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 |
---|---|---|---|---|
14.0.21235828992734375.1 | $x^{14} - 2 x^{13} - 5 x^{12} + 12 x^{11} - 10 x^{10} - 7 x^{9} + 55 x^{8} - 28 x^{7} + 65 x^{6} - 2 x^{5} + 106 x^{4} - 70 x^{3} + 50 x^{2} + 25 x + 25$ | $-\,5^{7}\cdot 43^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.0.30022991642848691.1 | $x^{14} - 5 x^{13} + 7 x^{12} + 5 x^{10} - 35 x^{9} + 23 x^{8} + 79 x^{7} - 172 x^{6} + 143 x^{5} - 28 x^{4} - 116 x^{3} + 271 x^{2} - 279 x + 107$ | $-\,71^{7}\cdot 3301$ | $C_2\wr D_7$ (as 14T38) | $[2]$ |
14.0.82184209159918343.1 | $x^{14} - x^{13} + 7 x^{12} - 8 x^{11} + 23 x^{10} - 25 x^{9} + 47 x^{8} - 36 x^{7} + 61 x^{6} - 21 x^{5} + 78 x^{4} + 20 x^{3} + 62 x^{2} + 8 x + 27$ | $-\,17^{6}\cdot 23^{7}$ | $D_{14}$ (as 14T3) | $[3]$ |
14.0.149014448675078144.1 | $x^{14} - x^{12} - 7 x^{10} + 15 x^{8} + 13 x^{6} - 49 x^{4} + 6 x^{2} + 71$ | $-\,2^{14}\cdot 71^{7}$ | $C_2^6:D_7$ (as 14T27) | $[2]$ |
14.0.149014448675078144.2 | $x^{14} - x^{12} - 7 x^{10} + 15 x^{8} + 13 x^{6} - 49 x^{4} + 6 x^{2} + 71$ | $-\,2^{14}\cdot 71^{7}$ | $C_2^6:D_7$ (as 14T27) | $[2]$ |
14.0.149014448675078144.3 | $x^{14} - x^{12} - 7 x^{10} + 15 x^{8} + 13 x^{6} - 49 x^{4} + 6 x^{2} + 71$ | $-\,2^{14}\cdot 71^{7}$ | $C_2^6:D_7$ (as 14T27) | $[2]$ |
14.0.160388518974780383.1 | $x^{14} - 6 x^{13} + 25 x^{12} - 68 x^{11} + 149 x^{10} - 219 x^{9} + 279 x^{8} - 193 x^{7} + 254 x^{6} + 10 x^{5} + 158 x^{4} + 341 x^{3} + 334 x^{2} + 135 x + 25$ | $-\,7^{7}\cdot 41^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.0.370903242964296875.1 | $x^{14} - 7 x^{13} + 28 x^{12} - 70 x^{11} + 119 x^{10} - 140 x^{9} + 105 x^{8} - 53 x^{7} + 14 x^{6} - 7 x^{5} + 42 x^{4} - 42 x^{3} + 35 x^{2} - 14 x + 4$ | $-\,5^{7}\cdot 7^{15}$ | $F_7$ (as 14T4) | $[2]$ |
14.0.371923669440000000.1 | $x^{14} - 3 x^{12} - 3 x^{10} + 13 x^{8} + 51 x^{6} + 111 x^{4} + 91 x^{2} + 15$ | $-\,2^{12}\cdot 3^{19}\cdot 5^{7}$ | $F_7$ (as 14T4) | $[2]$ |
14.0.710556262374296875.1 | $x^{14} - 4 x^{13} + 20 x^{12} - 52 x^{11} + 151 x^{10} - 284 x^{9} + 582 x^{8} - 776 x^{7} + 1257 x^{6} - 1312 x^{5} + 2111 x^{4} - 2209 x^{3} + 2979 x^{2} - 2242 x + 1589$ | $-\,5^{7}\cdot 71^{7}$ | $D_{14}$ (as 14T3) | $[4]$ |
14.0.139...831.1 | $x^{14} - 2 x^{13} - 7 x^{12} + 15 x^{11} + 28 x^{10} - 76 x^{9} - 28 x^{8} + 78 x^{7} - 136 x^{6} + 188 x^{5} + 421 x^{4} + 342 x^{3} + 995 x^{2} + 391 x + 391$ | $-\,17^{7}\cdot 23^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.0.147...091.1 | $x^{14} - 4 x^{13} + 9 x^{12} - 20 x^{11} + 64 x^{10} - 163 x^{9} + 248 x^{8} - 197 x^{7} + 73 x^{6} - 76 x^{5} + 182 x^{4} - 203 x^{3} + 113 x^{2} - 30 x + 4$ | $-\,7^{7}\cdot 13^{11}$ | $F_7$ (as 14T4) | $[2]$ |
14.0.175...184.1 | $x^{14} - 4 x^{13} + 10 x^{12} - 14 x^{11} + 54 x^{10} - 66 x^{9} + 68 x^{8} + 134 x^{7} + 369 x^{6} - 90 x^{5} + 194 x^{4} - 56 x^{3} + 264 x^{2} + 96 x + 64$ | $-\,2^{14}\cdot 101^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.0.202...487.1 | $x^{14} - 3 x^{13} + 11 x^{12} - 26 x^{11} + 65 x^{10} - 64 x^{9} + 69 x^{8} - 51 x^{7} + 82 x^{6} - 45 x^{5} + 30 x^{4} - 15 x^{3} + 22 x^{2} - 20 x + 8$ | $-\,23^{7}\cdot 29^{6}$ | $C_7 \wr C_2$ (as 14T8) | $[3]$ |
14.0.250...875.1 | $x^{14} - 2 x^{13} + x^{12} - 5 x^{11} + 23 x^{10} - 29 x^{9} + 28 x^{8} - 16 x^{7} + 42 x^{6} - 59 x^{5} - 66 x^{4} + 205 x^{3} - 61 x^{2} - 104 x + 69$ | $-\,5^{6}\cdot 107^{7}$ | $D_{14}$ (as 14T3) | $[3]$ |
14.0.276...911.1 | $x^{14} + 6 x^{12} + 65 x^{10} + 50 x^{8} + 430 x^{6} + 575 x^{4} + 895 x^{2} + 431$ | $-\,431^{7}$ | $D_{7}$ (as 14T2) | $[3]$ |
14.0.356...663.1 | $x^{14} - 4 x^{13} + 4 x^{12} - 5 x^{11} + 26 x^{10} - 14 x^{9} + 55 x^{8} - 379 x^{7} + 1252 x^{6} - 2247 x^{5} + 2859 x^{4} - 2493 x^{3} + 1674 x^{2} - 729 x + 729$ | $-\,3^{7}\cdot 149^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.2.415...224.1 | $x^{14} - x^{13} - 7 x^{12} + 9 x^{11} + 25 x^{10} + 3 x^{9} - 117 x^{8} - 73 x^{7} + 406 x^{6} + 26 x^{5} - 480 x^{4} - 164 x^{3} + 456 x^{2} + 204 x - 116$ | $2^{12}\cdot 317^{6}$ | $\PSL(2,7)$ (as 14T10) | $[3]$ |
14.2.415...224.2 | $x^{14} - x^{13} + x^{12} + 7 x^{11} + 9 x^{10} - 5 x^{9} + 21 x^{8} + 63 x^{7} + 32 x^{6} + 74 x^{5} + 188 x^{4} + 70 x^{3} - 230 x^{2} - 144 x - 22$ | $2^{12}\cdot 317^{6}$ | $\PSL(2,7)$ (as 14T10) | $[3]$ |
14.2.578...953.1 | $x^{14} - 6 x^{13} + 20 x^{12} - 51 x^{11} + 106 x^{10} - 190 x^{9} + 304 x^{8} - 447 x^{7} + 608 x^{6} - 760 x^{5} + 848 x^{4} - 816 x^{3} + 640 x^{2} - 384 x + 128$ | $17^{3}\cdot 23^{4}\cdot 64879^{2}$ | $C_2^7.S_7$ (as 14T57) | $[2]$ |
14.0.814...687.1 | $x^{14} - 4 x^{13} - 2 x^{12} + 21 x^{11} + 22 x^{10} - 101 x^{9} + 29 x^{8} - 40 x^{7} + 73 x^{6} - 222 x^{5} - 475 x^{4} + 867 x^{3} + 2445 x^{2} + 2446 x + 1403$ | $-\,503^{7}$ | $D_{7}$ (as 14T2) | $[3]$ |
14.0.909...671.1 | $x^{14} - 6 x^{12} + 59 x^{10} - 284 x^{8} + 1027 x^{6} - 1306 x^{4} + 2445 x^{2} + 511$ | $-\,7^{7}\cdot 73^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.2.952...608.1 | $x^{14} - 6 x^{13} + 9 x^{12} + 10 x^{11} - 35 x^{10} + 34 x^{9} - 39 x^{8} + 12 x^{7} + 15 x^{6} + 54 x^{5} + 47 x^{4} + 26 x^{3} + 3 x^{2} - 2 x - 1$ | $2^{15}\cdot 4129^{4}$ | $C_2^7.\GL(3,2)$ (as 14T51) | $[2]$ |
14.6.102...189.1 | $x^{14} - 7 x^{13} + 30 x^{12} - 89 x^{11} + 184 x^{10} - 271 x^{9} + 254 x^{8} - 83 x^{7} - 96 x^{6} + 119 x^{5} - 37 x^{4} - 17 x^{3} + 13 x^{2} - x - 1$ | $29^{13}$ | $C_2\times F_8$ (as 14T9) | $[2]$ |
14.0.122...799.1 | $x^{14} - 4 x^{13} + 26 x^{12} - 79 x^{11} + 272 x^{10} - 631 x^{9} + 1437 x^{8} - 2482 x^{7} + 3850 x^{6} - 4473 x^{5} + 4302 x^{4} - 2694 x^{3} + 1149 x^{2} - 54 x + 109$ | $-\,107^{3}\cdot 21557^{3}$ | $C_2^6.S_7$ (as 14T54) | $[2]$ |
14.0.125...375.1 | $x^{14} + 6 x^{12} - 85 x^{10} + 355 x^{8} - 695 x^{6} + 1091 x^{4} - 609 x^{2} + 535$ | $-\,5^{7}\cdot 107^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.0.127...096.1 | $x^{14} - 2 x^{13} + 3 x^{12} - 32 x^{11} + 95 x^{10} - 138 x^{9} + 293 x^{8} - 932 x^{7} + 1612 x^{6} - 776 x^{5} + 868 x^{4} - 2384 x^{3} + 1840 x^{2} - 640 x + 256$ | $-\,2^{21}\cdot 67^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.0.163...631.1 | $x^{14} - x^{13} + 4 x^{12} - x^{11} + 11 x^{10} - 26 x^{9} + 47 x^{8} - 143 x^{7} + 196 x^{6} - 223 x^{5} + 261 x^{4} - 126 x^{3} + 104 x^{2} - 56 x + 16$ | $-\,29^{6}\cdot 31^{7}$ | $D_{14}$ (as 14T3) | $[3]$ |
14.0.190...432.1 | $x^{14} + 16 x^{12} + 88 x^{10} + 64 x^{8} - 880 x^{6} - 1536 x^{4} + 4096 x^{2} + 9088$ | $-\,2^{21}\cdot 71^{7}$ | $D_{14}$ (as 14T3) | $[4]$ |
14.0.199...672.1 | $x^{14} + 28 x^{10} - 14 x^{9} + 56 x^{8} + 52 x^{7} + 98 x^{6} + 112 x^{5} + 84 x^{4} + 112 x^{3} + 56 x^{2} + 28 x + 18$ | $-\,2^{22}\cdot 7^{15}$ | $C_2^6:F_7$ (as 14T40) | $[2]$ |
14.0.258...375.1 | $x^{14} - 3 x^{13} + 6 x^{12} - 12 x^{11} + 18 x^{10} - 54 x^{9} + 91 x^{8} - 45 x^{7} + 120 x^{6} - 249 x^{5} + 63 x^{4} - 18 x^{3} + 97 x^{2} + 57 x + 9$ | $-\,3^{7}\cdot 5^{7}\cdot 73^{6}$ | $D_{14}$ (as 14T3) | $[2]$ |
14.0.267...816.1 | $x^{14} + 8 x^{12} + 66 x^{10} + 212 x^{8} + 673 x^{6} + 2684 x^{4} + 4804 x^{2} + 2384$ | $-\,2^{14}\cdot 149^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.0.287...904.1 | $x^{14} + 16 x^{12} + 94 x^{10} + 256 x^{8} + 337 x^{6} + 204 x^{4} + 52 x^{2} + 4$ | $-\,2^{26}\cdot 809^{4}$ | $\GL(3,2) \times C_2$ (as 14T19) | $[2]$ |
14.0.287...904.2 | $x^{14} + 17 x^{12} + 108 x^{10} + 328 x^{8} + 492 x^{6} + 328 x^{4} + 68 x^{2} + 4$ | $-\,2^{26}\cdot 809^{4}$ | $\GL(3,2) \times C_2$ (as 14T19) | $[2]$ |
14.2.287...904.1 | $x^{14} - 5 x^{13} + 12 x^{12} - 19 x^{11} + 30 x^{10} - 23 x^{9} - 83 x^{8} + 304 x^{7} - 470 x^{6} + 402 x^{5} - 152 x^{4} - 26 x^{3} + 50 x - 22$ | $2^{26}\cdot 809^{4}$ | $C_2^6:\GL(3,2)$ (as 14T50) | $[2]$ |
14.0.367...375.1 | $x^{14} - 3 x^{13} - 5 x^{12} + 20 x^{11} + 9 x^{10} - 44 x^{9} - 45 x^{8} + 53 x^{7} + 208 x^{6} - 165 x^{5} - 195 x^{4} + 16 x^{3} + 186 x^{2} + 12 x + 71$ | $-\,5^{7}\cdot 11^{7}\cdot 17^{6}$ | $D_{14}$ (as 14T3) | $[4]$ |
14.2.452...025.2 | $x^{14} - 5 x^{13} + 11 x^{12} - 22 x^{11} + 39 x^{10} - 75 x^{9} + 115 x^{8} - 179 x^{7} + 230 x^{6} - 300 x^{5} + 312 x^{4} - 352 x^{3} + 352 x^{2} - 320 x + 128$ | $5^{2}\cdot 7^{2}\cdot 577^{6}$ | $C_2^6:D_7$ (as 14T28) | $[3]$ |
14.0.464...912.1 | $x^{14} + 15 x^{12} + 83 x^{10} + 214 x^{8} + 278 x^{6} + 183 x^{4} + 58 x^{2} + 7$ | $-\,2^{14}\cdot 7\cdot 71^{2}\cdot 283583^{2}$ | $C_2^7.S_7$ (as 14T57) | $[8]$ |
14.2.506...000.1 | $x^{14} - 4 x^{13} + 2 x^{12} + 24 x^{11} - 50 x^{10} + 8 x^{9} + 106 x^{8} - 176 x^{7} + 89 x^{6} + 28 x^{5} - 72 x^{4} + 24 x^{3} + 68 x^{2} - 96 x + 64$ | $2^{27}\cdot 5^{7}\cdot 13^{6}$ | $D_7^2$ (as 14T13) | $[2]$ |
14.2.567...125.1 | $x^{14} - x^{13} - 3 x^{12} + 8 x^{11} + 6 x^{10} - 102 x^{9} + 161 x^{8} - 57 x^{7} + 207 x^{6} - 286 x^{5} + 106 x^{4} - 15 x^{3} - 350 x^{2} - 325 x + 25$ | $5^{7}\cdot 11^{6}\cdot 17^{7}$ | $D_{14}$ (as 14T3) | $[2]$ |
14.0.651...936.1 | $x^{14} - 5 x^{12} + x^{10} + 32 x^{8} - 69 x^{6} + 106 x^{4} - 107 x^{2} + 44$ | $-\,2^{12}\cdot 11^{7}\cdot 13^{8}$ | $C_2^6:F_7$ (as 14T40) | $[2]$ |
14.0.651...936.2 | $x^{14} + 10 x^{12} + 45 x^{10} + 118 x^{8} + 201 x^{6} + 235 x^{4} + 169 x^{2} + 44$ | $-\,2^{12}\cdot 11^{7}\cdot 13^{8}$ | $C_2^6:F_7$ (as 14T40) | $[2]$ |
14.0.759...448.1 | $x^{14} - 4 x^{13} + 24 x^{11} - 2 x^{10} - 80 x^{9} - 92 x^{8} + 432 x^{7} + 1005 x^{6} - 796 x^{5} - 2308 x^{4} + 328 x^{3} + 3076 x^{2} - 1920 x + 400$ | $-\,2^{14}\cdot 173^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.0.848...287.1 | $x^{14} - 4 x^{13} + 24 x^{12} - 32 x^{11} + 137 x^{10} - 54 x^{9} + 637 x^{8} - 148 x^{7} + 2542 x^{6} - 702 x^{5} + 4247 x^{4} - 755 x^{3} + 2028 x^{2} - 175 x + 25$ | $-\,19^{7}\cdot 37^{7}$ | $D_{7}$ (as 14T2) | $[2]$ |
14.0.849...375.1 | $x^{14} + 6 x^{12} + 35 x^{10} - 45 x^{9} + 135 x^{8} - 30 x^{7} + 250 x^{6} + 105 x^{5} + 96 x^{4} + 495 x^{3} + 711 x^{2} + 405 x + 135$ | $-\,3^{7}\cdot 5^{7}\cdot 89^{6}$ | $D_{14}$ (as 14T3) | $[2]$ |
14.0.894...683.1 | $x^{14} - 6 x^{13} + 19 x^{12} - 44 x^{11} + 67 x^{10} - 83 x^{9} + 82 x^{8} - 17 x^{7} + 118 x^{6} + 162 x^{5} + 361 x^{4} + 423 x^{3} + 528 x^{2} + 405 x + 171$ | $-\,3^{7}\cdot 587^{6}$ | $D_{14}$ (as 14T3) | $[7]$ |
14.0.104...027.1 | $x^{14} - x^{13} + 10 x^{12} - 19 x^{11} + 22 x^{10} - 46 x^{9} + 23 x^{8} + 223 x^{7} - 394 x^{6} - 152 x^{5} + 734 x^{4} - 191 x^{3} - 473 x^{2} + 185 x + 169$ | $-\,3^{19}\cdot 547^{4}$ | $A_7\times C_2$ (as 14T47) | $[2, 2]$ |
14.0.116...303.1 | $x^{14} - 4 x^{13} + 14 x^{12} - 33 x^{11} + 61 x^{10} - 86 x^{9} + 93 x^{8} - 91 x^{7} + 101 x^{6} - 422 x^{5} + 1176 x^{4} - 1770 x^{3} + 1611 x^{2} - 855 x + 243$ | $-\,3^{6}\cdot 19^{6}\cdot 23^{7}$ | $D_{14}$ (as 14T3) | $[3]$ |
14.0.122...987.1 | $x^{14} - 3 x^{13} - 2 x^{12} + 3 x^{11} + 29 x^{10} + 25 x^{9} - 69 x^{8} - 93 x^{7} + 579 x^{6} + 1357 x^{5} + 2826 x^{4} + 2263 x^{3} + 2130 x^{2} + 494 x + 361$ | $-\,3^{15}\cdot 29^{4}\cdot 59^{4}$ | $A_7\times C_2$ (as 14T47) | $[2]$ |
14.0.124...875.1 | $x^{14} - 3 x^{13} + 16 x^{12} - 22 x^{11} + 70 x^{10} - 33 x^{9} + 184 x^{8} - 53 x^{7} + 455 x^{6} - 76 x^{5} + 593 x^{4} - 125 x^{3} + 383 x^{2} - 242 x + 77$ | $-\,5^{6}\cdot 11^{7}\cdot 17^{7}$ | $D_{14}$ (as 14T3) | $[2]$ |