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 |
---|---|---|---|---|
9.3.422...147.2 | $x^{9} - 3 x^{7} - x^{6} + 5184 x^{5} + 3456 x^{4} - 2985408 x^{3} - 2985984 x^{2} - 995328 x - 110592$ | $-\,3^{13}\cdot 11^{6}\cdot 157^{6}$ | $S_3\times C_3$ (as 9T4) | $[2, 2, 32520]$ |
9.3.631...128.1 | $x^{9} - 3 x^{8} - 357 x^{7} + 7050 x^{6} - 67920 x^{5} + 393639 x^{4} - 1427271 x^{3} + 3165981 x^{2} - 3928704 x + 2089711$ | $-\,2^{6}\cdot 3^{15}\cdot 7^{7}\cdot 11^{3}\cdot 13^{7}$ | $S_3\times C_3$ (as 9T4) | $[6, 6, 12, 756]$ |
9.3.167...392.2 | $x^{9} - 3 x^{8} - 357 x^{7} - 1320 x^{6} + 46410 x^{5} + 450471 x^{4} - 785715 x^{3} - 31150623 x^{2} - 168595476 x - 306304831$ | $-\,2^{6}\cdot 3^{15}\cdot 7^{3}\cdot 127^{7}$ | $S_3\times C_3$ (as 9T4) | $[2, 6, 10386]$ |
9.3.573...187.2 | $x^{9} - 1911 x^{6} - 1527036 x^{3} - 258474853$ | $-\,3^{19}\cdot 7^{6}\cdot 127^{6}$ | $S_3\times C_3$ (as 9T4) | $[2, 2, 6, 18, 252]$ |
9.3.712...875.2 | $x^{9} - 705 x^{6} - 207600 x^{3} - 12977875$ | $-\,3^{13}\cdot 5^{6}\cdot 7^{6}\cdot 79^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 45, 1170]$ |
9.3.100...368.1 | $x^{9} - 2 x^{8} - 385 x^{7} + 7453 x^{6} - 71581 x^{5} + 415126 x^{4} - 1507540 x^{3} + 3349405 x^{2} - 4162063 x + 2216299$ | $-\,2^{9}\cdot 17^{3}\cdot 877^{7}$ | $S_3\times C_3$ (as 9T4) | $[2, 83174]$ |
9.3.148...312.2 | $x^{9} - 3 x^{8} - 525 x^{7} - 9498 x^{6} - 90516 x^{5} - 528051 x^{4} - 1934295 x^{3} - 4332405 x^{2} - 5419578 x - 2901079$ | $-\,2^{6}\cdot 3^{15}\cdot 7^{7}\cdot 13^{3}\cdot 19^{7}$ | $S_3\times C_3$ (as 9T4) | $[3, 3, 12, 5292]$ |
9.3.161...248.1 | $x^{9} - 471 x^{7} - 507 x^{6} + 238797 x^{5} - 5652 x^{4} - 153114 x^{3} + 18369 x^{2} - 86193 x + 4395$ | $-\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 157^{6}$ | $S_3\times C_3$ (as 9T4) | $[6, 6, 6, 2322]$ |
9.3.174...000.1 | $x^{9} - x^{8} - 413 x^{7} + 7858 x^{6} - 75284 x^{5} + 436979 x^{4} - 1589503 x^{3} + 3537221 x^{2} - 4401470 x + 2346343$ | $-\,2^{6}\cdot 5^{3}\cdot 7^{3}\cdot 937^{7}$ | $S_3\times C_3$ (as 9T4) | $[2, 2, 81342]$ |
9.3.197...432.1 | $x^{9} - 4 x^{8} - 558 x^{7} + 1489 x^{6} + 41181 x^{5} + 425593 x^{4} + 2005619 x^{3} + 6956364 x^{2} + 13241673 x + 17915283$ | $-\,2^{6}\cdot 11^{3}\cdot 1567^{7}$ | $S_3\times C_3$ (as 9T4) | $[5, 23170]$ |
9.3.235...448.2 | $x^{9} - 3 x^{7} - x^{6} + 10125 x^{5} + 6750 x^{4} - 11389500 x^{3} - 11390625 x^{2} - 3796875 x - 421875$ | $-\,2^{6}\cdot 3^{13}\cdot 7^{6}\cdot 241^{6}$ | $S_3\times C_3$ (as 9T4) | $[2, 2, 6, 24, 792]$ |
9.1.345...000.1 | $x^{9} - 144 x^{7} - 771 x^{6} - 6948 x^{5} - 92304 x^{4} - 690915 x^{3} - 3564324 x^{2} - 9455616 x - 16678913$ | $2^{6}\cdot 3^{16}\cdot 5^{7}\cdot 7^{7}\cdot 11^{7}$ | $S_3^2$ (as 9T8) | $[3, 3, 6, 6678]$ |
9.3.497...264.1 | $x^{9} - x^{8} - 469 x^{7} - 8674 x^{6} - 82816 x^{5} - 481783 x^{4} - 1758511 x^{3} - 3926029 x^{2} - 4898428 x - 2616799$ | $-\,2^{6}\cdot 37^{3}\cdot 1063^{7}$ | $S_3\times C_3$ (as 9T4) | $[2, 2, 2, 104, 936]$ |
9.3.524...227.2 | $x^{9} - 399 x^{7} - 2826 x^{6} - 39501 x^{5} - 1111215 x^{4} - 11901807 x^{3} - 93380364 x^{2} - 641574444 x - 2428189912$ | $-\,3^{13}\cdot 7^{6}\cdot 19^{6}\cdot 29^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 15, 10710]$ |
9.3.567...027.2 | $x^{9} - 375 x^{6} - 58614 x^{3} - 1953125$ | $-\,3^{13}\cdot 3907^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 6, 6, 7182]$ |
9.3.611...643.1 | $x^{9} + 1131 x^{7} - 546 x^{6} + 319410 x^{5} - 304707 x^{4} - 198744 x^{3} + 276822 x^{2} - 85683 x - 2197$ | $-\,3^{15}\cdot 13^{6}\cdot 211^{6}$ | $S_3\times C_3$ (as 9T4) | $[2, 6, 6, 9462]$ |
9.3.821...272.1 | $x^{9} - 2 x^{8} - 497 x^{7} - 9085 x^{6} - 86645 x^{5} - 504734 x^{4} - 1845556 x^{3} - 4127021 x^{2} - 5155979 x - 2757211$ | $-\,2^{9}\cdot 19^{3}\cdot 1129^{7}$ | $S_3\times C_3$ (as 9T4) | $[2, 2, 2, 2, 17486]$ |
9.3.104...048.2 | $x^{9} - 372 x^{6} - 57696 x^{3} - 1906624$ | $-\,2^{6}\cdot 3^{19}\cdot 7^{6}\cdot 103^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 6, 6, 2736]$ |
9.3.141...875.2 | $x^{9} - 75 x^{6} - 10646250 x^{3} - 15625$ | $-\,3^{15}\cdot 5^{6}\cdot 631^{6}$ | $S_3\times C_3$ (as 9T4) | $[2, 42, 2394]$ |
9.3.145...176.2 | $x^{9} - 3 x^{8} - 1677 x^{7} - 12090 x^{6} + 194712 x^{5} - 2410023 x^{4} + 13118637 x^{3} - 56776125 x^{2} + 128903838 x - 222062239$ | $-\,2^{6}\cdot 3^{15}\cdot 7^{7}\cdot 79^{7}$ | $S_3\times C_3$ (as 9T4) | $[3, 18, 18, 774]$ |
9.3.157...000.2 | $x^{9} - 6450 x^{6} - 17385000 x^{3} - 9938375000$ | $-\,2^{6}\cdot 3^{13}\cdot 5^{6}\cdot 463^{6}$ | $S_3\times C_3$ (as 9T4) | $[2, 6, 52668]$ |
9.3.188...000.1 | $x^{9} - 6300 x^{6} - 16560000 x^{3} - 9261000000$ | $-\,2^{6}\cdot 3^{15}\cdot 5^{6}\cdot 331^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 58590]$ |
9.3.270...875.2 | $x^{9} - 795 x^{6} - 263850 x^{3} - 18609625$ | $-\,3^{15}\cdot 5^{6}\cdot 19^{6}\cdot 37^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 3, 3, 3, 6966]$ |
9.3.314...875.2 | $x^{9} - 75 x^{6} - 12165000 x^{3} - 15625$ | $-\,3^{15}\cdot 5^{6}\cdot 7^{6}\cdot 103^{6}$ | $S_3\times C_3$ (as 9T4) | $[6, 6, 6, 1638]$ |
9.3.334...787.2 | $x^{9} - 7623 x^{6} - 24245496 x^{3} - 16406426421$ | $-\,3^{15}\cdot 11^{6}\cdot 331^{6}$ | $S_3\times C_3$ (as 9T4) | $[13, 19110]$ |
9.3.506...064.1 | $x^{9} - 3 x^{8} - 174 x^{7} + 467 x^{6} + 77319 x^{5} - 161625 x^{4} - 2738803 x^{3} + 7924692 x^{2} - 2095714128 x + 964112287$ | $-\,2^{9}\cdot 3^{9}\cdot 7^{3}\cdot 547^{7}$ | $S_3\times C_3$ (as 9T4) | $[6, 6, 13902]$ |
9.3.627...187.1 | $x^{9} - 972 x^{7} - 5833 x^{6} + 314928 x^{5} + 3779784 x^{4} - 22667039 x^{3} - 612325008 x^{2} - 3675839940 x - 7359239448$ | $-\,3^{13}\cdot 19^{6}\cdot 307^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 3, 3, 3, 2457]$ |
9.3.861...927.1 | $x^{9} - x^{8} - 1342 x^{7} + 31269 x^{6} - 353885 x^{5} + 2987747 x^{4} - 16016553 x^{3} + 66301140 x^{2} - 159070096 x + 205759651$ | $-\,7^{7}\cdot 17^{3}\cdot 577^{7}$ | $S_3\times C_3$ (as 9T4) | $[6, 43134]$ |
9.3.872...232.2 | $x^{9} - 1332 x^{6} - 739584 x^{3} - 87528384$ | $-\,2^{6}\cdot 3^{19}\cdot 13^{6}\cdot 79^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 3, 6, 6, 1134]$ |
9.3.985...000.2 | $x^{9} - 3 x^{8} - 780 x^{7} - 4407 x^{6} + 214440 x^{5} + 2926290 x^{4} - 8788200 x^{3} - 421505400 x^{2} - 3123636000 x - 7788259000$ | $-\,2^{9}\cdot 3^{15}\cdot 5^{3}\cdot 271^{7}$ | $S_3\times C_3$ (as 9T4) | $[3, 15, 2910]$ |
9.3.999...987.2 | $x^{9} - 1156 x^{7} - 3 x^{6} - 306 x^{5} + 2312 x^{4} - 24 x^{3} + 306 x^{2} - 1156 x - 1$ | $-\,3^{3}\cdot 37^{6}\cdot 1063^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 9, 25974]$ |
9.3.103...875.3 | $x^{9} - 1995 x^{6} - 4659900 x^{3} - 294079625$ | $-\,3^{13}\cdot 5^{6}\cdot 7^{6}\cdot 181^{6}$ | $S_3\times C_3$ (as 9T4) | $[9, 9, 1647]$ |
9.3.128...347.1 | $x^{9} - 1287 x^{6} - 690174 x^{3} - 78953589$ | $-\,3^{19}\cdot 7^{6}\cdot 313^{6}$ | $S_3\times C_3$ (as 9T4) | $[6, 6, 6, 2268]$ |
9.3.165...704.1 | $x^{9} - x^{8} - 959 x^{7} + 270 x^{6} + 130894 x^{5} + 1765845 x^{4} + 11378151 x^{3} + 46627247 x^{2} + 110528996 x + 147434209$ | $-\,2^{9}\cdot 7^{3}\cdot 2659^{7}$ | $S_3\times C_3$ (as 9T4) | $[19, 27949]$ |
9.3.169...000.1 | $x^{9} - 1893 x^{7} - 18299 x^{6} + 1220985 x^{5} + 23870730 x^{4} - 151440000 x^{3} - 7973174025 x^{2} - 79283809125 x - 264229593625$ | $-\,2^{6}\cdot 3^{12}\cdot 5^{3}\cdot 631^{7}$ | $S_3\times C_3$ (as 9T4) | $[30, 23310]$ |
9.1.174...424.1 | $x^{9} + 108 x^{7} - 5181 x^{6} + 3888 x^{5} + 187164 x^{4} + 9087609 x^{3} - 6714576 x^{2} - 645345360 x - 5231495807$ | $2^{6}\cdot 3^{10}\cdot 7^{7}\cdot 13^{7}\cdot 19^{7}$ | $S_3^2$ (as 9T8) | $[3, 3, 9, 54, 54]$ |
9.3.182...712.1 | $x^{9} - 6231 x^{7} - 143313 x^{6} - 6374313 x^{5} - 536987580 x^{4} - 33959764184 x^{3} - 1281819293415 x^{2} - 22598935517613 x - 162634049131679$ | $-\,2^{6}\cdot 3^{12}\cdot 31^{6}\cdot 67^{7}$ | $S_3\times C_3$ (as 9T4) | $[6, 6, 6, 4218]$ |
9.3.197...043.2 | $x^{9} - 1287 x^{6} - 1925586 x^{3} - 78953589$ | $-\,3^{19}\cdot 13^{6}\cdot 181^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 9, 4914]$ |
9.3.287...336.1 | $x^{9} - x^{8} - 765 x^{7} - 17688 x^{6} - 209034 x^{5} - 1507947 x^{4} - 6871473 x^{3} - 19300827 x^{2} - 30508758 x - 20768489$ | $-\,2^{9}\cdot 7^{7}\cdot 13^{7}\cdot 19^{7}\cdot 23^{3}$ | $S_3\times C_3$ (as 9T4) | $[3, 3, 3, 6789]$ |
9.3.417...987.1 | $x^{9} - 3 x^{8} - 2109 x^{7} - 53679 x^{6} - 646248 x^{5} - 6139749 x^{4} - 35586555 x^{3} - 167565045 x^{2} - 437806425 x - 650068687$ | $-\,3^{15}\cdot 7^{3}\cdot 19^{7}\cdot 37^{7}$ | $S_3\times C_3$ (as 9T4) | $[3, 3, 3, 6, 1806]$ |
9.3.451...664.1 | $x^{9} - 2757 x^{7} - 32165 x^{6} + 2580552 x^{5} + 60775308 x^{4} - 461422548 x^{3} - 29279240748 x^{2} - 349709062392 x - 1398653824392$ | $-\,2^{9}\cdot 3^{13}\cdot 919^{7}$ | $S_3\times C_3$ (as 9T4) | $[3, 78, 3042]$ |
9.3.454...152.1 | $x^{9} - 1369 x^{7} - 3 x^{6} + 333 x^{5} + 2738 x^{4} - 24 x^{3} - 333 x^{2} - 1369 x - 1$ | $-\,2^{6}\cdot 3^{3}\cdot 17^{6}\cdot 1489^{6}$ | $S_3\times C_3$ (as 9T4) | $[2, 2, 6, 4446]$ |
9.3.577...747.2 | $x^{9} - 10972 x^{6} + 14480427 x^{3} + 10604499373$ | $-\,3^{9}\cdot 7^{6}\cdot 13^{6}\cdot 193^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 3, 6, 36, 252]$ |
9.3.640...827.1 | $x^{9} - 168 x^{6} - 365785 x^{3} - 175616$ | $-\,3^{3}\cdot 7^{6}\cdot 13^{6}\cdot 19^{6}\cdot 31^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 3, 3, 3, 9, 9, 27]$ |
9.1.816...000.1 | $x^{9} + 228 x^{7} - 76 x^{6} + 17328 x^{5} - 11552 x^{4} + 455228 x^{3} - 438976 x^{2} + 1235152 x - 1245168$ | $2^{6}\cdot 3^{3}\cdot 5^{6}\cdot 7^{6}\cdot 307^{7}$ | $S_3^2$ (as 9T8) | $[9, 9, 9, 540]$ |
9.1.937...976.1 | $x^{9} + 270 x^{7} - 2955 x^{6} + 24300 x^{5} + 280530 x^{4} + 4127133 x^{3} - 23935500 x^{2} - 538282800 x - 1686858625$ | $2^{6}\cdot 3^{15}\cdot 17^{7}\cdot 59^{7}$ | $S_3^2$ (as 9T8) | $[6, 6, 4212]$ |
9.3.112...168.1 | $x^{9} + 69 x^{7} - 335 x^{6} + 1587 x^{5} - 721466 x^{4} - 203039588 x^{3} + 203872969 x^{2} + 6018523 x - 84397585$ | $-\,2^{6}\cdot 3^{3}\cdot 13^{6}\cdot 31^{6}\cdot 73^{6}$ | $S_3\times C_3$ (as 9T4) | $[6, 6, 18, 378]$ |
9.1.120...504.1 | $x^{9} - 1947 x^{6} - 35046 x^{5} - 420552 x^{4} - 2525259 x^{3} - 22744854 x^{2} - 421201$ | $2^{6}\cdot 3^{18}\cdot 11^{7}\cdot 59^{7}$ | $S_3^2$ (as 9T8) | $[3, 6, 6, 6, 180]$ |
9.3.132...027.2 | $x^{9} - 1029 x^{6} - 6564334 x^{3} - 40353607$ | $-\,3^{9}\cdot 7^{6}\cdot 43^{6}\cdot 67^{6}$ | $S_3\times C_3$ (as 9T4) | $[6, 6, 6, 18, 36]$ |
9.3.144...112.2 | $x^{9} - 1095 x^{7} - 2744 x^{6} - 190845 x^{5} + 1609440 x^{4} - 36547575 x^{3} + 112348278 x^{2} - 600693534 x - 712835718$ | $-\,2^{6}\cdot 3^{13}\cdot 7^{6}\cdot 19^{6}\cdot 37^{6}$ | $S_3\times C_3$ (as 9T4) | $[3, 3, 3, 3, 9, 180]$ |