (as 4T3) | $[104]$ |
4.0.3486025.1 | $x^{4} - x^{3} + 188 x^{2} - 67 x + 8779$ | $5^{2}\cdot 19\cdot 41\cdot 179$ | $D_{4}$ (as 4T3) | $[2, 52]$ |
4.0.3508288.2 | $x^{4} - 2 x^{3} + 119 x^{2} - 92 x + 3502$ | $2^{6}\cdot 7\cdot 41\cdot 191$ | $D_{4}$ (as 4T3) | $[2, 54]$ |
4.0.3559824.1 | $x^{4} + 79 x^{2} - 30 x + 1606$ | $2^{4}\cdot 3^{2}\cdot 59\cdot 419$ | $D_{4}$ (as 4T3) | $[106]$ |
4.0.3572076.2 | $x^{4} - 2 x^{3} + x^{2} - 12 x + 324$ | $2^{2}\cdot 3\cdot 19\cdot 15667$ | $S_4$ (as 4T5) | $[112]$ |
4.0.3582016.2 | $x^{4} - 2 x^{3} + 121 x^{2} - 120 x + 3528$ | $2^{6}\cdot 97\cdot 577$ | $D_{4}$ (as 4T3) | $[106]$ |
4.0.3585025.1 | $x^{4} - x^{3} + 199 x^{2} - 30 x + 9020$ | $5^{2}\cdot 143401$ | $D_{4}$ (as 4T3) | $[103]$ |
4.0.3609664.2 | $x^{4} - 2 x^{3} + 125 x^{2} - 124 x + 3556$ | $2^{6}\cdot 56401$ | $D_{4}$ (as 4T3) | $[111]$ |
4.0.3624000.2 | $x^{4} + 60 x^{2} - 140 x + 735$ | $2^{6}\cdot 3\cdot 5^{3}\cdot 151$ | $D_{4}$ (as 4T3) | $[4, 28]$ |
4.0.3624025.1 | $x^{4} - x^{3} + 198 x^{2} - 37 x + 9119$ | $5^{2}\cdot 144961$ | $D_{4}$ (as 4T3) | $[103]$ |
4.0.3645504.2 | $x^{4} - 2 x^{3} + 153 x^{2} - 152 x + 3598$ | $2^{6}\cdot 3^{2}\cdot 6329$ | $D_{4}$ (as 4T3) | $[110]$ |
4.0.3664809.1 | $x^{4} - 2 x^{3} + 63 x^{2} - 62 x + 808$ | $3^{2}\cdot 17^{2}\cdot 1409$ | $D_{4}$ (as 4T3) | $[106]$ |
4.0.3687025.1 | $x^{4} - x^{3} + 193 x^{2} - 72 x + 9284$ | $5^{2}\cdot 147481$ | $D_{4}$ (as 4T3) | $[101]$ |
4.0.3698184.1 | $x^{4} - 2 x^{3} + 42 x^{2} + 42 x + 45$ | $2^{3}\cdot 3\cdot 7\cdot 22013$ | $S_4$ (as 4T5) | $[103]$ |
4.0.3722225.1 | $x^{4} - 2 x^{3} + 37 x^{2} - 36 x + 64$ | $5^{2}\cdot 13^{2}\cdot 881$ | $D_{4}$ (as 4T3) | $[2, 54]$ |